**Meet the editor**

Dogan Ugur Sanli obtained his PhD from Newcastle University, UK. For his PhD thesis, he studied sea level rise using GPS. In particular, he specialized in vertical crustal deformation monitoring using GPS. He then moved into the area of GPS positioning accuracy and he managed to model both vertical and horizontal accuracy for relative-PPP and PPP. He also studied GPS posi-

tioning accuracy for rapid-static positioning for BERNESE and OPUS-RS software. He has also continued to co-author sea level studies. He was involved in NEAMTWS Tsunami Warning efforts under the auspices of UNESCO. He was a member of Sea Level Working Group 3. Currently he is interested in assessing the accuracy of GPS positioning velocities with the focus on PPP derived positions from repeated GPS surveys.

Contents

**Preface VII**

Dogan Ugur Sanli

**Performance 9**

**Conditions 27**

Enik Shytermeja

**of HRUH Station 73** Mustafa Ulukavak

**Section 2 Performance Evaluation of GNSS 7**

Chapter 1 **Introductory Chapter: The Philosophy Behind the Accuracy**

**Section 3 Accuracy of GNSS Positioning Under Severe Environmental**

Chapter 4 **GPS Scintillations and Total Electron Content Climatology in**

Chapter 5 **Evaluation of GNSS Data with Internet Based Services: The Case**

Emília Correia, Marcio Tadeu de Assis Honorato Muella, Lucilla Alfonsi, Fabricio dos Santos Prol and Paulo de Oliveira Camargo

**Assessment of GNSS Methods 3**

Chapter 2 **Evaluation Methods of Satellite Navigation System**

Chapter 3 **Robust GNSS Positioning in Urban Environment 29**

**Section 4 Present Day Accuracy of GNSS Point Positioning 71**

**the Southern American Sector 47**

Ershen Wang, He He and Chaoying Jia

**Section 1 Introduction 1**

## Contents



Chapter 6 **Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria 89** Olalekan Adekunle Isioye, Mefe Moses and Lukman Abdulmumin

Preface

gation Satellite System (IRNSS).

GPS has revolutionised the history of positioning in terms of monitoring global deforma‐ tions of the earth and in the establishment of geodetic control networks. It followed the mis‐ sion of its predecessor TRANSIT by producing more accurate position information and enabling far better achievements. As a young PhD student, I was always amazed that the GPS results were changing (sometimes significantly) when applying different processing strategies on the same data! Following my PhD, I have spent more than two decades study‐ ing analysis and surveying strategies to assess GPS positioning and velocity accuracies.

Studying the positioning accuracy of satellite systems is important considering the wide va‐ riety of surveying methods, software, equipment, and processing strategies available. Fur‐ thermore, the quality of satellite orbits, terrestrial reference frames (TRF), atmospheric models, etc. is continuously improved by the development of new mathematical theories by their vendors. Therefore, various combinations of the above items in producing results would terminate in different positioning accuracies. For this reason, research assessing the accuracy of satellite positioning techniques should keep playing a key role in the future. Our era is now prone to the emergence of new satellite positioning systems called Global Navi‐ gation Satellite Systems (GNSS). Almost nearing the quality of GPS is the satellite position‐ ing system of Russia's GLONASS, which is already available on the market today. Another two systems that are nearing completion are the European's GALILEO and China's BeiDou. There are also other satellite positioning systems that are especially developed to serve their countries such as Japan's Quasi-Zenith Satellite System (QZSS) and India's Regional Navi‐

Researchers have spent a lot of time improving the positioning accuracy of GPS either by experience from various geophysical experiments or directly developing new mathematical and analysis theories followed by the new instrumentation providing the data. With the emer‐ gence of the new GNSS, multi-GNSS experiments designed by the International GNSS Service (IGS) were carried out. In this book, I aimed to gather results from various GNSS techniques and methodologies as well as multi-GNSS experiments assessing positioning accuracy. My mind is now broadened since the book contains accuracy results not only based on the appli‐ cation of different processing and surveying strategies but also based on designing new re‐ ceiver infrastructures to improve the quality of GNSS signal, assessing performance status of GNSS constellations, and assessing the accuracy of GNSS signal under the effect of severe atmospheric disturbances such as scintillations in the ionosphere. Therefore, the book title has been given as "Accuracy of GNSS methods". With the term "accuracy", we mean "the accuracy of the results delivered by the method". I hope this book will emphasize the crucial role of the

accuracy assessment and make the necessary impact on future generations.


## Preface

Chapter 6 **Comparative Study of Some Online GNSS Post-Processing**

**Section 5 Accuracy of Positions Derived from the Combination of Terrestrial Geodetic Techniques and GNSS 107**

Chapter 7 **Development of Recurrent Method with Rotation for**

Ha Minh Hoa

**VI** Contents

**Services at Selected Permanent GNSS Sites in Nigeria 89** Olalekan Adekunle Isioye, Mefe Moses and Lukman Abdulmumin

**Combined Adjustment of Terrestrial Geodetic and GNSS Networks in National Spatial Reference System 109**

GPS has revolutionised the history of positioning in terms of monitoring global deforma‐ tions of the earth and in the establishment of geodetic control networks. It followed the mis‐ sion of its predecessor TRANSIT by producing more accurate position information and enabling far better achievements. As a young PhD student, I was always amazed that the GPS results were changing (sometimes significantly) when applying different processing strategies on the same data! Following my PhD, I have spent more than two decades study‐ ing analysis and surveying strategies to assess GPS positioning and velocity accuracies.

Studying the positioning accuracy of satellite systems is important considering the wide va‐ riety of surveying methods, software, equipment, and processing strategies available. Fur‐ thermore, the quality of satellite orbits, terrestrial reference frames (TRF), atmospheric models, etc. is continuously improved by the development of new mathematical theories by their vendors. Therefore, various combinations of the above items in producing results would terminate in different positioning accuracies. For this reason, research assessing the accuracy of satellite positioning techniques should keep playing a key role in the future. Our era is now prone to the emergence of new satellite positioning systems called Global Navi‐ gation Satellite Systems (GNSS). Almost nearing the quality of GPS is the satellite position‐ ing system of Russia's GLONASS, which is already available on the market today. Another two systems that are nearing completion are the European's GALILEO and China's BeiDou. There are also other satellite positioning systems that are especially developed to serve their countries such as Japan's Quasi-Zenith Satellite System (QZSS) and India's Regional Navi‐ gation Satellite System (IRNSS).

Researchers have spent a lot of time improving the positioning accuracy of GPS either by experience from various geophysical experiments or directly developing new mathematical and analysis theories followed by the new instrumentation providing the data. With the emer‐ gence of the new GNSS, multi-GNSS experiments designed by the International GNSS Service (IGS) were carried out. In this book, I aimed to gather results from various GNSS techniques and methodologies as well as multi-GNSS experiments assessing positioning accuracy. My mind is now broadened since the book contains accuracy results not only based on the appli‐ cation of different processing and surveying strategies but also based on designing new re‐ ceiver infrastructures to improve the quality of GNSS signal, assessing performance status of GNSS constellations, and assessing the accuracy of GNSS signal under the effect of severe atmospheric disturbances such as scintillations in the ionosphere. Therefore, the book title has been given as "Accuracy of GNSS methods". With the term "accuracy", we mean "the accuracy of the results delivered by the method". I hope this book will emphasize the crucial role of the accuracy assessment and make the necessary impact on future generations.

The IGS has been home to GPS products for more than two decades now with the effort of colleagues from different nations. This period corresponds to my past career life! Therefore, I am indebted to the IGS, which played a crucial role in my entire career and its motivation to young researchers, GPS data, and various other products. I hope IGS will also be host to upcoming GNSS products and activities. We have witnessed it with applications such as the Multi GNSS Experiment (MGEX).

Before I leave the reader alone with the book, I would like to mention the name of my teacher, my PhD supervisor, Professor Geoffrey Blewitt. I first heard the term "processing strategy" from him. Last but not least, I also thank him for inspiring me and introducing me to those magic words that were going to take most of my time in doing research throughout my career.

> **Dogan Ugur Sanli** Department of Geomatic Engineering Civil Engineering Faculty Yildiz Technical University Istanbul, Turkey

**Introduction**

**Section 1**

**Section 1**

## **Introduction**

The IGS has been home to GPS products for more than two decades now with the effort of colleagues from different nations. This period corresponds to my past career life! Therefore, I am indebted to the IGS, which played a crucial role in my entire career and its motivation to young researchers, GPS data, and various other products. I hope IGS will also be host to upcoming GNSS products and activities. We have witnessed it with applications such as the

Before I leave the reader alone with the book, I would like to mention the name of my teacher, my PhD supervisor, Professor Geoffrey Blewitt. I first heard the term "processing strategy" from him. Last but not least, I also thank him for inspiring me and introducing me to those magic words that were going to take most of my time in doing research throughout my career.

**Dogan Ugur Sanli**

Istanbul, Turkey

Civil Engineering Faculty Yildiz Technical University

Department of Geomatic Engineering

Multi GNSS Experiment (MGEX).

VIII Preface

**Chapter 1**

**Provisional chapter**

**Introductory Chapter: The Philosophy Behind the**

**Introductory Chapter: The Philosophy Behind the** 

DOI: 10.5772/intechopen.81288

Satellite geodesy was developed to overcome the tasks which cannot be accomplished using traditional geodetic techniques, for instance, to measure the motion of continents more precisely, to eliminate the difficulty in line of site problems, to gain performance in all weather conditions, and to be able to monitor global deformations of the earth leading to the contribution in the emerge of a terrestrial reference frame (TRF) which is compatible with the

Today, global navigation satellite system (GNSS) data are used for various purposes, not only in geodesy but also in all earth science disciplines such as geophysics, geology, meteorology, oceanography, and others. In geodesy, applications range from establishing geodetic control networks to detail surveys. The GNSS instrumentation is designed according to various purposes. Cost-effective instrumentation, hardware, and software are preferred suitable to application and accuracy expectations. The accuracy expectation of users according to their aims is multifold. The instrumentation and the GNSS products are always improved with the developments in technology and analysis methodologies, coding, etc. Hence the user, the GNSS community, needs to be updated in terms of accuracy of the positioning results, orbital

The accuracy of GNSS was studied by many researchers; however, the first organized study in which the accuracy prediction formulas for coordinate components were developed for

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Accuracy Assessment of GNSS Methods**

**Accuracy Assessment of GNSS Methods**

Additional information is available at the end of the chapter

products, TRF quality, etc. with continuous research.

**2. Positioning accuracy of GNSS**

Dogan Ugur SanliAdditional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.81288

Dogan Ugur Sanli

**1. Introduction**

geodynamic events of the earth.

#### **Introductory Chapter: The Philosophy Behind the Accuracy Assessment of GNSS Methods Introductory Chapter: The Philosophy Behind the Accuracy Assessment of GNSS Methods**

DOI: 10.5772/intechopen.81288

Dogan Ugur Sanli

Additional information is available at the end of the chapter Dogan Ugur SanliAdditional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.81288

#### **1. Introduction**

Satellite geodesy was developed to overcome the tasks which cannot be accomplished using traditional geodetic techniques, for instance, to measure the motion of continents more precisely, to eliminate the difficulty in line of site problems, to gain performance in all weather conditions, and to be able to monitor global deformations of the earth leading to the contribution in the emerge of a terrestrial reference frame (TRF) which is compatible with the geodynamic events of the earth.

Today, global navigation satellite system (GNSS) data are used for various purposes, not only in geodesy but also in all earth science disciplines such as geophysics, geology, meteorology, oceanography, and others. In geodesy, applications range from establishing geodetic control networks to detail surveys. The GNSS instrumentation is designed according to various purposes. Cost-effective instrumentation, hardware, and software are preferred suitable to application and accuracy expectations. The accuracy expectation of users according to their aims is multifold. The instrumentation and the GNSS products are always improved with the developments in technology and analysis methodologies, coding, etc. Hence the user, the GNSS community, needs to be updated in terms of accuracy of the positioning results, orbital products, TRF quality, etc. with continuous research.

### **2. Positioning accuracy of GNSS**

The accuracy of GNSS was studied by many researchers; however, the first organized study in which the accuracy prediction formulas for coordinate components were developed for

the user was produced by [1] based on an experiment using only GPS data. There the authors emphasized that the accuracy of GNSS positioning was mainly dependent on observation session duration. The dependency on baseline length, which for instance was the essence as emphasized in [2–4], was mainly changed with the release of the IGS precise orbit (i.e., with the improvement in orbit quality).

architecture is proposed. In the second chapter, how the GNSS signal is degraded under severe atmospheric disturbances such as ionospheric scintillations is investigated. A calibra-

Introductory Chapter: The Philosophy Behind the Accuracy Assessment of GNSS Methods

http://dx.doi.org/10.5772/intechopen.81288

5

Chapter 1 in Section 3 assesses GPS relative positioning accuracy for a single-frequency GPS receiver. Single-frequency receivers are economic and suitable for nationwide surveying practices. Therefore, researchers are eager to develop methodologies in which single-frequency receivers are employed. Here the positioning accuracy is assessed taking into consideration the mode of surveying, baseline, and precision dilution of position (PDOP), signal-to-noise ratio (SNR), and occupation time. Chapters 2 and 3 in this section assess results from online GNSS software. Results from available software are compared. Chapter 2 presents results in

The fourth section is devoted to the construction of national spatial reference systems by combining terrestrial geodetic networks with GNSS networks. A recurrent adjustment methodology which uses GPS data from GNSS methods is presented applying sparse matrix operations, outlier detection, and simplified subsystem of observation equations. Namely, present day accuracy of establishing national spatial reference systems based on

[1] Eckl MC, Snay RA, Soler T, Cline MW, Mader GL. Accuracy of GPS-derived relative positions as a function of inter-station distance and observing-session duration. Journal

[2] Dong DN, Bock Y. Global positioning system network analysis with phase ambiguity resolution applied to crustal deformation studies in California. Journal of Geophysical

[3] Larson KM, Agnew DC. Application of the global positioning system to crustal deformation measurement, 1, precision and accuracy. Journal of Geophysical Research.

[4] Feigl KL, Agnew DC, Bock Y, Dong D, Donellan A, Hager BH, et al. Space geodetic measurement of crustal deformation in central and Southern California, 1984-1992. Journal

tion model improving single-frequency PPP results is presented.

The third section is devoted to GNSS positioning assessments:

ITRF14 and Chapter 3 in a national grid system.

Address all correspondence to: usanli@yildiz.edu.tr

Yildiz Technical University, Turkey

of Geodesy. 2001;**75**:633-640

Research. 1989;**94**(B4):3949-3966

of Geophysical Research. 1993;**98**(B12):21677-21712

1991;**96**(B10):16547-16565

GNSS is presented.

**Author details**

Dogan Ugur Sanli

**References**

Eckl et al. [1] were targeting GPS studies at the national level with Continuously Operating Reference Station (CORS) inter-station distances of up to 300 km. Sanli and Engin [5] changed the angle to tectonic studies in which GPS processing was handled using baseline lengths of up to thousands of kilometers. Again, the dependency on baseline length came back to the agenda. From these studies the authors produced prediction formulas for north, east, and up positioning components. The formulas were useful for the GPS community with various accuracy expectations for various applications. Before field works, they were able to obtain a priory accuracy levels and hence taking necessary precautions in the field to guarantee the desired position accuracy.

Then, the research continued to present details in the accuracy assessment of point positions. For instance, Ozturk and Sanli [6] made an attempt to unify accuracy models for baselines of 1–3000 km resulting in a complete accuracy model. Sanli and Kurumahmut [7] took into account the effect of large height difference on positioning and extended the traditional formulation. Ghoddousi-Fard and Dare [8] were among those who studied the accuracy of GPS positioning for web-based GPS software. Schwarz et al. [9] and Hastaoglu and Sanli [10] assessed the accuracy of GPS rapid static positioning. At the end of the day, GPS positioning accuracy prediction formulas from static GPS surveys were produced for three major GNSS software, Bernese, GIPSY/OASIS II, and GAMIT by [11–13], respectively.

#### **3. Scope of book**

Besides the GPS positioning accuracy efforts that are well documented in the literature and discussed above, this book embraces the present day work documenting the performance evaluation of GNSS systems and new receiver designs to improve GNSS signal quality before the processing. The up-to-date experiment results on positioning accuracy are also evaluated for online GNSS software which is freely available to user community. In addition, the positioning accuracy under severe atmospheric disturbances is evaluated for single-frequency receivers which are widespread in surveying practice today. The structure of the sections and chapters is as in the following:

In the first section, the performance of the two GNSS systems, GPS and BeiDou, is evaluated. Referring to well-established standards developed for the GPS, the performance assessment of BeiDou satellite navigation system is performed. The available signal in space (SIS) model is improved based on the reliability theory using exponential distribution and Gauss-Markov process, and constellation models are refined taking into consideration satellite failure rate, repair rate, and backup situation.

The second section reviews the quality of the GNSS measurements. In the first chapter, a new GNSS receiver design in which the GNSS signal is repaired using a new vector tracking architecture is proposed. In the second chapter, how the GNSS signal is degraded under severe atmospheric disturbances such as ionospheric scintillations is investigated. A calibration model improving single-frequency PPP results is presented.

The third section is devoted to GNSS positioning assessments:

Chapter 1 in Section 3 assesses GPS relative positioning accuracy for a single-frequency GPS receiver. Single-frequency receivers are economic and suitable for nationwide surveying practices. Therefore, researchers are eager to develop methodologies in which single-frequency receivers are employed. Here the positioning accuracy is assessed taking into consideration the mode of surveying, baseline, and precision dilution of position (PDOP), signal-to-noise ratio (SNR), and occupation time. Chapters 2 and 3 in this section assess results from online GNSS software. Results from available software are compared. Chapter 2 presents results in ITRF14 and Chapter 3 in a national grid system.

The fourth section is devoted to the construction of national spatial reference systems by combining terrestrial geodetic networks with GNSS networks. A recurrent adjustment methodology which uses GPS data from GNSS methods is presented applying sparse matrix operations, outlier detection, and simplified subsystem of observation equations. Namely, present day accuracy of establishing national spatial reference systems based on GNSS is presented.

#### **Author details**

the user was produced by [1] based on an experiment using only GPS data. There the authors emphasized that the accuracy of GNSS positioning was mainly dependent on observation session duration. The dependency on baseline length, which for instance was the essence as emphasized in [2–4], was mainly changed with the release of the IGS precise orbit (i.e., with

Eckl et al. [1] were targeting GPS studies at the national level with Continuously Operating Reference Station (CORS) inter-station distances of up to 300 km. Sanli and Engin [5] changed the angle to tectonic studies in which GPS processing was handled using baseline lengths of up to thousands of kilometers. Again, the dependency on baseline length came back to the agenda. From these studies the authors produced prediction formulas for north, east, and up positioning components. The formulas were useful for the GPS community with various accuracy expectations for various applications. Before field works, they were able to obtain a priory accuracy levels and hence taking necessary precautions in the field to guarantee the

Then, the research continued to present details in the accuracy assessment of point positions. For instance, Ozturk and Sanli [6] made an attempt to unify accuracy models for baselines of 1–3000 km resulting in a complete accuracy model. Sanli and Kurumahmut [7] took into account the effect of large height difference on positioning and extended the traditional formulation. Ghoddousi-Fard and Dare [8] were among those who studied the accuracy of GPS positioning for web-based GPS software. Schwarz et al. [9] and Hastaoglu and Sanli [10] assessed the accuracy of GPS rapid static positioning. At the end of the day, GPS positioning accuracy prediction formulas from static GPS surveys were produced for three major GNSS

Besides the GPS positioning accuracy efforts that are well documented in the literature and discussed above, this book embraces the present day work documenting the performance evaluation of GNSS systems and new receiver designs to improve GNSS signal quality before the processing. The up-to-date experiment results on positioning accuracy are also evaluated for online GNSS software which is freely available to user community. In addition, the positioning accuracy under severe atmospheric disturbances is evaluated for single-frequency receivers which are widespread in surveying practice today. The structure of the sections and

In the first section, the performance of the two GNSS systems, GPS and BeiDou, is evaluated. Referring to well-established standards developed for the GPS, the performance assessment of BeiDou satellite navigation system is performed. The available signal in space (SIS) model is improved based on the reliability theory using exponential distribution and Gauss-Markov process, and constellation models are refined taking into consideration satellite failure rate,

The second section reviews the quality of the GNSS measurements. In the first chapter, a new GNSS receiver design in which the GNSS signal is repaired using a new vector tracking

software, Bernese, GIPSY/OASIS II, and GAMIT by [11–13], respectively.

the improvement in orbit quality).

4 Accuracy of GNSS Methods

desired position accuracy.

**3. Scope of book**

chapters is as in the following:

repair rate, and backup situation.

Dogan Ugur Sanli Address all correspondence to: usanli@yildiz.edu.tr Yildiz Technical University, Turkey

#### **References**


[5] Sanli DU, Engin C. Accuracy of GPS positioning over regional scales. Survey Review. 2009;**41**:192-200

**Section 2**

**Performance Evaluation of GNSS**


**Performance Evaluation of GNSS**

[5] Sanli DU, Engin C. Accuracy of GPS positioning over regional scales. Survey Review.

[6] Ozturk D, Sanli DU. Accuracy of GPS positioning from local to regional scales: A unified

[7] Sanli DU, Kurumahmut F. Accuracy of GPS positioning in the presence of large height

[8] Ghoddousi-Fard R, Dare P. Online GPS processing services: An initial study. GPS Solu-

[9] Schwarz CR, Snay RA, Soler T. Accuracy assessment of the national geodetic survey's

[10] Hastaoglu KO, Sanli DU. Monitoring Koyulhisar landslide using rapid static GPS: A strategy to remove biases from vertical velocities. Natural Hazards. 2011;**58**:1275-1294

[11] Doğan U. Accuracy analysis of relative positions of permanent GPS stations in the

[12] Sanli DU, Tekic S. Accuracy of GPS precise point positioning: A tool for GPS accuracy

[13] Firuzabadi D, King RW. GPS precision as a function of session duration and reference

prediction. Saarbrücken: LAP Lambert Academic Publishing; 2010. 60 p

frame using multi-point software. GPS Solutions. 2012;**16**:191-196

prediction model. Survey Review. 2011;**43**:79-589

differences. Survey Review. 2011;**43**(320):162-176

OPUS-RS utility. GPS Solutions. 2009;**13**:119-132

Marmara region, Turkey. Survey Review. 2007;**39**:156-165

2009;**41**:192-200

6 Accuracy of GNSS Methods

tions. 2006;**10**:12-20

**Chapter 2**

Provisional chapter

**Evaluation Methods of Satellite Navigation System**

DOI: 10.5772/intechopen.81034

With the development of global satellite navigation system, for example, global positioning system (GPS) and so on, some regional navigation systems and augmentation systems are developing rapidly. The continuous development of satellite navigation system has attracted the users' attention to satellite navigation performance, which makes the navigation system performance become the key of satellite navigation system competition in the field of GNSS applications. The signal in space (SIS) continuity evaluation model based on the reliability is established, and the mean time between failures (MTBF) is used to characterize the probability that there is no continuity loss in unit time. Aiming at the incompleteness of the current availability model, a per-satellite availability evaluation models based on Markov process is established. Moreover, the constellation availability evaluation model is proposed by combining the satellite failure rate, repair rate and backup situation. By analyzing the measured data, the probability of the continuity and availability of GPS and BeiDou Navigation Satellite System (BDS) are calculated respectively. The results are instructive for the study of the availability performance monitoring

Keywords: GNSS, performance evaluating, accuracy, integrity, availability

With the development of global satellite navigation system, for example, GPS and so on, some regional navigation systems and augmentation systems are developing rapidly. The continuous development of satellite navigation system has attracted the users' attention to satellite navigation performance, which makes the navigation system performance become the key of satellite navigation system competition in the field of GNSS application [1–4]. Meanwhile, the

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Evaluation Methods of Satellite Navigation System

**Performance**

Abstract

1. Introduction

Performance

Ershen Wang, He He and Chaoying Jia

Ershen Wang, He He and Chaoying Jia

http://dx.doi.org/10.5772/intechopen.81034

and the evaluation of global BDS.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Evaluation Methods of Satellite Navigation System Performance** Evaluation Methods of Satellite Navigation System Performance

DOI: 10.5772/intechopen.81034

Ershen Wang, He He and Chaoying Jia Ershen Wang, He He and Chaoying Jia

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.81034

#### Abstract

With the development of global satellite navigation system, for example, global positioning system (GPS) and so on, some regional navigation systems and augmentation systems are developing rapidly. The continuous development of satellite navigation system has attracted the users' attention to satellite navigation performance, which makes the navigation system performance become the key of satellite navigation system competition in the field of GNSS applications. The signal in space (SIS) continuity evaluation model based on the reliability is established, and the mean time between failures (MTBF) is used to characterize the probability that there is no continuity loss in unit time. Aiming at the incompleteness of the current availability model, a per-satellite availability evaluation models based on Markov process is established. Moreover, the constellation availability evaluation model is proposed by combining the satellite failure rate, repair rate and backup situation. By analyzing the measured data, the probability of the continuity and availability of GPS and BeiDou Navigation Satellite System (BDS) are calculated respectively. The results are instructive for the study of the availability performance monitoring and the evaluation of global BDS.

Keywords: GNSS, performance evaluating, accuracy, integrity, availability

#### 1. Introduction

With the development of global satellite navigation system, for example, GPS and so on, some regional navigation systems and augmentation systems are developing rapidly. The continuous development of satellite navigation system has attracted the users' attention to satellite navigation performance, which makes the navigation system performance become the key of satellite navigation system competition in the field of GNSS application [1–4]. Meanwhile, the

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

compatibility, interoperability and service performance of GNSS have become an important issue regarding the system construction and the users' requirements [5]. However, there is not a unified standard for satellite navigation service, e.g., there are non-negligible differences in the indicators of each navigation system [6–8], including the name, the manner and the prescribed scope. GPS is the earliest construction and longest-developing satellite navigation system. Since its official operation, research on GPS performance has continued, and the results are relatively rich [9]. So far, there are four different versions of the "GPS Standard Positioning Service Performance Standard" [10–13], this document was published by the US Department of Defense and played a leading role in the development of satellite navigation system performance evaluation systems. In addition, in order to ensure the safe and efficient operation of GPS and its enhanced systems WAAS and LAAS, and to analyze the navigation performance and the cause of service interruption, the United States Federal Aviation Administration (FAA) has set the GPS Standard Positioning Service (GPS SPS) and wide area enhancement since 1993. The performance of the system (WAAS) is monitored and analyzed, and a corresponding performance analysis report is provided on a quarterly basis [14]. Amongst existing standards, the GPS Standard Positioning Service Performance Standards released by USA is more widely used to evaluate satellite navigation systems [15].

instantaneous availability based on failure rate and reliability without considering on-orbit restoration performance [18]. In fact, most satellite failures can be restored by ground control segments or resolved by spare satellites. Based on this, Section 2.1 mainly introduces and analyzes the definition and performance evaluation indicators of GNSS. Based on the "GPS Standard Positioning Service Performance Standards" and "Beidou Satellite Navigation System Open Service Performance Specification", the accuracy, integrity, continuity and availability definition as well as evaluation indicators of GPS and BDS are analyzed respectively, which is convenient for subsequent performance evaluation. The results provide the basis. In Section 2.1.2, the SIS availability of GPS and BDS are evaluated and analyzed. The model of satellite availability algorithm is constructed based on the Markov process. Based on the evaluation models, the performance of GPS SIS and BDS SIS is evaluated by using the measured data in Section 2.2. Finally, combined with the backup situation of satellites, the constellation avail-

Evaluation Methods of Satellite Navigation System Performance

http://dx.doi.org/10.5772/intechopen.81034

11

Accuracy, integrity, continuity and availability are the four basic properties of satellite navigation systems. Performance indicators and assessment methods vary for different navigation systems. Compared with GLONASS and Galileo, GPS navigation system is more perfect for performance evaluation indicators and results, especially the release of GPS SPS PS, which is the leading

GPS is the first satellite navigation system to perform performance evaluation, and its civilian standard location service is applicable to civilian users (L1 C/A code) worldwide. Compared with the precision positioning service and the enhanced system WAAS service, the civilian standard positioning service has the lowest positioning accuracy, but the user quantity is the largest.

Up to now, the US Department of Defense has released four versions of GPS SPS PS to show GPS service performance to users around the world [10–13]. Based on the comprehensive comparison, it is found that with the improvement of GPS performance level, the relevant performance evaluation theory is gradually improved. In the late 1990s, GPS service performance was greatly improved by the implementation of a series of performance enhancement programs. With the cancelation of the optional availability SA policy, the third edition of the GPS SPS PS released in 2001 was revised accordingly. Although the overall framework has not changed, the connotation of the accuracy index has changed a lot, the index parameters of the SIS precision are compressed, and the service reliability is also redefined. At present, the latest version of GPS SPS PS was released in 2008. Based on the summary of the first three editions,

The space segment of the Beidou satellite navigation system consists of five geostationary orbit (GEO) satellites, 27 medium-Earth orbit (MEO) satellites and three inclined geosynchronous

direction of satellite navigation system performance standards and evaluation system.

ability evaluation models of SIS and service are proposed in Section 2.3.

2.1. Satellite navigation system performance evaluation criteria

2.1.1. Standard positioning service performance standard of GPS

the original index system was reorganized and improved.

2.1.2. Satellite navigation system public service performance specification of Beidou

Each stage of a satellite navigation system is inseparable from its performance assessment. The performance evaluation of a navigation system can not only verify whether the performance meets the original design requirements, but also monitor the operating status of the system in real time, provide a basis for performance enhancement of the system, and promote the modernization process of the navigation system [16]. Therefore, in the development of satellite navigation systems, the evaluation of the performance of navigation systems has become a very important part.

At present, China's Beidou satellite navigation system has been able to be compatible with other satellite navigation systems. The development of Beidou satellite navigation system follows the "three-step" strategy, namely: firstly to achieve navigation services in China, secondly to achieve regional navigation services in the Asia-Pacific region, and finally to build a global satellite navigation system with global navigation capabilities. Now it has completed the construction of the second-step regional navigation system and will achieve global coverage in 2020.

The construction of BDS has very important practical significance, but at present it has not yet established a complete performance evaluation system, and it faces severe performance test evaluation problems [17]. Therefore, considering the construction and subsequent development of BDS in China, it is very necessary to carry out research on the performance evaluation method of the satellite navigation system. In-depth analysis of the evaluation index system and method, and the use of measured data to verify it, in order to establish a sound BDS performance evaluation system to accumulate certain experience.

#### 2. Evaluation algorithm of GNSS signal in space availability

There are lots of researches working on per-satellite availability and constellation availability. Ochieng et al. established a per-satellite availability evaluation model that calculates instantaneous availability based on failure rate and reliability without considering on-orbit restoration performance [18]. In fact, most satellite failures can be restored by ground control segments or resolved by spare satellites. Based on this, Section 2.1 mainly introduces and analyzes the definition and performance evaluation indicators of GNSS. Based on the "GPS Standard Positioning Service Performance Standards" and "Beidou Satellite Navigation System Open Service Performance Specification", the accuracy, integrity, continuity and availability definition as well as evaluation indicators of GPS and BDS are analyzed respectively, which is convenient for subsequent performance evaluation. The results provide the basis. In Section 2.1.2, the SIS availability of GPS and BDS are evaluated and analyzed. The model of satellite availability algorithm is constructed based on the Markov process. Based on the evaluation models, the performance of GPS SIS and BDS SIS is evaluated by using the measured data in Section 2.2. Finally, combined with the backup situation of satellites, the constellation availability evaluation models of SIS and service are proposed in Section 2.3.

#### 2.1. Satellite navigation system performance evaluation criteria

compatibility, interoperability and service performance of GNSS have become an important issue regarding the system construction and the users' requirements [5]. However, there is not a unified standard for satellite navigation service, e.g., there are non-negligible differences in the indicators of each navigation system [6–8], including the name, the manner and the prescribed scope. GPS is the earliest construction and longest-developing satellite navigation system. Since its official operation, research on GPS performance has continued, and the results are relatively rich [9]. So far, there are four different versions of the "GPS Standard Positioning Service Performance Standard" [10–13], this document was published by the US Department of Defense and played a leading role in the development of satellite navigation system performance evaluation systems. In addition, in order to ensure the safe and efficient operation of GPS and its enhanced systems WAAS and LAAS, and to analyze the navigation performance and the cause of service interruption, the United States Federal Aviation Administration (FAA) has set the GPS Standard Positioning Service (GPS SPS) and wide area enhancement since 1993. The performance of the system (WAAS) is monitored and analyzed, and a corresponding performance analysis report is provided on a quarterly basis [14]. Amongst existing standards, the GPS Standard Positioning Service Performance Standards

10 Accuracy of GNSS Methods

released by USA is more widely used to evaluate satellite navigation systems [15].

of the second-step regional navigation system and will achieve global coverage in 2020.

performance evaluation system to accumulate certain experience.

2. Evaluation algorithm of GNSS signal in space availability

The construction of BDS has very important practical significance, but at present it has not yet established a complete performance evaluation system, and it faces severe performance test evaluation problems [17]. Therefore, considering the construction and subsequent development of BDS in China, it is very necessary to carry out research on the performance evaluation method of the satellite navigation system. In-depth analysis of the evaluation index system and method, and the use of measured data to verify it, in order to establish a sound BDS

There are lots of researches working on per-satellite availability and constellation availability. Ochieng et al. established a per-satellite availability evaluation model that calculates

Each stage of a satellite navigation system is inseparable from its performance assessment. The performance evaluation of a navigation system can not only verify whether the performance meets the original design requirements, but also monitor the operating status of the system in real time, provide a basis for performance enhancement of the system, and promote the modernization process of the navigation system [16]. Therefore, in the development of satellite navigation systems, the evaluation of the performance of navigation systems has become a very important part. At present, China's Beidou satellite navigation system has been able to be compatible with other satellite navigation systems. The development of Beidou satellite navigation system follows the "three-step" strategy, namely: firstly to achieve navigation services in China, secondly to achieve regional navigation services in the Asia-Pacific region, and finally to build a global satellite navigation system with global navigation capabilities. Now it has completed the construction

Accuracy, integrity, continuity and availability are the four basic properties of satellite navigation systems. Performance indicators and assessment methods vary for different navigation systems. Compared with GLONASS and Galileo, GPS navigation system is more perfect for performance evaluation indicators and results, especially the release of GPS SPS PS, which is the leading direction of satellite navigation system performance standards and evaluation system.

#### 2.1.1. Standard positioning service performance standard of GPS

GPS is the first satellite navigation system to perform performance evaluation, and its civilian standard location service is applicable to civilian users (L1 C/A code) worldwide. Compared with the precision positioning service and the enhanced system WAAS service, the civilian standard positioning service has the lowest positioning accuracy, but the user quantity is the largest.

Up to now, the US Department of Defense has released four versions of GPS SPS PS to show GPS service performance to users around the world [10–13]. Based on the comprehensive comparison, it is found that with the improvement of GPS performance level, the relevant performance evaluation theory is gradually improved. In the late 1990s, GPS service performance was greatly improved by the implementation of a series of performance enhancement programs. With the cancelation of the optional availability SA policy, the third edition of the GPS SPS PS released in 2001 was revised accordingly. Although the overall framework has not changed, the connotation of the accuracy index has changed a lot, the index parameters of the SIS precision are compressed, and the service reliability is also redefined. At present, the latest version of GPS SPS PS was released in 2008. Based on the summary of the first three editions, the original index system was reorganized and improved.

#### 2.1.2. Satellite navigation system public service performance specification of Beidou

The space segment of the Beidou satellite navigation system consists of five geostationary orbit (GEO) satellites, 27 medium-Earth orbit (MEO) satellites and three inclined geosynchronous orbit (IGSO) satellites. Taking into account the characteristics of the BDS, the China Satellite Navigation System Management Office released the BDS-OS-PS-1.0, which is used to illustrate the performance characteristics and indicators of the public service B1I signal in the regional phase of the Beidou satellite navigation system [19, 20].

In Figure 1, 0 indicates the system status is normal; 1 indicates the system status is failed; λ is the failure rate of satellite, it is the inverse of mean time between failure (MTBF); μ is the restoration rate of satellite, it is the inverse of mean time to restoration (MTTR); and Δt is the

According to reliability theory [25, 26], we can get the instantaneous availability of per-slot by

In order to express the per-slot availability more reasonably, when t ! ∞, we get the steady

<sup>A</sup> <sup>¼</sup> <sup>μ</sup>

According to the relationship between and MTBF, and the relationship between and MTTR,

where A is the per-satellite availability; MTBF is the reciprocal of λ, andMTTRis the reciprocal ofμ. In Figure 2, λ<sup>i</sup> (i = 1, 2, 3, 4) is the satellite failure rate of different failure type. μ <sup>i</sup> (i = 1, 2, 3, 4) is the satellite restoration rate of different failure type. Considering the influence of different failure type, the satellite failure rate λ and the satellite restoration μ rate in formula (2) are

λ ¼ λ<sup>1</sup> þ λ<sup>2</sup> þ λ<sup>3</sup> þ λ<sup>4</sup>

In the previous constellation availability models [27], a specific constellation with a defined number (generally 24) of space vehicles was considered, when more space vehicles than required for the constellation have actually been on orbit for most of the time since the declaration of Full

:

<sup>μ</sup> <sup>¼</sup> <sup>λ</sup> λ1 μ1 þ λ2 μ2 þ λ3 μ3 þ λ4 μ4

8 >><

>>:

2.2.2. Evaluation algorithm for constellation availability

Figure 1. Markov state transition process of per-slot.

<sup>A</sup> <sup>¼</sup> MTBF

: (1)

(4)

<sup>λ</sup> <sup>þ</sup> <sup>μ</sup> : (2)

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MTBF <sup>þ</sup> MTTR : (3)

A tðÞ¼ <sup>μ</sup>

state availability of per-slot through formula (1), and it would be as follows:

λ þ μ þ λ λ þ μ e �ð Þ <sup>λ</sup>þ<sup>μ</sup> <sup>t</sup>

time interval of state transition.

formula (1) is equivalent to:

equivalent to the following formula:

utilizing the Markov state transition process:

#### 2.2. SIS evaluation algorithm based on Markov process

GPS SPS PS pointed out that the availability of navigation system refers to the percentage of time that the navigation system can provide users with available services within its service area, which characterizes the service capability of satellite navigation systems [13]. As one of the four basic service performances of satellite navigation systems, usability has become a key performance indicator in civil aviation and other application fields, and is an important basis for judging whether the navigation system is reliable [21, 22]. The usability study content of the four released versions of GPS SPS PS is compared, and the development trend is shown in Table 1.

SIS from the development trend of the availability indicators is given in Table 1, as the research progresses, the availability of satellites is gradually divided into SIS layer availability and service layer availability, and SIS availability is receiving more and more attention.

SIS availability can be described in terms of per-satellite availability and constellation availability [13]. From the definition of availability, the availability of SIS is essentially an assessment of satellite availability, i.e., the availability of per-satellite is analyzed, and then the study of per-satellite availability transitions to constellation availability, which in turn reflects the SIS availability of all satellites.

#### 2.2.1. Evaluation model for per-satellite availability

The instantaneous reliability function of a satellite is given in the literature, which only considered the failure rate but ignored the restoration rate. In fact, part of satellite failures can be resolved by the repair of ground control section or the backup of spare satellites. And this is one of the functions of the Markov chain. The life distribution and the failure restoration time distribution are assumed to follow exponential distributions. As long as the satellite navigation system status is given properly, the system can always be described by theMarkov process [23, 24]. The exponential distribution model is used to describe the reliability of the satellites in many of the literature. When the failure rate of a satellite is assumed to be of exponential distribution, the Markov state transition process of per-slot is shown as Figure 1.


Table 1. Comparison of GPS SPS PS to usability research content.

In Figure 1, 0 indicates the system status is normal; 1 indicates the system status is failed; λ is the failure rate of satellite, it is the inverse of mean time between failure (MTBF); μ is the restoration rate of satellite, it is the inverse of mean time to restoration (MTTR); and Δt is the time interval of state transition.

According to reliability theory [25, 26], we can get the instantaneous availability of per-slot by utilizing the Markov state transition process:

$$A(t) = \frac{\mu}{\lambda + \mu} + \frac{\lambda}{\lambda + \mu} e^{-(\lambda + \mu)t}. \tag{1}$$

In order to express the per-slot availability more reasonably, when t ! ∞, we get the steady state availability of per-slot through formula (1), and it would be as follows:

$$A = \frac{\mu}{\lambda + \mu}.\tag{2}$$

According to the relationship between and MTBF, and the relationship between and MTTR, formula (1) is equivalent to:

$$A = \frac{MTBF}{MTBF + MTTR} \,\text{.}\tag{3}$$

where A is the per-satellite availability; MTBF is the reciprocal of λ, andMTTRis the reciprocal ofμ.

In Figure 2, λ<sup>i</sup> (i = 1, 2, 3, 4) is the satellite failure rate of different failure type. μ <sup>i</sup> (i = 1, 2, 3, 4) is the satellite restoration rate of different failure type. Considering the influence of different failure type, the satellite failure rate λ and the satellite restoration μ rate in formula (2) are equivalent to the following formula:

$$\begin{cases} \lambda = \lambda\_1 + \lambda\_2 + \lambda\_3 + \lambda\_4\\ \mu = \frac{\lambda}{\mu\_1} + \frac{\lambda\_2}{\mu\_2} + \frac{\lambda\_3}{\mu\_3} + \frac{\lambda\_4}{\mu\_4} \end{cases} \tag{4}$$

#### 2.2.2. Evaluation algorithm for constellation availability

orbit (IGSO) satellites. Taking into account the characteristics of the BDS, the China Satellite Navigation System Management Office released the BDS-OS-PS-1.0, which is used to illustrate the performance characteristics and indicators of the public service B1I signal in the regional

GPS SPS PS pointed out that the availability of navigation system refers to the percentage of time that the navigation system can provide users with available services within its service area, which characterizes the service capability of satellite navigation systems [13]. As one of the four basic service performances of satellite navigation systems, usability has become a key performance indicator in civil aviation and other application fields, and is an important basis for judging whether the navigation system is reliable [21, 22]. The usability study content of the four released versions of GPS SPS PS is compared, and the development trend is shown in

SIS from the development trend of the availability indicators is given in Table 1, as the research progresses, the availability of satellites is gradually divided into SIS layer availability and

SIS availability can be described in terms of per-satellite availability and constellation availability [13]. From the definition of availability, the availability of SIS is essentially an assessment of satellite availability, i.e., the availability of per-satellite is analyzed, and then the study of per-satellite availability transitions to constellation availability, which in turn reflects the SIS

The instantaneous reliability function of a satellite is given in the literature, which only considered the failure rate but ignored the restoration rate. In fact, part of satellite failures can be resolved by the repair of ground control section or the backup of spare satellites. And this is one of the functions of the Markov chain. The life distribution and the failure restoration time distribution are assumed to follow exponential distributions. As long as the satellite navigation system status is given properly, the system can always be described by theMarkov process [23, 24]. The exponential distribution model is used to describe the reliability of the satellites in many of the literature. When the failure rate of a satellite is assumed to be of exponential distribution, the

2008 edition SIS Availability Standard, SPS Service Availability Standard, PDOP Availability Standard

service layer availability, and SIS availability is receiving more and more attention.

phase of the Beidou satellite navigation system [19, 20].

2.2. SIS evaluation algorithm based on Markov process

Table 1.

12 Accuracy of GNSS Methods

availability of all satellites.

2.2.1. Evaluation model for per-satellite availability

GPS SPS PS document Research content

1993 edition Service availability standard 1995 edition Service availability standard

Table 1. Comparison of GPS SPS PS to usability research content.

Markov state transition process of per-slot is shown as Figure 1.

2001 edition SPS Service Availability Standard, PDOP Availability Standard

In the previous constellation availability models [27], a specific constellation with a defined number (generally 24) of space vehicles was considered, when more space vehicles than required for the constellation have actually been on orbit for most of the time since the declaration of Full

Figure 1. Markov state transition process of per-slot.

Figure 2. Markov state transition process of satellite based on different failure types.

Operational Capability (FOC); Zheng and Ren pointed out that a study on constellation availability is based on per-satellite availability, and MTBF and MTTR of different per-satellite outages directly influence constellation availability in different states [28]; U.S. Department of Defense refers that constellation availability model is based on binomial probability distribution [15], and it can be described as the following formula:

$$p(k) = \mathsf{C}\_N^k (1 - A)^k A^{N-k}.\tag{5}$$

change. When the base orbit satellite fails, the ground control station will repair the faulty

Failure state of constellation system will change with the number of failed satellites. Therefore, on the condition of the above assumptions, the failure state spaces of baseline satellites and spare satellites respectively are 0f g ; 1; 2; ⋯; N and 0f g ; 1; 2; ⋯; M . The SIS constellation availability model based on Markov chain is set up. In addition, this model the baseline satellites constellation availability and the spare satellites constellation availability are considered respectively. Moreover, the backup situations of spare satellites are combined with the failure state of baseline satellites constellation. Finally, the availability of whole constellation system

λið Þ i ¼ 1; 2; 3; ⋯; N are used to indicate the failure rates of baseline satellites constellation;

If the state of failure state space is i at the time of t, then the probability of this situation can be indicated with Gið Þt ð Þ i ¼ 0; 1; 2; ⋯; N , and assuming that the time of initial state is t ¼ t0. When time increases to t ¼ t<sup>0</sup> þ Δt, the probability that the baseline constellation not having failed

The failure state space of baseline constellation also has other states, and the probability of

Markov failure state transition process of baseline satellites is shown in Figure 3.

<sup>N</sup>þ1�<sup>i</sup> � <sup>λ</sup> � ð Þ <sup>1</sup> � <sup>λ</sup> <sup>N</sup>�<sup>i</sup>

<sup>i</sup> � <sup>μ</sup> � <sup>1</sup> � <sup>μ</sup> <sup>i</sup>�<sup>1</sup>

G1ð Þ¼ t<sup>0</sup> þ Δt G0ð Þ� t<sup>0</sup> λ1Δt þ G1ð Þ� t<sup>0</sup> 1 � λ<sup>2</sup> þ μ<sup>1</sup>

G2ð Þ¼ t<sup>0</sup> þ Δt G1ð Þ� t<sup>0</sup> λ2Δt þ G2ð Þ� t<sup>0</sup> 1 � λ<sup>3</sup> þ μ<sup>2</sup>

GN�<sup>1</sup>ð Þ¼ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>Δ</sup><sup>t</sup> GN�<sup>2</sup>ð Þ� <sup>t</sup><sup>0</sup> <sup>λ</sup><sup>N</sup>�<sup>1</sup>Δ<sup>t</sup> <sup>þ</sup> GN�<sup>1</sup>ð Þ� <sup>t</sup><sup>0</sup> <sup>1</sup> � <sup>λ</sup><sup>N</sup> <sup>þ</sup> <sup>μ</sup><sup>N</sup>�<sup>1</sup>

Figure 3. Markov failure state transition process of baseline constellation.

ð Þ i ¼ 1; 2; 3; ⋯; N are used to indicate the restoration rates of baseline satellites constellation, and both failure rates and restoration rates are on different failure conditions. The corresponding

ð Þ i ¼ 1; 2; ⋯; N (λ is the average failure rates of N

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ð Þ i ¼ 1; 2; ⋯; N (μ is the average restoration rates of

<sup>Δ</sup><sup>t</sup> <sup>þ</sup> <sup>G</sup>2ð Þ� <sup>t</sup><sup>0</sup> <sup>μ</sup>2Δ<sup>t</sup> (7)

<sup>Δ</sup><sup>t</sup> <sup>þ</sup> <sup>G</sup>3ð Þ� <sup>t</sup><sup>0</sup> <sup>μ</sup>3Δ<sup>t</sup> (8)

<sup>Δ</sup><sup>t</sup> <sup>þ</sup> GNð Þ� <sup>t</sup><sup>0</sup> <sup>μ</sup>NΔ<sup>t</sup> (9)

G0ð Þ¼ t<sup>0</sup> þ Δt G0ð Þ� t<sup>0</sup> ð Þþ 1 � λ1Δt G1ð Þ� t<sup>0</sup> μ1Δt (6)

GNð Þ¼ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>Δ</sup><sup>t</sup> GN�<sup>1</sup>ð Þ� <sup>t</sup><sup>0</sup> <sup>λ</sup>NΔ<sup>t</sup> <sup>þ</sup> GNð Þ� <sup>t</sup><sup>0</sup> <sup>1</sup> � <sup>μ</sup>NΔ<sup>t</sup> (10)

satellite while replacing the non-orbital satellite, and only repair one satellite at a time.

can be attained.

In Figure 3, <sup>λ</sup><sup>i</sup> <sup>¼</sup> <sup>C</sup><sup>1</sup>

N baseline satellites).

satellites is:

baseline satellites); <sup>μ</sup><sup>i</sup> <sup>¼</sup> <sup>C</sup><sup>1</sup>

these states is as follows:

μi

where, p kð Þ is the constellation availability when there are faulted satellites. N represents the total number of satellites in the constellation. k is the number of faulted satellites, and A is the availability of per-satellite.

Formula (5) calculates the constellation availability based on the stationary state of per-satellite availability. The model calculates the availability of the constellation based on the availability of per satellite steady-state. Although it reflects the availability of the constellation under different fault conditions to some extent, it ignores the impact of satellite backup strategy on constellation availability and is a relatively static constellation availability. The availability of constellations is affected by many factors. Because the factors affecting the state of the constellation are more complicated, this section proposes a mathematical model of constellation availability considering the satellite's failure rate, repair rate and backup situation based on the traditional constellation availability model.

Let's explain the state of the constellation: suppose the constellation consists of a basic orbital satellite and a non-orbital satellite. When there is no satellite failure, the state of the constellation is N. if there is a failure of the basic orbital satellite, and the faulty satellite is replaced by the nonorbiting satellite in time, the state of the constellation is considered to have not changed. If the failed satellite is not replaced by the non-orbital satellite in time, the state of the constellation will change. When the base orbit satellite fails, the ground control station will repair the faulty satellite while replacing the non-orbital satellite, and only repair one satellite at a time.

Failure state of constellation system will change with the number of failed satellites. Therefore, on the condition of the above assumptions, the failure state spaces of baseline satellites and spare satellites respectively are 0f g ; 1; 2; ⋯; N and 0f g ; 1; 2; ⋯; M . The SIS constellation availability model based on Markov chain is set up. In addition, this model the baseline satellites constellation availability and the spare satellites constellation availability are considered respectively. Moreover, the backup situations of spare satellites are combined with the failure state of baseline satellites constellation. Finally, the availability of whole constellation system can be attained.

λið Þ i ¼ 1; 2; 3; ⋯; N are used to indicate the failure rates of baseline satellites constellation; μi ð Þ i ¼ 1; 2; 3; ⋯; N are used to indicate the restoration rates of baseline satellites constellation, and both failure rates and restoration rates are on different failure conditions. The corresponding Markov failure state transition process of baseline satellites is shown in Figure 3.

In Figure 3, <sup>λ</sup><sup>i</sup> <sup>¼</sup> <sup>C</sup><sup>1</sup> <sup>N</sup>þ1�<sup>i</sup> � <sup>λ</sup> � ð Þ <sup>1</sup> � <sup>λ</sup> <sup>N</sup>�<sup>i</sup> ð Þ i ¼ 1; 2; ⋯; N (λ is the average failure rates of N baseline satellites); <sup>μ</sup><sup>i</sup> <sup>¼</sup> <sup>C</sup><sup>1</sup> <sup>i</sup> � <sup>μ</sup> � <sup>1</sup> � <sup>μ</sup> <sup>i</sup>�<sup>1</sup> ð Þ i ¼ 1; 2; ⋯; N (μ is the average restoration rates of N baseline satellites).

If the state of failure state space is i at the time of t, then the probability of this situation can be indicated with Gið Þt ð Þ i ¼ 0; 1; 2; ⋯; N , and assuming that the time of initial state is t ¼ t0. When time increases to t ¼ t<sup>0</sup> þ Δt, the probability that the baseline constellation not having failed satellites is:

$$\mathbf{G}\_{0}(t\_{0} + \Delta t) = \mathbf{G}\_{0}(t\_{0}) \cdot (1 - \lambda\_{1}\Delta t) + \mathbf{G}\_{1}(t\_{0}) \cdot \mu\_{1}\Delta t \tag{6}$$

The failure state space of baseline constellation also has other states, and the probability of these states is as follows:

$$\mathbf{G}\_{1}(t\_{0} + \Delta t) = \mathbf{G}\_{0}(t\_{0}) \cdot \lambda\_{1} \Delta t + \mathbf{G}\_{1}(t\_{0}) \cdot \left(1 - \left(\lambda\_{2} + \mu\_{1}\right) \Delta t\right) + \mathbf{G}\_{2}(t\_{0}) \cdot \mu\_{2} \Delta t \tag{7}$$

$$\mathbf{G}\_{2}(t\_{0} + \Delta t) = \mathbf{G}\_{1}(t\_{0}) \cdot \lambda\_{2} \Delta t + \mathbf{G}\_{2}(t\_{0}) \cdot \left(\mathbf{1} - \left(\lambda\_{3} + \mu\_{2}\right)\Delta t\right) + \mathbf{G}\_{3}(t\_{0}) \cdot \mu\_{3} \Delta t \tag{8}$$

$$\mathbf{G}\_{\rm N-1}(t\_0 + \Delta t) = \mathbf{G}\_{\rm N-2}(t\_0) \cdot \lambda\_{\rm N-1} \Delta t + \mathbf{G}\_{\rm N-1}(t\_0) \cdot \left(\mathbf{1} - \left(\lambda\_{\rm N} + \mu\_{\rm N-1}\right) \Delta t\right) + \mathbf{G}\_{\rm N}(t\_0) \cdot \mu\_{\rm N} \Delta t \tag{9}$$

$$\mathbf{G}\_{N}(t\_{0} + \Delta t) = \mathbf{G}\_{N-1}(t\_{0}) \cdot \lambda\_{N} \Delta t + \mathbf{G}\_{N}(t\_{0}) \cdot \left(1 - \mu\_{N} \Delta t\right) \tag{10}$$

Figure 3. Markov failure state transition process of baseline constellation.

Operational Capability (FOC); Zheng and Ren pointed out that a study on constellation availability is based on per-satellite availability, and MTBF and MTTR of different per-satellite outages directly influence constellation availability in different states [28]; U.S. Department of Defense refers that constellation availability model is based on binomial probability distribution

<sup>N</sup>ð Þ <sup>1</sup> � <sup>A</sup> <sup>k</sup>

where, p kð Þ is the constellation availability when there are faulted satellites. N represents the total number of satellites in the constellation. k is the number of faulted satellites, and A is the

Formula (5) calculates the constellation availability based on the stationary state of per-satellite availability. The model calculates the availability of the constellation based on the availability of per satellite steady-state. Although it reflects the availability of the constellation under different fault conditions to some extent, it ignores the impact of satellite backup strategy on constellation availability and is a relatively static constellation availability. The availability of constellations is affected by many factors. Because the factors affecting the state of the constellation are more complicated, this section proposes a mathematical model of constellation availability considering the satellite's failure rate, repair rate and backup situation based on

Let's explain the state of the constellation: suppose the constellation consists of a basic orbital satellite and a non-orbital satellite. When there is no satellite failure, the state of the constellation is N. if there is a failure of the basic orbital satellite, and the faulty satellite is replaced by the nonorbiting satellite in time, the state of the constellation is considered to have not changed. If the failed satellite is not replaced by the non-orbital satellite in time, the state of the constellation will

AN�<sup>k</sup>

: (5)

p kð Þ¼ Ck

[15], and it can be described as the following formula:

Figure 2. Markov state transition process of satellite based on different failure types.

the traditional constellation availability model.

availability of per-satellite.

14 Accuracy of GNSS Methods

Failure state space of baseline constellation has different states in different time. The formulas (6)–(10) can be shown by matrix form, then the probabilities of the above different states can be expressed as:

$$
\overrightarrow{G}\left(t\_0 + k\Delta t\right) = \overrightarrow{G}\left(\Delta t\right) \cdot \overrightarrow{G}\left(t\_0 + (k-1)\Delta t\right) \tag{11}
$$

2.3. Per-satellite availability evaluation

obtained.

lites to some extent.

in Figure 5.

2.3.1. Per-satellite availability evaluation of GPS

restoration rate can be obtained, which are shown in Figure 4.

Figure 4. Average failure rate and restoration rate of GPS satellites.

According to the Markov state transition model, it can be seen that the key to calculate satellite availability is to get satellite failure rate λ and restoration rate μ. Therefore, by analyzing the GPS status report provided by the FAA, the MTBF and MTTR of each satellite with different types of failures can be respectively obtained, and then the availability of the satellite can be

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In order to guarantee the reliability of the evaluated results, this paper makes the statistics based on all outages according to the GPS failure report of FAA. According to analysis, it can be seen that a total number of 51 satellites generates different types of outages from 1999 to 2015. By processing the MTBF and MTTR of satellites, the per-satellite average failure rate and

The spacecraft number (SVN) has a certain relationship with the order of launch of GPS satellites. Satellites with smaller numbers are launched earlier and satellite models are lower; while satellites with larger numbers are launched later, and satellite models are relatively high. From the analysis of Figure 4 in general, the average repair rate of the higher-model satellites is generally far greater than the average failure rate compared with the low-model satellites. Combined with the analysis of formula (4), it can be inferred that the availability of higherprofile satellites is generally higher, which reflects the continuous development of GPS satel-

By bringing the average failure rate and restoration rate of each of the above satellites into the per-satellite availability model, the availability of GPS per-satellite can be obtained, as shown

The dotted line is the per-satellite availability minimum standard (0.957) of GPS SPS PS (2008) in Figure 5. If the availability of the satellite is greater than this value, the satellite is considered to meet the availability criteria. As can be seen from Figure 5, except for the availability of

Therefore,

G ! ð Þ¼ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> ½ � <sup>G</sup>0ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> <sup>G</sup>1ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> <sup>⋯</sup> GNð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> T, G ! <sup>ð</sup>t<sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>Δ</sup>tÞ ¼ ½ � <sup>G</sup>0ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>Δ</sup><sup>t</sup> <sup>G</sup>1ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>Δ</sup><sup>t</sup> <sup>⋯</sup> GNð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>k</sup>Δ<sup>t</sup> T, G ! ð Þ¼ Δt 1 � λ1Δt μ1Δt 0 0 ⋯ ⋯ 00 0 λ1Δt 1 � λ<sup>2</sup> þ μ<sup>1</sup> � �Δ<sup>t</sup> <sup>μ</sup>2Δ<sup>t</sup> <sup>0</sup> ⋯⋯ ⋮ <sup>⋮</sup> <sup>⋮</sup> 0 λ2Δt 1 � λ<sup>3</sup> þ μ<sup>2</sup> � �Δ<sup>t</sup> <sup>μ</sup>3Δ<sup>t</sup> <sup>0</sup> ⋮⋮ ⋮ ⋮ ⋮ 0 ⋮ ⋮ ⋮⋱ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮⋮ ⋮ ⋱ 0 <sup>0</sup> ⋯ ⋯⋯ 0 0 <sup>λ</sup><sup>N</sup>�<sup>1</sup>Δ<sup>t</sup> <sup>1</sup> � <sup>λ</sup><sup>N</sup> <sup>þ</sup> <sup>μ</sup><sup>N</sup>�<sup>1</sup> � �Δ<sup>t</sup> <sup>μ</sup>NΔ<sup>t</sup> 0 ⋯ ⋯⋯ 00 0 λNΔt 1 � μNΔt 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 8 >>>>>>>>>>>>>>>>>>>>>>>>>>< >>>>>>>>>>>>>>>>>>>>>>>>>>:

According to the formula (11) and the initial condition, the probabilities of different states of baseline constellation after the time of T ¼ kΔt can be calculated.

Similar to the baseline constellation, failure state space of spare satellites constellation also has different states in different time. And the probabilities of these states can be expressed as:

$$
\overrightarrow{F}\left(t\_0 + k\Delta t\right) = \overrightarrow{F}\left(\Delta t\right) \cdot \overrightarrow{F}\left(t\_0 + (k-1)\Delta t\right) \tag{12}
$$

According to the formula (12) and the initial condition of spare satellites constellation, the probabilities of different states of spare satellites constellation after the time of T ¼ kΔt can be also calculated.

Both baseline constellation and spare satellites constellation have important influence on SIS constellation availability. Considering these influences comprehensively, the model of SIS constellation availability is considered:

$$\begin{cases} \begin{aligned} \mathbf{P}\_{s}(t\_{0} + k\Delta t) &= \mathbf{G}\_{0}(t\_{0} + k\Delta t) + \mathbf{G}\_{1}(t\_{0} + k\Delta t) \cdot (\mathbf{F}\_{0}(t\_{0} + k\Delta t) + \mathbf{F}\_{1}(t\_{0} + k\Delta t) + \cdots + \mathbf{F}\_{M-1}(t\_{0} + k\Delta t)) \\ &+ \mathbf{G}\_{2}(t\_{0} + k\Delta t) \cdot (\mathbf{F}\_{0}(t\_{0} + k\Delta t) + \mathbf{F}\_{1}(t\_{0} + k\Delta t) + \cdots + \mathbf{F}\_{M-2}(t\_{0} + k\Delta t)) + \cdots \\ &+ \mathbf{G}\_{M}(t\_{0} + k\Delta t) \cdot \mathbf{F}\_{0}(t\_{0} + k\Delta t) \quad (\text{s} = 0) \\\\ \mathbf{P}\_{s}(t\_{0} + k\Delta t) &= \sum\_{q=s}^{M+s} \mathbf{G}\_{q}(t\_{0} + k\Delta t) \cdot \mathbf{F}\_{M+s-q}(t\_{0} + k\Delta t) \quad (\text{s} = 1, 2, \cdots, N) \end{aligned} \end{cases} \tag{13}$$

In this formula, when the number of failed satellites is S, the probability of SIS constellation availability is Psð Þ t<sup>0</sup> þ kΔt .

#### 2.3. Per-satellite availability evaluation

Failure state space of baseline constellation has different states in different time. The formulas (6)–(10) can be shown by matrix form, then the probabilities of the above different states can be

1 � λ1Δt μ1Δt 0 0 ⋯ ⋯ 00 0

⋮ 0 ⋮ ⋮ ⋮⋱ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮⋮ ⋮ ⋱ 0

0 ⋯ ⋯⋯ 00 0 λNΔt 1 � μNΔt

<sup>0</sup> ⋯ ⋯⋯ 0 0 <sup>λ</sup><sup>N</sup>�<sup>1</sup>Δ<sup>t</sup> <sup>1</sup> � <sup>λ</sup><sup>N</sup> <sup>þ</sup> <sup>μ</sup><sup>N</sup>�<sup>1</sup>

According to the formula (11) and the initial condition, the probabilities of different states of

Similar to the baseline constellation, failure state space of spare satellites constellation also has different states in different time. And the probabilities of these states can be expressed as:

According to the formula (12) and the initial condition of spare satellites constellation, the probabilities of different states of spare satellites constellation after the time of T ¼ kΔt can be

Both baseline constellation and spare satellites constellation have important influence on SIS constellation availability. Considering these influences comprehensively, the model of SIS

Psð Þ¼ t<sup>0</sup> þ kΔt G0ð Þþ t<sup>0</sup> þ kΔt G1ð Þ� t<sup>0</sup> þ kΔt ð Þ F0ð Þþ t<sup>0</sup> þ kΔt F1ð Þþ t<sup>0</sup> þ kΔt ⋯ þ FM�<sup>1</sup>ð Þ t<sup>0</sup> þ kΔt

Gqð Þ� t<sup>0</sup> þ kΔt FMþs�<sup>q</sup>ð Þ t<sup>0</sup> þ kΔt ð Þ s ¼ 1; 2; ⋯; N

þ G2ð Þ� t<sup>0</sup> þ kΔt ðF0ð Þþ t<sup>0</sup> þ kΔt F1ð Þþ t<sup>0</sup> þ kΔt ⋯ þ FM�<sup>2</sup>ð Þ t<sup>0</sup> þ kΔt Þ þ ⋯

In this formula, when the number of failed satellites is S, the probability of SIS constellation

! ð Þ� Δt F !

� �Δ<sup>t</sup> <sup>μ</sup>2Δ<sup>t</sup> <sup>0</sup> ⋯⋯ ⋮ <sup>⋮</sup> <sup>⋮</sup>

� �Δ<sup>t</sup> <sup>μ</sup>3Δ<sup>t</sup> <sup>0</sup> ⋮⋮ ⋮ ⋮

ð Þ t<sup>0</sup> þ ð Þ k � 1 Δt (11)

ð Þ t<sup>0</sup> þ ð Þ k � 1 Δt (12)

� �Δ<sup>t</sup> <sup>μ</sup>NΔ<sup>t</sup>

(13)

! ð Þ� Δt G !

G !

ð Þ¼ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> ½ � <sup>G</sup>0ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> <sup>G</sup>1ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> <sup>⋯</sup> GNð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> <sup>k</sup>Δ<sup>t</sup> T,

0 λ2Δt 1 � λ<sup>3</sup> þ μ<sup>2</sup>

baseline constellation after the time of T ¼ kΔt can be calculated.

ð Þ¼ t<sup>0</sup> þ kΔt F

þ GMð Þ� t<sup>0</sup> þ kΔt F0ð Þ t<sup>0</sup> þ kΔt ð Þ s ¼ 0

F !

λ1Δt 1 � λ<sup>2</sup> þ μ<sup>1</sup>

ð Þ¼ t<sup>0</sup> þ kΔt G

<sup>ð</sup>t<sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>Δ</sup>tÞ ¼ ½ � <sup>G</sup>0ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>Δ</sup><sup>t</sup> <sup>G</sup>1ð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>Δ</sup><sup>t</sup> <sup>⋯</sup> GNð Þ <sup>t</sup><sup>0</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>1</sup> <sup>k</sup>Δ<sup>t</sup> T,

expressed as:

16 Accuracy of GNSS Methods

Therefore,

also calculated.

8

>>>>>>>>>>>><

>>>>>>>>>>>>:

Psð Þ¼ t<sup>0</sup> þ kΔt

availability is Psð Þ t<sup>0</sup> þ kΔt .

constellation availability is considered:

M Xþs q¼s

G !

8

>>>>>>>>>>>>>>>>>>>>>>>>>><

G !

G ! ð Þ¼ Δt

>>>>>>>>>>>>>>>>>>>>>>>>>>:

#### 2.3.1. Per-satellite availability evaluation of GPS

According to the Markov state transition model, it can be seen that the key to calculate satellite availability is to get satellite failure rate λ and restoration rate μ. Therefore, by analyzing the GPS status report provided by the FAA, the MTBF and MTTR of each satellite with different types of failures can be respectively obtained, and then the availability of the satellite can be obtained.

In order to guarantee the reliability of the evaluated results, this paper makes the statistics based on all outages according to the GPS failure report of FAA. According to analysis, it can be seen that a total number of 51 satellites generates different types of outages from 1999 to 2015. By processing the MTBF and MTTR of satellites, the per-satellite average failure rate and restoration rate can be obtained, which are shown in Figure 4.

The spacecraft number (SVN) has a certain relationship with the order of launch of GPS satellites. Satellites with smaller numbers are launched earlier and satellite models are lower; while satellites with larger numbers are launched later, and satellite models are relatively high. From the analysis of Figure 4 in general, the average repair rate of the higher-model satellites is generally far greater than the average failure rate compared with the low-model satellites. Combined with the analysis of formula (4), it can be inferred that the availability of higherprofile satellites is generally higher, which reflects the continuous development of GPS satellites to some extent.

By bringing the average failure rate and restoration rate of each of the above satellites into the per-satellite availability model, the availability of GPS per-satellite can be obtained, as shown in Figure 5.

The dotted line is the per-satellite availability minimum standard (0.957) of GPS SPS PS (2008) in Figure 5. If the availability of the satellite is greater than this value, the satellite is considered to meet the availability criteria. As can be seen from Figure 5, except for the availability of

Figure 4. Average failure rate and restoration rate of GPS satellites.

enhanced. With the continuous advancement of GPS modernization, the availability of GPS

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BDS has not yet established a sound outage forecasting mechanism. Therefore, there is no FAA-like department in China to provide a measured fault report on BDS. Therefore, the paper mainly obtains the Beidou navigation message published by IGS, and extracts its "health word" data as the data source according to the Beidou satellite navigation system spatial signal interface control file (2.1) [29–31]. The average failure rate and average repair rate

Since December 24, 2013, the C13 satellite is in the unhealthy state, and its restoration rate is zero. Comparing Figure 4 and Figure 7, it can be found that the average restoration rate of BDS satellites is generally higher than that of GPS, indicating that the BDS satellite system can repair the satellites more timely when the satellites fail. However, the average failure rate of BDS satellites is also significantly higher than that of GPS, indicating that the frequency of BDS

Bringing the average failure rate and average restoration rate of the BDS into the per-satellite availability model, you can get the single-star availability probability of the BDS, as shown in

of the satellites obtained by collating the data sources are shown in Figure 7.

satellites is constantly improving.

failures is greater.

Figure 8.

2.3.2. Per-satellite availability evaluation of BDS

Figure 7. Average failure rate and restoration rate of BDS satellites.

Figure 5. Distribution of GPS per-satellite availability.

retired SVN14, 15, 16 and 31 satellites, the availability of the remaining satellites is greater than 0.957, which satisfies the availability criteria of GPS SPS PS (2008), and basically verifies the above GPS. The correctness and effectiveness of the single-star usability assessment model. It can also be seen from Figure 5 that the average availability of GPS satellites can reach 0.9891, and it is calculated that as of 2015, the average availability of all GPS satellites in orbit is 0.9985, far exceeding 0.957.

In addition, the section compares the availability of satellites according to the type of satellite, as shown in Figure 6.

As can be seen from Figure 6, the average availability of the BLOCK II series satellites is the lowest, and the average availability of the BLOCK IIF series satellites is the highest. With the continuous upgrading of satellite models, the availability of GPS satellites is significantly

Figure 6. Availability of different satellite types.

enhanced. With the continuous advancement of GPS modernization, the availability of GPS satellites is constantly improving.

#### 2.3.2. Per-satellite availability evaluation of BDS

retired SVN14, 15, 16 and 31 satellites, the availability of the remaining satellites is greater than 0.957, which satisfies the availability criteria of GPS SPS PS (2008), and basically verifies the above GPS. The correctness and effectiveness of the single-star usability assessment model. It can also be seen from Figure 5 that the average availability of GPS satellites can reach 0.9891, and it is calculated that as of 2015, the average availability of all GPS satellites in orbit is 0.9985,

In addition, the section compares the availability of satellites according to the type of satellite,

As can be seen from Figure 6, the average availability of the BLOCK II series satellites is the lowest, and the average availability of the BLOCK IIF series satellites is the highest. With the continuous upgrading of satellite models, the availability of GPS satellites is significantly

far exceeding 0.957.

18 Accuracy of GNSS Methods

Figure 5. Distribution of GPS per-satellite availability.

as shown in Figure 6.

Figure 6. Availability of different satellite types.

BDS has not yet established a sound outage forecasting mechanism. Therefore, there is no FAA-like department in China to provide a measured fault report on BDS. Therefore, the paper mainly obtains the Beidou navigation message published by IGS, and extracts its "health word" data as the data source according to the Beidou satellite navigation system spatial signal interface control file (2.1) [29–31]. The average failure rate and average repair rate of the satellites obtained by collating the data sources are shown in Figure 7.

Since December 24, 2013, the C13 satellite is in the unhealthy state, and its restoration rate is zero. Comparing Figure 4 and Figure 7, it can be found that the average restoration rate of BDS satellites is generally higher than that of GPS, indicating that the BDS satellite system can repair the satellites more timely when the satellites fail. However, the average failure rate of BDS satellites is also significantly higher than that of GPS, indicating that the frequency of BDS failures is greater.

Bringing the average failure rate and average restoration rate of the BDS into the per-satellite availability model, you can get the single-star availability probability of the BDS, as shown in Figure 8.

Figure 7. Average failure rate and restoration rate of BDS satellites.

satellites is 0.1144. Then both the state transition matrix G

time interval of state transition is 1 h, then as long as the initial state G

spare satellites at the beginning time. Therefore, it can be attained as follows.

G !

> F !

Table 3. SIS constellation availability (regardless of the per-slot availability in initial state).

SIS constellation availability of navigation system can be calculated according to the formulas

Slot A2 A4 A5 A6 B1 B2 B3 B4 C1 SVN 52 48 65 64 56 62 44 58 57 Slot C2 C3 C4 D1 D2 D3 D4 D5 D6 SVN 66 59 53 61 63 45 34 46 67 Slot E1 E2 E3 E4 E5 F1 F2 F3 F4 SVN 51 47 50 54 23 41 55 43 60

ð Þ t<sup>0</sup> can be divided into two cases:

Regardless of the per-slot availability means that there is no failed baseline constellation and

ð Þ¼ <sup>t</sup><sup>0</sup> ½ � <sup>100</sup> <sup>⋯</sup> <sup>0</sup> <sup>T</sup>

ð Þ¼ <sup>t</sup><sup>0</sup> ½ � <sup>1000</sup> <sup>T</sup>

Through the experiment, the constellation availability has been in stable state under the condition of T ¼ 300Δt. Then the constellation availability probability of SIS on different

The initial state of baseline constellation and spare satellites constellation will be changed after considering the per-slot availability. In order to simplify the calculation process, the average per-slot availability probabilities of 24 baseline constellation and 3 spare satellites are calculated, respectively. And the calculation is in terms of the per-slot availability probability showed in Figure 7. Therefore, p<sup>0</sup> is the average per-slot availability probability of 24 baseline

P<sup>0</sup> P<sup>1</sup> P<sup>2</sup> P<sup>3</sup> P<sup>4</sup> … 0.999999963 3.6599e�08 3.0692e�10 2.4458e�12 1.9073e�14 …

state transition matrix F!

Table 2. Distribution of the satellites.

(11)–(13).

The initial state G

constellation and the initial state F!

!

failure conditions is listed in Table 3.

ð Þ <sup>t</sup><sup>0</sup> and F!

1. Regardless of the per-slot availability in initial state.

2. Considering the per-slot availability in initial state.

!

ð Þ Δt of spare satellites constellation can be calculated. Assuming the

ð Þ t<sup>0</sup> of spare satellites constellation can be determined, the

Evaluation Methods of Satellite Navigation System Performance

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ð Þ Δt of baseline constellation and the

!

ð Þ t<sup>0</sup> of baseline

21

Figure 8. Distribution of BDS per-satellite availability.

In Figure 8, since the restoration rate of the C13(MEO) satellite is zero, the satellite's persatellite availability is 0 (indicated by a circle). As can be seen from Figure 8, except for the C13 satellite, the availability of other MEO satellites is in line with the minimum availability standard of 0.91 for MEO satellites in BDS-OS-PS-1.0. In addition to the poor SIS availability of C03(GEO) and C08(IGSO) satellites due to factors such as switching satellites and system instability, the remaining GEO and IGSO satellites meet their respective minimum availability standards of 0.98.

#### 2.4. Constellation availability evaluation

#### 2.4.1. Constellation availability evaluation of GPS SIS

As of 2015, the number of remaining in-orbit satellites was 27 except for satellites that were unable to count MTBF and MTTR values just after launch. The 27 satellites in orbit are distributed over six orbital planes, as shown in Table 2.

In order to keep the status that four baseline slot satellites located on the same orbital plane, the satellites of SVN23, SVN46, SVN67 were selected as non-orbital satellites according to the satellite distribution principle, and the remaining 24 satellites are based on the orbital position, that is, the constellation consists of 24 + 3 satellites.

Through the analysis of per-slot availability, the average failure rate of the 24 baseline constellation is 1.6551e04, and the average restoration rate is 0.1796. Similarly, the average failure rate of the 3 spare satellites is 1.4881e04, and the average restoration rate of the 3 spare


Table 2. Distribution of the satellites.

In Figure 8, since the restoration rate of the C13(MEO) satellite is zero, the satellite's persatellite availability is 0 (indicated by a circle). As can be seen from Figure 8, except for the C13 satellite, the availability of other MEO satellites is in line with the minimum availability standard of 0.91 for MEO satellites in BDS-OS-PS-1.0. In addition to the poor SIS availability of C03(GEO) and C08(IGSO) satellites due to factors such as switching satellites and system instability, the remaining GEO and IGSO satellites meet their respective minimum availability

As of 2015, the number of remaining in-orbit satellites was 27 except for satellites that were unable to count MTBF and MTTR values just after launch. The 27 satellites in orbit are

In order to keep the status that four baseline slot satellites located on the same orbital plane, the satellites of SVN23, SVN46, SVN67 were selected as non-orbital satellites according to the satellite distribution principle, and the remaining 24 satellites are based on the orbital position,

Through the analysis of per-slot availability, the average failure rate of the 24 baseline constellation is 1.6551e04, and the average restoration rate is 0.1796. Similarly, the average failure rate of the 3 spare satellites is 1.4881e04, and the average restoration rate of the 3 spare

standards of 0.98.

20 Accuracy of GNSS Methods

2.4. Constellation availability evaluation

Figure 8. Distribution of BDS per-satellite availability.

2.4.1. Constellation availability evaluation of GPS SIS

distributed over six orbital planes, as shown in Table 2.

that is, the constellation consists of 24 + 3 satellites.

satellites is 0.1144. Then both the state transition matrix G ! ð Þ Δt of baseline constellation and the state transition matrix F! ð Þ Δt of spare satellites constellation can be calculated. Assuming the time interval of state transition is 1 h, then as long as the initial state G ! ð Þ t<sup>0</sup> of baseline constellation and the initial state F! ð Þ t<sup>0</sup> of spare satellites constellation can be determined, the SIS constellation availability of navigation system can be calculated according to the formulas (11)–(13).

The initial state G ! ð Þ <sup>t</sup><sup>0</sup> and F! ð Þ t<sup>0</sup> can be divided into two cases:

1. Regardless of the per-slot availability in initial state.

Regardless of the per-slot availability means that there is no failed baseline constellation and spare satellites at the beginning time. Therefore, it can be attained as follows.

$$
\overrightarrow{G}\begin{pmatrix} t\_0 \end{pmatrix} = \begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \end{bmatrix}^T
$$

$$
\overrightarrow{F}\begin{pmatrix} t\_0 \end{pmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 \end{bmatrix}^T
$$

Through the experiment, the constellation availability has been in stable state under the condition of T ¼ 300Δt. Then the constellation availability probability of SIS on different failure conditions is listed in Table 3.

2. Considering the per-slot availability in initial state.

The initial state of baseline constellation and spare satellites constellation will be changed after considering the per-slot availability. In order to simplify the calculation process, the average per-slot availability probabilities of 24 baseline constellation and 3 spare satellites are calculated, respectively. And the calculation is in terms of the per-slot availability probability showed in Figure 7. Therefore, p<sup>0</sup> is the average per-slot availability probability of 24 baseline


Table 3. SIS constellation availability (regardless of the per-slot availability in initial state).


Based on the above reasons, the constellation usability should be evaluated after the Beidou global satellite navigation system constellation is fully completed and the corresponding evaluation indicators are perfected. At present, the practical significance of analyzing the

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23

This chapter mainly studies the per-satellite availability and constellation availability evaluation methods of GPS and BDS SIS, including the establishment of evaluation models and

The first part of this chapter establishes a single-star usability evaluation model based on Markov process from the reliability principle, and proposes a constellation usability evaluation model that considers the satellite's failure rate, repair rate and backup situation. On this basis, the second part of this chapter combines the measured data from the 1999–2015 GPS quarterly performance report released by the FAA and the BDS navigation message issued by IGS to obtain the single-star availability and constellation usability evaluation results of GPS and BDS. The results show that, except for the retired SVN14, SVN15, SVN16 and SVN31 GPS satellites, the availability of the remaining GPS satellites meets the GPS SPS PS (2008) availability standard. In the absence of satellite failure, the GPS SIS layer constellation availability can reach 0.999999963. Except for the C13 BDS satellite, the other MEO satellites meet the minimum availability standard of 0.91 for MEO satellites in BDS-OS-PS-1.0. The SIS availability of the C03 (GEO) and C08 (IGSO) satellites is poor due to factors such as switching satellites and system instability, and the remaining GEO and IGSO satellites meet their corresponding

[1] Jin SG, Luo OF, Gleason S. Characterization of diurnal cycles in ZTD from a decade of global GPS observations. Journal of Geodesy. 2009;83(6):537-545. DOI: 10.1007/s00190-

[2] Jin SG, van Dam T, Wdowinski S. Observing and understanding the earth system variations from space geodesy. Journal of Geodynamics. 2013;72:1-10. DOI: 10.1016/j.jog.2013.08.001

availability of BDS SIS constellation is not significant.

performance verification based on measured data.

minimum availability standards of 0.98.

Ershen Wang\*, He He and Chaoying Jia

\*Address all correspondence to: wanges\_2016@126.com

Shenyang Aerospace University, Shenyang, China

Author details

References

008-0264-3

3. Conclusions

Table 4. SIS constellation availability (considering the per-slot availability in initial state).

constellation, its value is 0.9988. And p<sup>1</sup> is the average per-slot availability probability of 3 spare satellites, its value is 0.9963. Then, it can be calculated as follows:

$$\begin{aligned} \overrightarrow{G} \begin{pmatrix} t\_0 \\ \end{pmatrix} &= \begin{bmatrix} \left(p\_0\right)^{24} & \mathbf{C}\_{24}^1 \left(1 - p\_0\right) \left(p\_0\right)^{23} \mathbf{C}\_{24}^2 \left(1 - p\_0\right)^2 \left(p\_0\right)^{22} \cdots \left(1 - p\_0\right)^{24} \end{bmatrix}^T \\ &= \begin{bmatrix} 0.9713 & 0.02830.00043.5036 \mathbf{e} - 0 \mathbf{6} \cdots 9.882 \mathbf{e} \text{-} \mathbf{7} \mathbf{1} \end{bmatrix}^T \\\\ \overrightarrow{F}(t\_0) &= \begin{bmatrix} \left(p\_1\right)^3 & \mathbf{C}\_3^1 \left(1 - p\_1\right) \left(p\_1\right)^2 & \mathbf{C}\_3^2 \left(1 - p\_1\right)^2 p\_1 & \left(1 - p\_1\right)^3 \end{bmatrix}^T \\ &= \begin{bmatrix} 0.9889 & 0.0110 & \mathbf{4.1056e-05} & 5.0911 \text{e-} \mathbf{08} \end{bmatrix}^T \end{aligned}$$

By the experiment, the constellation availability probability of SIS under the condition of considering the per-slot availability in initial state is listed in Table 4.

Analyzing the above two cases, it can be concluded that:


#### 2.4.2. Constellation availability evaluation of BDS SIS

The spatial constellation of the BDS consists of 35 satellites. At present, BDS is in the construction stage of global satellite navigation system. As of the end of 2015, there are only 20 BDS satellites launched, which is not enough to form a complete constellation. Moreover, due to the small number of satellites, the BDS does not currently have a backup satellite dedicated to replacing faulty satellites. Therefore, the constellation availability model of GPS SIS is not suitable for the current BDS system.

In addition, due to the incomplete BDS constellation, only BDS SIS availability in BDS-OS-PS-1.0 and BDS-SIS-ICD-2.1 is indicated by per-satellite availability, and there is no definition of BDS SIS constellation availability and related indicators [22].

Based on the above reasons, the constellation usability should be evaluated after the Beidou global satellite navigation system constellation is fully completed and the corresponding evaluation indicators are perfected. At present, the practical significance of analyzing the availability of BDS SIS constellation is not significant.

#### 3. Conclusions

constellation, its value is 0.9988. And p<sup>1</sup> is the average per-slot availability probability of 3

P<sup>0</sup> P<sup>1</sup> P<sup>2</sup> P<sup>3</sup> P<sup>4</sup> … 0.999999963 3.6599e�08 3.0692e�10 2.4458e�12 1.9073e�14 …

� �<sup>23</sup>C<sup>2</sup>

� �<sup>2</sup> C<sup>2</sup>

By the experiment, the constellation availability probability of SIS under the condition of

1. On the condition of considering the per-slot availability in initial state, since the on-orbit satellites all have a large per-slot availability probability, G0ð Þ t<sup>0</sup> and F0ð Þ t<sup>0</sup> are basically close to 1. In other words, whether considering per-slot availability in initial state have little influence on the element values of initial state matrix. When T ¼ kΔt is large enough, the constellation availability reaches stable state. Then, the tiny gaps between the initial state matrix of the above two cases have no effect on the system availability. So, when perslot availability is large enough, whether or not to consider per-slot availability in initial

2. Tables 2–4 show that when there are no failed satellites in satellite constellation, the constellation availability probability can reach 0.999999963. It is basically close to 1. By contrast, the probability of other failure states can be neglected. Thus, it can be seen that

The spatial constellation of the BDS consists of 35 satellites. At present, BDS is in the construction stage of global satellite navigation system. As of the end of 2015, there are only 20 BDS satellites launched, which is not enough to form a complete constellation. Moreover, due to the small number of satellites, the BDS does not currently have a backup satellite dedicated to replacing faulty satellites. Therefore, the constellation availability model of GPS SIS is not

In addition, due to the incomplete BDS constellation, only BDS SIS availability in BDS-OS-PS-1.0 and BDS-SIS-ICD-2.1 is indicated by per-satellite availability, and there is no definition of

the constellation, which is made up of the 27 satellites has a very high availability.

<sup>¼</sup> ½ � <sup>0</sup>:9713 0:02830:00043:5036e-06⋯9:882e-71 <sup>T</sup>

<sup>¼</sup> ½ � <sup>0</sup>:9889 0:0110 4:1056e-05 5:0911e-08 <sup>T</sup>

<sup>24</sup> 1 � p<sup>0</sup> � �<sup>2</sup>

> <sup>3</sup> 1 � p<sup>1</sup> � �<sup>2</sup>

� �<sup>24</sup> h i<sup>T</sup>

h i<sup>T</sup>

p0

� �<sup>22</sup><sup>⋯</sup> <sup>1</sup> � <sup>p</sup><sup>0</sup>

<sup>p</sup><sup>1</sup> <sup>1</sup> � <sup>p</sup><sup>1</sup> � �<sup>3</sup>

spare satellites, its value is 0.9963. Then, it can be calculated as follows:

Table 4. SIS constellation availability (considering the per-slot availability in initial state).

<sup>24</sup> 1 � p<sup>0</sup> � � <sup>p</sup><sup>0</sup>

> <sup>3</sup> 1 � p<sup>1</sup> � � <sup>p</sup><sup>1</sup>

considering the per-slot availability in initial state is listed in Table 4.

G !

22 Accuracy of GNSS Methods

F !

ð Þ¼ t<sup>0</sup> p<sup>0</sup>

ð Þ¼ t<sup>0</sup> p<sup>1</sup>

� �<sup>24</sup> C<sup>1</sup>

� �<sup>3</sup> C<sup>1</sup>

Analyzing the above two cases, it can be concluded that:

state has no effect on SIS constellation availability.

BDS SIS constellation availability and related indicators [22].

2.4.2. Constellation availability evaluation of BDS SIS

suitable for the current BDS system.

This chapter mainly studies the per-satellite availability and constellation availability evaluation methods of GPS and BDS SIS, including the establishment of evaluation models and performance verification based on measured data.

The first part of this chapter establishes a single-star usability evaluation model based on Markov process from the reliability principle, and proposes a constellation usability evaluation model that considers the satellite's failure rate, repair rate and backup situation. On this basis, the second part of this chapter combines the measured data from the 1999–2015 GPS quarterly performance report released by the FAA and the BDS navigation message issued by IGS to obtain the single-star availability and constellation usability evaluation results of GPS and BDS. The results show that, except for the retired SVN14, SVN15, SVN16 and SVN31 GPS satellites, the availability of the remaining GPS satellites meets the GPS SPS PS (2008) availability standard. In the absence of satellite failure, the GPS SIS layer constellation availability can reach 0.999999963. Except for the C13 BDS satellite, the other MEO satellites meet the minimum availability standard of 0.91 for MEO satellites in BDS-OS-PS-1.0. The SIS availability of the C03 (GEO) and C08 (IGSO) satellites is poor due to factors such as switching satellites and system instability, and the remaining GEO and IGSO satellites meet their corresponding minimum availability standards of 0.98.

#### Author details

Ershen Wang\*, He He and Chaoying Jia \*Address all correspondence to: wanges\_2016@126.com Shenyang Aerospace University, Shenyang, China

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tioning Service (SPS) Performance Analysis Report #90


**Section 3**

**Accuracy of GNSS Positioning Under Severe**

**Environmental Conditions**

**Accuracy of GNSS Positioning Under Severe Environmental Conditions**

**Chapter 3**

Provisional chapter

**Robust GNSS Positioning in Urban Environment**

DOI: 10.5772/intechopen.80412

In the past years, global navigation satellite systems (GNSS) have gained the core position concerning the geolocalization applications and services in urban environments. The major issue of the GNSS-based urban application expansion is related to the positioning service quality assurance, expressed in terms of accuracy, integrity, availability, and continuity of the localization service. The dense urban environments, such as city centers, are challenging to the GNSS signal reception causing the frequent blockage of the line-of-sight (LOS) signals and the multipath phenomenon, referred to as the reception of the diffracted/reflected echoes of the transmitted signal. These effects severely affect the pseudorange and Doppler measurements, used by a GNSS receiver for the user's position computation, which will further induce the computation of an erroneous positioning solution by the navigation processor down to a positioning loss in the presence of limited satellite visibility and few provided measurements. Therefore, advanced signal processing techniques do represent viable solutions aiming at the mitigation of these undesired effects in order to foster the accuracy and availability of the localization solution. This chapter will address in details the GNSS vector tracking (VT) receiver's configuration able to cope with

Keywords: GNSS, extended Kalman filter, vector tracking, multipath, NLOS, correlators

Global navigation satellite systems (GNSS) are increasingly present in our life and represent a key player in the world economy mostly due to the expansion of location-based services. An important part of the GNSS applications is found for the automotive usage in urban environments that are characterized by difficult signal reception conditions. These services do exhibit by very stringent quality of service demands. In these harsh environments, the received signals are severely affected by the urban obstacles including buildings, road infrastructure, and foliage

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Robust GNSS Positioning in Urban Environment

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

the urban environment-induced effects.

http://dx.doi.org/10.5772/intechopen.80412

Enik Shytermeja

Enik Shytermeja

Abstract

1. Introduction

#### **Robust GNSS Positioning in Urban Environment** Robust GNSS Positioning in Urban Environment

DOI: 10.5772/intechopen.80412

#### Enik Shytermeja Enik Shytermeja

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.80412

#### Abstract

In the past years, global navigation satellite systems (GNSS) have gained the core position concerning the geolocalization applications and services in urban environments. The major issue of the GNSS-based urban application expansion is related to the positioning service quality assurance, expressed in terms of accuracy, integrity, availability, and continuity of the localization service. The dense urban environments, such as city centers, are challenging to the GNSS signal reception causing the frequent blockage of the line-of-sight (LOS) signals and the multipath phenomenon, referred to as the reception of the diffracted/reflected echoes of the transmitted signal. These effects severely affect the pseudorange and Doppler measurements, used by a GNSS receiver for the user's position computation, which will further induce the computation of an erroneous positioning solution by the navigation processor down to a positioning loss in the presence of limited satellite visibility and few provided measurements. Therefore, advanced signal processing techniques do represent viable solutions aiming at the mitigation of these undesired effects in order to foster the accuracy and availability of the localization solution. This chapter will address in details the GNSS vector tracking (VT) receiver's configuration able to cope with the urban environment-induced effects.

Keywords: GNSS, extended Kalman filter, vector tracking, multipath, NLOS, correlators

#### 1. Introduction

Global navigation satellite systems (GNSS) are increasingly present in our life and represent a key player in the world economy mostly due to the expansion of location-based services. An important part of the GNSS applications is found for the automotive usage in urban environments that are characterized by difficult signal reception conditions. These services do exhibit by very stringent quality of service demands. In these harsh environments, the received signals are severely affected by the urban obstacles including buildings, road infrastructure, and foliage

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

generating strong signals' fading and fast phase oscillations. Consequently, the generated pseudo-range and Doppler measurements are degraded. In the worst-case scenario, the direct signal can be totally blocked by the urban obstacles generating the GNSS signal blockage phenomena that introduce large biases on the pseudo-range measurements and cycle slips for the carrier phase observations.

The scalar tracking process, employed for each tracked satellite, comprised the following main

• Code tracking: in charge of estimating the code delay offset ð Þ ετ between the incoming signal's code and the locally generated replica based on the closed feedback loop referred to as the delay lock loop (DLL). In this process, at least three delayed code replicas, known as the early, prompt, and late replica, are generated according to the correlation process

is called as frequency lock loop (FLL), while the carrier phase error εφ

The scalar tracking architecture, whose high-level representation is provided in Figure 1,

• Correlators: accumulating the combination of the sampled signal with the code and carrier replicas through mixing the in-phase and quadrature signal branches with the three delayed (early, prompt, and late) code-spreading sequences from the GNSS code generator block • Code/carrier discriminators: in charge of estimating the code delay and carrier frequency/

• Low-pass filters: filtering the discriminators' outputs for noise reduction at the entry of the

• Numerical control oscillator (NCO): operating in a feedback loop manner and providing the required correction to the code and carrier generators based on the filtered discriminator output, which is further used to generate the local replicas for the successive measurement

The association of the low-pass filters and the NCOs provides the equivalent loop filter, whose response to the user's dynamics is strictly related to two parameters such as the filter's loop order and the equivalent noise bandwidth. In details, a higher noise bandwidth implies faster loop response time (and thus better response to high user's dynamics) but with the drawback of dealing with noisier results due to the shorter integration time. Considering the filter's loop order, the higher the loop filter, the better the filter capability to follow the high-order user's

The scalar tracking is continuously run for each satellite-user channel in order to precisely estimate the code delay and carrier frequency/phase evolution in time [2]. In the GNSS

The code delay tracking process is directly performed after the acquisition stage, responsible among other tasks of the detection of the incoming signal. The code delay tracking process

dynamics is [3]. Keen readers may find detailed description of the loop filters in [3–5].

receiver, the code delay and carrier frequency/phase lock loops are jointly used.

pensation is conducted by the phase lock loops (PLL) [2]. It is important to highlight the fact that for certain applications with important user's dynamics, an FLL-aided PLL may

. The carrier tracking module that provides the estimation of the Doppler

and the carrier

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412

com-

31

• Carrier tracking: responsible of estimating the residual Doppler shift ε<sup>f</sup> <sup>D</sup>

modules:

with the incoming signal.

phase offset εφ

be also employed.

includes the following main processing blocks:

code/carrier local oscillators

2.1.1. GNSS code delay tracking

phase errors based on the three correlator output pairs

shift ε<sup>f</sup> <sup>D</sup>

epoch

Standard GNSS receivers, which track each satellite independently through the technique referred to as scalar tracking, fail to cope with these harsh urban conditions. Therefore, this work is particularly focused on the proposal and detailed design of the dual-constellation single-frequency vector tracking architecture for the automotive usage in urban environment. This architecture can improve the tracking of some attenuated or blocked signals due to the channel-aiding property based on the navigation solution estimation and thus assure a robust navigation solution estimation.

#### 2. GNSS receiver structure

This section aims at providing a detailed description of the GNSS receiver structure with an emphasis on the GNSS signal processing stage from the GNSS signal reception up to the measurement generation process.

#### 2.1. GNSS digital signal processing

The digital signal processing is the consecutive stage of the analog front end, taking as input of the sampled and discretized received signals from each satellite in view. Herein, the digitized signal is fed to multiple channel processing blocks, corresponding to each received satellite signal. The digital signal processing blocks conduct three main operations, the correlation, the acquisition, and the code/carrier tracking [1]. The scalar tracking process is achieved in a channelized structure for all the satellites in view. The objective of the tracking process is to refine the coarse estimations of the code delay and Doppler frequency provided by the acquisition block and to precisely follow the signal properties changing over time [2]. The GNSS scalar tracking architecture is illustrated in Figure 1.

Figure 1. The conventional GNSS tracking architecture.

The scalar tracking process, employed for each tracked satellite, comprised the following main modules:


The scalar tracking architecture, whose high-level representation is provided in Figure 1, includes the following main processing blocks:


The association of the low-pass filters and the NCOs provides the equivalent loop filter, whose response to the user's dynamics is strictly related to two parameters such as the filter's loop order and the equivalent noise bandwidth. In details, a higher noise bandwidth implies faster loop response time (and thus better response to high user's dynamics) but with the drawback of dealing with noisier results due to the shorter integration time. Considering the filter's loop order, the higher the loop filter, the better the filter capability to follow the high-order user's dynamics is [3]. Keen readers may find detailed description of the loop filters in [3–5].

The scalar tracking is continuously run for each satellite-user channel in order to precisely estimate the code delay and carrier frequency/phase evolution in time [2]. In the GNSS receiver, the code delay and carrier frequency/phase lock loops are jointly used.

#### 2.1.1. GNSS code delay tracking

generating strong signals' fading and fast phase oscillations. Consequently, the generated pseudo-range and Doppler measurements are degraded. In the worst-case scenario, the direct signal can be totally blocked by the urban obstacles generating the GNSS signal blockage phenomena that introduce large biases on the pseudo-range measurements and cycle slips for

Standard GNSS receivers, which track each satellite independently through the technique referred to as scalar tracking, fail to cope with these harsh urban conditions. Therefore, this work is particularly focused on the proposal and detailed design of the dual-constellation single-frequency vector tracking architecture for the automotive usage in urban environment. This architecture can improve the tracking of some attenuated or blocked signals due to the channel-aiding property based on the navigation solution estimation and thus assure a robust

This section aims at providing a detailed description of the GNSS receiver structure with an emphasis on the GNSS signal processing stage from the GNSS signal reception up to the

The digital signal processing is the consecutive stage of the analog front end, taking as input of the sampled and discretized received signals from each satellite in view. Herein, the digitized signal is fed to multiple channel processing blocks, corresponding to each received satellite signal. The digital signal processing blocks conduct three main operations, the correlation, the acquisition, and the code/carrier tracking [1]. The scalar tracking process is achieved in a channelized structure for all the satellites in view. The objective of the tracking process is to refine the coarse estimations of the code delay and Doppler frequency provided by the acquisition block and to precisely follow the signal properties changing over time [2]. The GNSS

the carrier phase observations.

30 Accuracy of GNSS Methods

navigation solution estimation.

2. GNSS receiver structure

measurement generation process.

2.1. GNSS digital signal processing

scalar tracking architecture is illustrated in Figure 1.

Figure 1. The conventional GNSS tracking architecture.

The code delay tracking process is directly performed after the acquisition stage, responsible among other tasks of the detection of the incoming signal. The code delay tracking process assures the alignment between the incoming signal's code and the local replica's code by refining the code delay error measurement from the discriminator block that further steers the code NCO [5]. The code tracking is performed by means of a DLL that is a feedback loop capable of steering the local PRN code delay based on the estimation of the code delay error ετ [6]. This code delay error measurement is later used to compute the pseudo-range observation.

binary offset carrier (BOC) signals, respectively [3]. In order to remove the amplitude sensitivity of the code discriminators, normalization factors shall be applied to have a direct access to

The carrier phase tracking is achieved by the phase lock loop (PLL) that is responsible of keeping the carrier phase alignment between the incoming signal and the locally generated

• The computation of a phase reference for the detection of the GNSS modulated data signal

To fulfill these objectives, the PLL uses a carrier phase discriminator to estimate the resultant phase estimation error εφð Þ<sup>k</sup> between the incoming signal phase and the replica phase, according to the in-phase and quadrature prompt correlator output pairs (IP, QP). Afterward, the PLL filter filters out the noise, and afterward, the carrier NCO transforms the estimated phase error into a

• The provision of precise Doppler measurements by using the phase rate information

frequency offset that modifies the NCO nominal frequency for the successive epoch [6].

The main phase discriminators used for the data channels are the following [4]:

DDP εφ, <sup>k</sup>

DAtan<sup>2</sup> εφ, <sup>k</sup>

<sup>¼</sup> atan2 QPk

The urban environment causes important threats to the GNSS signal reception and its posteriori processing, severely deteriorating the navigation solution accuracy and availability. The prob-

• Multipath: denoted as the joint reception of both the direct LOS signal and the reflected or

• Attenuation or blockage of the GNSS LOS signal: arising due to the partial or total obstruction

lems of the urban environment in the navigation domain can be summarized as follows:

IPk

<sup>¼</sup> QPk∙IPk (3)

(4)

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412 33

the code tracking error according to [7, 8].

replica. The main goals of the phase tracking loop are:

• Dot product (DP) or the generic Costas discriminator

• The extended arctangent (Atan2) phase discriminator [9]

diffracted GNSS LOS echoes from the urban obstacles

of the GNSS LOS from the urban environment characteristics

3. Vector tracking architecture

3.1. Urban environment-induced effects

2.1.2. GNSS carrier phase tracking

The correlation between each local replica with the in-phase and quadrature signal samples generates one correlator pair. Finally, three correlator pairs are obtained at the end of this operation, expressed by

IEk <sup>¼</sup> <sup>A</sup> <sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> <sup>þ</sup> kc∙Tc 2 <sup>∙</sup> cos εφ, <sup>k</sup> <sup>∙</sup> sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup> ∙t <sup>þ</sup> nIE, <sup>k</sup> IPk <sup>¼</sup> <sup>A</sup> <sup>2</sup> <sup>∙</sup>dk∙Rcð Þ ετ, <sup>k</sup> <sup>∙</sup> cos εφ, <sup>k</sup> <sup>∙</sup> sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup> ∙t <sup>þ</sup> nIP, <sup>k</sup> ILk <sup>¼</sup> <sup>A</sup> <sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> � kc∙Tc 2 <sup>∙</sup> cos εφ, <sup>k</sup> <sup>∙</sup>sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup> ∙t <sup>þ</sup> nIL, <sup>k</sup> QEk <sup>¼</sup> <sup>A</sup> <sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> <sup>þ</sup> kc∙Tc 2 <sup>∙</sup> sin εφ, <sup>k</sup> <sup>∙</sup>sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup> ∙t <sup>þ</sup> nQE, <sup>k</sup> QPk <sup>¼</sup> <sup>A</sup> <sup>2</sup> <sup>∙</sup>dk∙Rcð Þ ετ, <sup>k</sup> <sup>∙</sup>sin εφ, <sup>k</sup> <sup>∙</sup> sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup> ∙t <sup>þ</sup> nQP, <sup>k</sup> QLk <sup>¼</sup> <sup>A</sup> <sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> � kc∙Tc 2 <sup>∙</sup> sin εφ, <sup>k</sup> <sup>∙</sup>sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup> ∙t <sup>þ</sup> nQL, <sup>k</sup> (1)

where


The most common discriminators employed in GNSS receivers are the noncoherent earlyminus-late power (EMLP) and the dot product (DP) discriminators due to their tracking robustness since insensitive toward the carrier phase information. These two discriminators are defined by

$$\begin{aligned} D\_{\text{EM},P}(\varepsilon\_{\text{\tiny t,k}}) &= \left( \text{IE}\_k^2 + \text{QE}\_k^2 \right) - \left( \text{IL}\_k^2 + \text{QL}\_k^2 \right) \\ D\_{\text{DP}}(\varepsilon\_{\text{\tiny t,k}}) &= \left( \text{IE}\_K - \text{IL}\_K \right) \cdot \text{IP}\_k + \left( \text{QE}\_K - \text{QL}\_K \right) \cdot \text{QP}\_k \end{aligned} \tag{2}$$

The chip spacing is a crucial parameter for the discriminator function and thus must be selected so that the early and late correlator outputs are always evaluated at the correlation function main peak. Therefore, the EMLP and DP discriminators require a correlator spacing set less than 1 chip and 0.5 chip for the GPS L1 binary phase-shift keying (BPSK) and Galileo binary offset carrier (BOC) signals, respectively [3]. In order to remove the amplitude sensitivity of the code discriminators, normalization factors shall be applied to have a direct access to the code tracking error according to [7, 8].

#### 2.1.2. GNSS carrier phase tracking

assures the alignment between the incoming signal's code and the local replica's code by refining the code delay error measurement from the discriminator block that further steers the code NCO [5]. The code tracking is performed by means of a DLL that is a feedback loop capable of steering the local PRN code delay based on the estimation of the code delay error ετ [6]. This code delay error measurement is later used to compute the pseudo-range observation. The correlation between each local replica with the in-phase and quadrature signal samples generates one correlator pair. Finally, three correlator pairs are obtained at the end of this

∙ cos εφ, <sup>k</sup>

<sup>∙</sup> sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup>

∙ cos εφ, <sup>k</sup>

∙ sin εφ, <sup>k</sup>

<sup>∙</sup> sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup>

∙ sin εφ, <sup>k</sup>

• kc∙Tc refers to the early-late code chip spacing with kc and Tc representing the fraction of

• nxy denotes the noise term at the correlator output (where x stands for the in-phase (I) or quadrature (Q) and y for the early (E), prompt (P), or late (L) code delays), which is

The most common discriminators employed in GNSS receivers are the noncoherent earlyminus-late power (EMLP) and the dot product (DP) discriminators due to their tracking robustness since insensitive toward the carrier phase information. These two discriminators

DDPð Þ¼ ετ, <sup>k</sup> ð Þ IEK � ILK ∙IPk þ ð Þ QEK � QLK ∙QPk

The chip spacing is a crucial parameter for the discriminator function and thus must be selected so that the early and late correlator outputs are always evaluated at the correlation function main peak. Therefore, the EMLP and DP discriminators require a correlator spacing set less than 1 chip and 0.5 chip for the GPS L1 binary phase-shift keying (BPSK) and Galileo

<sup>k</sup> <sup>þ</sup> QE<sup>2</sup> k � IL<sup>2</sup>

<sup>∙</sup> sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup>

∙t 

<sup>∙</sup>sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup>

<sup>∙</sup>sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup>

∙t 

<sup>∙</sup>sinc <sup>π</sup>∙ε<sup>f</sup> D, <sup>k</sup>

<sup>k</sup> <sup>þ</sup> QL<sup>2</sup> k 

∙t 

∙t 

> ∙t

∙t 

þ nQP, <sup>k</sup>

represents the code delay, carrier phase, and frequency esti-

þ nIP, <sup>k</sup>

þ nIE, <sup>k</sup>

þ nIL, <sup>k</sup>

þ nQE, <sup>k</sup>

(1)

(2)

þ nQL, <sup>k</sup>

nxy .

operation, expressed by

32 Accuracy of GNSS Methods

where

are defined by

IEk <sup>¼</sup> <sup>A</sup>

IPk <sup>¼</sup> <sup>A</sup>

ILk <sup>¼</sup> <sup>A</sup>

QEk <sup>¼</sup> <sup>A</sup>

QPk <sup>¼</sup> <sup>A</sup>

QLk <sup>¼</sup> <sup>A</sup>

mation errors at the current epoch k.

• The triplet ετ, <sup>k</sup>; εφ, <sup>k</sup>; ε<sup>f</sup> D, <sup>k</sup>

<sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> <sup>þ</sup>

<sup>2</sup> <sup>∙</sup>dk∙Rcð Þ ετ, <sup>k</sup> <sup>∙</sup> cos εφ, <sup>k</sup>

<sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> � kc∙Tc

<sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> <sup>þ</sup>

chip spacing and the code chip period, respectively.

DEMLPð Þ¼ ετ, <sup>k</sup> IE<sup>2</sup>

<sup>2</sup> <sup>∙</sup>dk∙Rcð Þ ετ, <sup>k</sup> <sup>∙</sup>sin εφ, <sup>k</sup>

<sup>2</sup> <sup>∙</sup>dk∙Rc ετ, <sup>k</sup> � kc∙Tc

kc∙Tc 2 

2 

kc∙Tc 2 

2 

correlated and Gaussian distributed with zero mean and variance σ<sup>2</sup>

The carrier phase tracking is achieved by the phase lock loop (PLL) that is responsible of keeping the carrier phase alignment between the incoming signal and the locally generated replica. The main goals of the phase tracking loop are:


To fulfill these objectives, the PLL uses a carrier phase discriminator to estimate the resultant phase estimation error εφð Þ<sup>k</sup> between the incoming signal phase and the replica phase, according to the in-phase and quadrature prompt correlator output pairs (IP, QP). Afterward, the PLL filter filters out the noise, and afterward, the carrier NCO transforms the estimated phase error into a frequency offset that modifies the NCO nominal frequency for the successive epoch [6].

The main phase discriminators used for the data channels are the following [4]:

• Dot product (DP) or the generic Costas discriminator

$$D\_{\mathcal{DP}}\left(\varepsilon\_{\psi,k}\right) = \mathcal{QP}\_k \cdot \mathcal{IP}\_k \tag{3}$$

• The extended arctangent (Atan2) phase discriminator [9]

$$D\_{A\text{atm2}}\left(\varepsilon\_{\varphi,k}\right) = \text{atan2}\left(\frac{QP\_k}{IP\_k}\right) \tag{4}$$

#### 3. Vector tracking architecture

#### 3.1. Urban environment-induced effects

The urban environment causes important threats to the GNSS signal reception and its posteriori processing, severely deteriorating the navigation solution accuracy and availability. The problems of the urban environment in the navigation domain can be summarized as follows:


• Interference: resulting from the presence of wide signal sources transmitting in the adjacent GNSS frequency bands

capability of the GNSS receiver [6]. As it can be clearly observed in Figure 3, the central

ð Þ i ¼ 1 ÷ N1 and Galileo ð Þ i ¼ 1 ÷ N2 tracked channel as its input vector. Furthermore, the code and carrier NCO update process is achieved by projecting the predicted navigation solution

The VDFLL navigation block employs a Kalman filter (KF) that is a Bayesian estimation technique, which incorporates the measurements from the past epochs to obtain a more accurate navigation solution. In this work, the selection criteria of the extended Kalman filter

Figure 2. The high-level comparison of (a) conventional or scalar tracking and (b) vector tracking architectures.

ð Þi f D

discriminator outputs for each GPS

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412 35

and carrier <sup>ε</sup>

ð Þi τ

navigation filter accepts the code ε

Figure 3. The noncoherent L1/E1 VDFLL architecture.

into the pseudo-range and pseudo-range rate domains.

The resulting consequences of these urban environment error sources from the GNSS receiver's point of view are the following [10]:


Finally, the resulting degraded measurements cause the navigation processor to calculate an inaccurate position solution or even to be unable to compute one in the case of few available measurements.

#### 3.2. Vector tracking motivation

Vector tracking algorithms represent advanced GNSS signal processing methods, having the ability to function at lower carrier-to-noise power ð Þ C=N<sup>0</sup> ratios and in higher user's dynamics than traditional GNSS receivers [11]. Contrary to the conventional or scalar tracking architecture, where each visible satellite channel is being independently tracked, vector tracking performs a joint signal tracking of all the available satellites. It exploits the knowledge of the estimated receiver's position and velocity to control the tracking loops' feedback [6]. The comparison between the scalar tracking and vector tracking architectures is illustrated in Figure 2.

Concerning the vector tracking architecture, depicted in Figure 2(b), the code and carrier tracking loops of all the visible satellites are connected via the navigation solution computed by the navigation filter. The individual code/carrier loop filters and NCOs, illustrated by the dashed red line in the left figure, are abolished and substituted by the vectorized code/carrier update block depicted in blue.

#### 3.3. Proposed vectorized GNSS receiver architecture

Aiming at a robust GNSS signal tracking and navigation technique in urban environment, a dual-constellation GPS + Galileo single-frequency L1/E1 vector delay/frequency-locked loop (VDFLL) architecture is proposed and implemented for the automotive usage, whose architecture is illustrated in Figure 3.

In fact, the use of dual-constellation measurements significantly improves the availability of a navigation solution in urban canyons. Moreover, the implementation of the VDFLL tracking architecture, where the navigation filter is responsible of estimating both the code delay and the Doppler frequency change of each received signal, enhances the vehicle dynamic tracking capability of the GNSS receiver [6]. As it can be clearly observed in Figure 3, the central navigation filter accepts the code ε ð Þi τ and carrier <sup>ε</sup> ð Þi f D discriminator outputs for each GPS ð Þ i ¼ 1 ÷ N1 and Galileo ð Þ i ¼ 1 ÷ N2 tracked channel as its input vector. Furthermore, the code and carrier NCO update process is achieved by projecting the predicted navigation solution into the pseudo-range and pseudo-range rate domains.

• Interference: resulting from the presence of wide signal sources transmitting in the adjacent

The resulting consequences of these urban environment error sources from the GNSS receiver's

• Distortion of the correlation function: computed between the received multipath-contaminated signal and the NCO-generated replica. The tracking of the multipath-affected signals leads to a deterioration of code delay and carrier frequency/phase estimation accuracy down to the loss of lock of the tracking loops. As a result, the estimated pseudo-ranges and pseudorange rate measurements from the code and carrier tracking loops, respectively, which are

• Only non-LOS (NLOS) signal reception: resulting from the total obstruction of the direct LOS GNSS signals and thus inducing large biases on the pseudo-range and Doppler

Finally, the resulting degraded measurements cause the navigation processor to calculate an inaccurate position solution or even to be unable to compute one in the case of few available

Vector tracking algorithms represent advanced GNSS signal processing methods, having the ability to function at lower carrier-to-noise power ð Þ C=N<sup>0</sup> ratios and in higher user's dynamics than traditional GNSS receivers [11]. Contrary to the conventional or scalar tracking architecture, where each visible satellite channel is being independently tracked, vector tracking performs a joint signal tracking of all the available satellites. It exploits the knowledge of the estimated receiver's position and velocity to control the tracking loops' feedback [6]. The comparison

Concerning the vector tracking architecture, depicted in Figure 2(b), the code and carrier tracking loops of all the visible satellites are connected via the navigation solution computed by the navigation filter. The individual code/carrier loop filters and NCOs, illustrated by the dashed red line in the left figure, are abolished and substituted by the vectorized code/carrier

Aiming at a robust GNSS signal tracking and navigation technique in urban environment, a dual-constellation GPS + Galileo single-frequency L1/E1 vector delay/frequency-locked loop (VDFLL) architecture is proposed and implemented for the automotive usage, whose architec-

In fact, the use of dual-constellation measurements significantly improves the availability of a navigation solution in urban canyons. Moreover, the implementation of the VDFLL tracking architecture, where the navigation filter is responsible of estimating both the code delay and the Doppler frequency change of each received signal, enhances the vehicle dynamic tracking

between the scalar tracking and vector tracking architectures is illustrated in Figure 2.

GNSS frequency bands

34 Accuracy of GNSS Methods

point of view are the following [10]:

measurements.

3.2. Vector tracking motivation

update block depicted in blue.

ture is illustrated in Figure 3.

3.3. Proposed vectorized GNSS receiver architecture

fed to the navigation filter are significantly corrupted.

measurements if only NLOS signals are tracked.

The VDFLL navigation block employs a Kalman filter (KF) that is a Bayesian estimation technique, which incorporates the measurements from the past epochs to obtain a more accurate navigation solution. In this work, the selection criteria of the extended Kalman filter

Figure 2. The high-level comparison of (a) conventional or scalar tracking and (b) vector tracking architectures.

Figure 3. The noncoherent L1/E1 VDFLL architecture.

(EKF) algorithm are related to its capability to resolve the nonlinearity issues for the GNSS navigation system.

where

and <sup>m</sup> s

• <sup>A</sup><sup>2</sup>�<sup>2</sup> <sup>¼</sup> 0 1

matrices.

filter can be detailed as follows:

transition matrix is provided by

� �, respectively.

• B represents the colored noise transition matrix.

• X is the state vector with the following entries to be estimated such as the user's position

• F denotes the state transition matrix characterizing the user's motion and clock dynamics.

• w is the process noise vector reflecting the user's dynamics (position and velocity) and receiver's oscillator (clock bias and drift) uncertainties affecting the system model

The main tuning factors of the process noise vector w and its associated covariance matrix Q

• User's dynamics: expressing the vehicle's dynamic uncertainties concerning the velocity

• Receiver's oscillator noise: expressed in terms of the oscillator's phase and frequency noise

Passing to the discrete time domain, the system or dynamic model of the VDFLL navigation

where Xk is the state vector forward projection from the <sup>k</sup> � <sup>1</sup>th to the kth time epoch and <sup>Φ</sup>

Substituting Eq. (7) into the continuous state transition matrix of Eq. (5), the final discrete state

Ad, <sup>2</sup>�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup> �<sup>2</sup> Ad,<sup>2</sup>�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup> �<sup>2</sup> 02�<sup>2</sup> Ad, <sup>2</sup>�<sup>2</sup> 02�<sup>2</sup> �<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup> Ad,<sup>2</sup>�<sup>2</sup>

0 0 � � represents the position/velocity and clock biases/drift state transition sub-

x\_ ; σ<sup>2</sup> y\_ ; σ<sup>2</sup> y\_

<sup>b</sup> and drift σ<sup>2</sup>

bRx h i expressed in unit of ½ � <sup>m</sup>

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412 � � that are further projected in

<sup>d</sup> biases

Xk ¼ Φ ∙ Xk�<sup>1</sup> þ wk (6)

Φ ¼ I þ F ∙ ΔT, (7)

(8)

½ � xyz , velocity ½ � <sup>x</sup>\_y\_z\_ , and user's clock bias and drift terms bRx \_

can be summarized into two main categories according to their nature:

the position domain through the state transition sub-matrix A<sup>2</sup>�<sup>2</sup>

represents the dynamics of the user platform and clock, expressed as follows

where ΔT ¼ tk�<sup>1</sup> � tk is the time step between two successive epochs.

Φ ¼

error variance terms along the three ECEF axes σ<sup>2</sup>

spectral densities affecting the receiver's clock σ<sup>2</sup>

The EKF estimation process is composed of two main stages:


#### 3.3.1. VDFLL EKF state space description

The continuous-time EKF state model is given by

$$\begin{aligned} \frac{d}{dt} \mathbf{X}(t) &= F(t) \cdot \mathbf{X}(t) + B(t) \cdot \mathbf{w}(t) \\\\ \begin{bmatrix} x \\ \dot{x} \\ \dot{y} \\ \dot{d} \\ \dot{d} \\ \dot{z} \\ \dot{z} \\ \dot{y} \\ \dot{p}\_{\text{Rx}} \end{bmatrix} &= \begin{bmatrix} A\_{2\times2} & \mathbf{0}\_{2\times2} & \mathbf{0}\_{2\times2} & \mathbf{0}\_{2\times2} \\ \mathbf{0}\_{2\times2} & A\_{2\times2} & \mathbf{0}\_{2\times2} & \mathbf{0}\_{2\times2} \\ \mathbf{0}\_{2\times2} & \mathbf{0}\_{2\times2} & A\_{2\times2} & \mathbf{0}\_{2\times2} \\ \mathbf{0}\_{2\times2} & \mathbf{0}\_{2\times2} & \mathbf{0}\_{2\times2} & A\_{2\times2} \end{bmatrix} \begin{bmatrix} x \\ \dot{x} \\ y \\ \dot{y} \\ \dot{z} \\ \dot{y} \\ \dot{z} \\ \dot{y} \\ \dot{p}\_{\text{Rx}} \end{bmatrix} \\ &+ \begin{bmatrix} 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix} . \end{aligned} \tag{5}$$

where

(EKF) algorithm are related to its capability to resolve the nonlinearity issues for the GNSS

• State prediction: performing the time propagation between two consecutive epochs ð Þ k � 1

• Measurement correction: refining the a priori state vector and covariance matrix estimations

A<sup>2</sup>�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup>

x

x\_

y

y\_

z

z\_

bRx \_ bRx

∙

<sup>∙</sup> wx\_ wy\_ wz\_wbwd h i

�<sup>2</sup> A<sup>2</sup>�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup>

�<sup>2</sup> 02�<sup>2</sup> A<sup>2</sup>�<sup>2</sup> 02�<sup>2</sup>

�<sup>2</sup> 02�<sup>2</sup> 02�<sup>2</sup> A<sup>2</sup>�<sup>2</sup>

� �

� � into the filter and thus

(5)

to the current one k of the state vector Xk k<sup>j</sup> �<sup>1</sup> and its covariance matrix Pk k<sup>j</sup> �<sup>1</sup>

dt X tð Þ¼ F tð Þ∙X tðÞþ B tð Þ∙w tð Þ

� � by feeding the current epoch measurements zinput

The EKF estimation process is composed of two main stages:

obtaining the improved a posteriori estimates Xk k<sup>j</sup> ; Pk k<sup>j</sup>

navigation system.

Accuracy of GNSS Methods

Xk k<sup>j</sup> �<sup>1</sup>; Pk k<sup>j</sup> �<sup>1</sup>

3.3.1. VDFLL EKF state space description

d dt

The continuous-time EKF state model is given by

d

x

x\_

y

y\_

z

þ

z\_

bRx \_ bRx


The main tuning factors of the process noise vector w and its associated covariance matrix Q can be summarized into two main categories according to their nature:


Passing to the discrete time domain, the system or dynamic model of the VDFLL navigation filter can be detailed as follows:

$$X\_k = \begin{array}{c} \spadesuit \,\, X\_{k-1} + w\_k \,\, \end{array} \tag{6}$$

where Xk is the state vector forward projection from the <sup>k</sup> � <sup>1</sup>th to the kth time epoch and <sup>Φ</sup> represents the dynamics of the user platform and clock, expressed as follows

$$
\Phi = I + F \cdot \Delta T\_\prime \tag{7}
$$

where ΔT ¼ tk�<sup>1</sup> � tk is the time step between two successive epochs.

Substituting Eq. (7) into the continuous state transition matrix of Eq. (5), the final discrete state transition matrix is provided by

$$\mathbf{O} = \begin{bmatrix} A\_{d,2\times2} & 0\_{2\times2} & 0\_{2\times2} & 0\_{2\times2} \\ 0\_{2\times2} & A\_{d,2\times2} & 0\_{2\times2} & 0\_{2\times2} \\ 0\_{2\times2} & 0\_{2\times2} & A\_{d,2\times2} & 0\_{2\times2} \\ 0\_{2\times2} & 0\_{2\times2} & 0\_{2\times2} & A\_{d,2\times2} \end{bmatrix} \tag{8}$$

where Ad,<sup>2</sup>�<sup>2</sup> <sup>¼</sup> <sup>1</sup> <sup>Δ</sup><sup>T</sup> 0 1 � �:

The process noise covariance matrix Qk ¼ diag Qx, <sup>k</sup>; Qy, <sup>k</sup>; Qz, <sup>k</sup>; Qclk, <sup>k</sup> h i in the discrete domain per each entry can be expressed as

$$\begin{split} Q\_k &= E\left[w\_k \cdot w\_k^T\right] \\ &= \int\_{t\_{k-1}}^{t\_k} \Phi(t\_k, \tau) \cdot Q(\tau) \cdot \Phi^T(t\_k, \tau) \cdot d\tau \end{split} \tag{9}$$

where

channels [12]:

where

• ε ð Þi

where

• a ð Þi <sup>x</sup> ; a ð Þi <sup>y</sup> ; a ð Þi z

• j j rið Þ� k ruð Þk ¼

x ð Þi <sup>s</sup> ; yð Þ<sup>i</sup> <sup>s</sup> ; z ð Þi s

• h is the nonlinear function relating the measurement zk to the state Xk.

zk <sup>¼</sup> <sup>r</sup>ð Þ<sup>1</sup> <sup>r</sup>ð Þ<sup>2</sup> <sup>⋯</sup>rð Þ <sup>N</sup> � �<sup>⋮</sup> <sup>r</sup>\_

noise process and independent to the process noise wk.

ð Þ N2 satellites in view) at epoch k are rewritten as

x ð Þi

in the ECEF reference frame, respectively.

ð Þi 2 � � [6]:

þ z\_ ð Þi

ð Þi

<sup>s</sup> ð Þ� k Xkð Þ2 � �∙að Þ<sup>i</sup>

<sup>s</sup> ð Þ� k Xkð Þ6 � �∙að Þ<sup>i</sup>

� � ð Þ<sup>k</sup> denotes the LOS projections along the three navigation axes.

• Xkð Þ8 is the receiver's clock drift state common for both the GPS and Galileo Doppler

<sup>2</sup> ð Þ¼ Xk x\_

<sup>s</sup> ð Þ� k Xkð Þ1 � �<sup>2</sup>

� �ð Þ<sup>k</sup> and ð Þ Xkð Þ<sup>1</sup> ; Xkð Þ<sup>3</sup> ; Xkð Þ<sup>5</sup> represent the <sup>i</sup>

• Xkð Þ7 represents the receiver's clock bias term w.r.t the GPS time.

8 < :

<sup>r</sup>ð Þ<sup>i</sup> ð Þ¼ <sup>k</sup>

r

centered Gaussian distributed.

h ð Þi

the observation function h

measurements.

• vk is the measurement noise vector that is modeled as a zero-mean uncorrelated Gaussian

The measurement vector zk comprises pseudo-ranges rð Þ<sup>i</sup> and Doppler measurements r\_ð Þ<sup>i</sup> and output from the code/carrier tracking process for the i ¼ 1 ÷ N GPS L1/Galileo E1 tracking

h i

The GNSS pseudo-range measurements of a given satellite i (from the GPS ð Þ N1 and Galileo

j j rið Þ� k ruð Þk þ Xkð Þþ 7 ε

j jþ rið Þ� k ruð Þk Xkð Þþ 7 ε

þ y ð Þi

ð Þ<sup>1</sup> r\_ ð Þ<sup>2</sup> ⋯r\_ ð Þ <sup>N</sup> � �ð Þ<sup>k</sup>

ð Þi

ð Þi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �<sup>2</sup> <sup>2</sup>

satellite-to-user Euclidian distance at the current epoch k where the triplets

n,GPS=Galð Þk represents the error due to the receiver's thermal noise, assumed to be white,

<sup>x</sup> ð Þþ k y\_

<sup>z</sup> þ Xkð Þþ 8 ε\_

ð Þi

<sup>s</sup> ð Þ� k Xkð Þ4 � �∙að Þ<sup>i</sup>

> ð Þi n,GPS=Galð Þk

Meanwhile, the remaining N-entries of the measurement vector zk, constituted by the Doppler measurements from both the GPS and Galileo satellites, are related to the state vector through

<sup>s</sup> ð Þ� k Xkð Þ3 � �<sup>2</sup>

n,GPSð Þk , 0 < i ≤ N1

n,Galð Þk , N1 < i ≤ N

þ z ð Þi

<sup>s</sup> ð Þ� k Xkð Þ5

th satellite and user's coordinates

<sup>y</sup> ð Þk

<sup>2</sup>N�<sup>1</sup> (13)

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412

(14)

39

(15)

is the actual

Therefore, the process noise discretization for the position and velocity states along the three reference axes is computed as

$$\begin{aligned} Q\_{x|y|z,k} &= \int\_{t\_{k-1}}^{t\_k} A\_{d,2\times2}(t\_k, \tau) \cdot Q\_{2\times2}(\tau) \cdot A\_{d,2\times2}^T(t\_k, \tau) \cdot d\tau \\ &= \int\_{t\_{k-1}}^{t\_k} \begin{bmatrix} 1 & \varDelta T\\ 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} 0 & 0\\ 0 & \sigma\_{\dot{X}|\dot{y}|\dot{z}}^2 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0\\ \varDelta T & 1 \end{bmatrix} \cdot d\tau \\ &= \sigma\_{\dot{X}|\dot{y}|\dot{z}}^2 \cdot \begin{bmatrix} \varDelta^{T^3}/\_3 & \varDelta^{T^2}/\_2\\ \varDelta^{T^3}/\_2 & \varDelta T \end{bmatrix} \end{aligned} \tag{10}$$

where σ<sup>2</sup> x\_ ; σ<sup>2</sup> y\_ ; σ<sup>2</sup> z\_ � � are the velocity noise error variances along the three navigation axes.

Applying the discretization process of Eq. (9) to the user's clock covariance states, the following relation is obtained:

$$\begin{split} Q\_{clk,k} &= \int\_{t\_{k-1}}^{t\_k} A\_{d,2\times2}(t\_k, \tau) \cdot Q\_{clk,2\times2}(\tau) \cdot A\_{d,2\times2}^T(t\_k, \tau) \cdot d\tau \\ &= \int\_{t\_{k-1}}^{t\_k} \begin{bmatrix} 1 & \varDelta T\\ 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} \sigma\_b^2 & 0\\ 0 & \sigma\_d^2 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0\\ \varDelta T & 1 \end{bmatrix} \cdot d\tau \\ &= \begin{bmatrix} \sigma\_b^2 \cdot \varDelta T + \sigma\_d^2 \cdot \varDelta T^3 / 3\\ \sigma\_d^2 \cdot \varDelta T^2 / 2\\ & \sigma\_d^2 \cdot \varDelta T \end{bmatrix} \end{split} \tag{11}$$

The discrete receiver's clock process noise covariance matrix is modeled based on the Allan variance parameters [12].

#### 3.3.2. VDFLL EKF observation model

The nonlinear relation between the state and measurement vector in an EKF is provided by

$$
\omega\_k = h(X\_k) + \upsilon\_k \tag{12}
$$

where

where Ad,<sup>2</sup>�<sup>2</sup> <sup>¼</sup> <sup>1</sup> <sup>Δ</sup><sup>T</sup>

38 Accuracy of GNSS Methods

0 1 � �

per each entry can be expressed as

reference axes is computed as

where σ<sup>2</sup>

x\_ ; σ<sup>2</sup> y\_ ; σ<sup>2</sup> z\_

ing relation is obtained:

variance parameters [12].

3.3.2. VDFLL EKF observation model

� �

:

Qx y<sup>j</sup> <sup>j</sup>z, <sup>k</sup> ¼

The process noise covariance matrix Qk ¼ diag Qx, <sup>k</sup>; Qy, <sup>k</sup>; Qz, <sup>k</sup>; Qclk, <sup>k</sup>

Qk <sup>¼</sup> E wk∙wT

<sup>¼</sup> <sup>Ð</sup>tk

ðtk tk�<sup>1</sup>

¼ ðtk tk�<sup>1</sup>

<sup>¼</sup> <sup>σ</sup><sup>2</sup> <sup>x</sup>\_jy\_jz\_ <sup>∙</sup>

Qclk, <sup>k</sup> ¼

¼ ðtk tk�<sup>1</sup>

¼

σ2 <sup>b</sup> <sup>∙</sup>ΔTþσ<sup>2</sup> d∙ΔT<sup>3</sup>

> σ2 d∙<sup>Δ</sup>T<sup>2</sup>

ðtk tk�<sup>1</sup>

k � �

tk�<sup>1</sup> <sup>Φ</sup> tk ð Þ ; <sup>τ</sup> <sup>∙</sup>Qð Þ<sup>τ</sup> <sup>∙</sup>Φ<sup>T</sup> tk ð Þ ; <sup>τ</sup> <sup>∙</sup>d<sup>τ</sup>

Therefore, the process noise discretization for the position and velocity states along the three

Ad,<sup>2</sup>�<sup>2</sup> tk ð Þ ; <sup>τ</sup> <sup>∙</sup>Q<sup>2</sup>�<sup>2</sup>ð Þ<sup>τ</sup> <sup>∙</sup>AT

2 4

=<sup>2</sup> ΔT

Applying the discretization process of Eq. (9) to the user's clock covariance states, the follow-

Ad, <sup>2</sup>�<sup>2</sup>ð Þ tk; <sup>τ</sup> <sup>∙</sup>Qclk,<sup>2</sup>�<sup>2</sup>ð Þ<sup>τ</sup> <sup>∙</sup>A<sup>T</sup>

" #

<sup>d</sup>∙ΔT

∙

∙ σ2 <sup>b</sup> 0 0 σ<sup>2</sup> d

=<sup>3</sup> σ<sup>2</sup> d∙<sup>Δ</sup>T<sup>2</sup> =2

" #

=<sup>2</sup> σ<sup>2</sup>

The discrete receiver's clock process noise covariance matrix is modeled based on the Allan

The nonlinear relation between the state and measurement vector in an EKF is provided by

" #

0 0

0 σ<sup>2</sup> <sup>x</sup>\_jy\_jz\_

∙

1 ΔT

" #

0 1

ΔT<sup>3</sup> =3 ΔT<sup>2</sup> =2

ΔT<sup>2</sup>

1 ΔT

" #

0 1

h i

d,2�<sup>2</sup> tk ð Þ ; <sup>τ</sup> <sup>∙</sup>d<sup>τ</sup>

1 0

∙dτ

" #

ΔT 1

d, <sup>2</sup>�<sup>2</sup>ð Þ tk; <sup>τ</sup> <sup>∙</sup>d<sup>τ</sup>

∙dτ

zk ¼ h Xð Þþ <sup>k</sup> vk (12)

1 0

" #

ΔT 1

3 5 ∙

are the velocity noise error variances along the three navigation axes.

in the discrete domain

(9)

(10)

(11)


The measurement vector zk comprises pseudo-ranges rð Þ<sup>i</sup> and Doppler measurements r\_ð Þ<sup>i</sup> and output from the code/carrier tracking process for the i ¼ 1 ÷ N GPS L1/Galileo E1 tracking channels [12]:

$$z\_k = \left[ \left( \rho^{(1)} \rho^{(2)} \cdots \rho^{(N)} \right) ; \left( \dot{\rho}^{(1)} \dot{\rho}^{(2)} \cdots \dot{\rho}^{(N)} \right) (k) \right]\_{2N \times 1} \tag{13}$$

The GNSS pseudo-range measurements of a given satellite i (from the GPS ð Þ N1 and Galileo ð Þ N2 satellites in view) at epoch k are rewritten as

$$\rho^{(i)}(k) = \begin{cases} |r\_i(k) - r\_u(k)| + \mathcal{X}\_k(\mathcal{T}) + \varepsilon^{(i)}\_{n, \text{GPS}}(k), & 0 < i \le \mathcal{N}1 \\\\ |r\_i(k) - r\_u(k)| + \mathcal{X}\_k(\mathcal{T}) + \varepsilon^{(i)}\_{n, \text{Grid}}(k), & \mathcal{N}1 < i \le \mathcal{N} \end{cases} \tag{14}$$

where


Meanwhile, the remaining N-entries of the measurement vector zk, constituted by the Doppler measurements from both the GPS and Galileo satellites, are related to the state vector through the observation function h ð Þi 2 � � [6]:

$$\begin{split} h\_2^{(i)}(\mathbf{X}\_k) &= \left( \dot{\mathbf{x}}\_s^{(i)}(k) - \mathbf{X}\_k(\mathbf{2}) \right) \cdot \mathbf{a}\_x^{(i)}(k) + \left( \dot{\mathbf{y}}\_s^{(i)}(k) - \mathbf{X}\_k(\mathbf{4}) \right) \cdot \mathbf{a}\_y^{(i)}(k) \\ &+ \left( \dot{\boldsymbol{z}}\_s^{(i)}(k) - \mathbf{X}\_k(\mathbf{6}) \right) \cdot \mathbf{a}\_z^{(i)} + \mathbf{X}\_k(\mathbf{8}) + \dot{\boldsymbol{\varepsilon}}\_{n, \text{GPS}/\text{Gal}}^{(i)}(k) \end{split} \tag{15}$$

where


• ε\_ ð Þi n,GPS=Galð Þk denotes the receiver's thermal noise effect on the GPS and Galileo pseudorange rate measurements.

The measurement noise vector vk is modeled as a zero-mean uncorrelated Gaussian noise process with the measurement noise covariance matrix Rk that has the following entries in the main diagonal:

$$R\_{\vec{\eta}} = \begin{cases} \sigma\_{\text{Cade\\_Discri},j}^2 & \text{for} \quad j = 1 \cdots N \\ \sigma\_{\text{Carr} - \text{Discri},j}^2 & \text{for} \quad j = 1 \cdots N \end{cases} \tag{16}$$

The navigation performance assessment of the proposed vectorized architecture with respect to the classic receiver configuration is performed in degraded signal reception conditions.

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412 41

In this work, a widely used urban propagation channel model has been used to generate a representative of urban environment signal's reception conditions. This model, known as the DLR land mobile multipath channel model, was developed thanks to an extensive measurement campaign conducted by DLR in Munich urban and suburban areas in 2002. This model is

Parameters ST VT

Discriminator Early-minus-late power (EMLP)

DLL order 1st Not used DLL configuration Carrier-aided DLL Not used

DLL noise bandwidth Bð Þ DLL�<sup>n</sup> ð Þ Hz 1 Not used

Carrier estimation Phase Frequency PLL order 3 Not used

PLL noise bandwidth Bð Þ PLL�<sup>n</sup> ð Þ Hz 10 Not used

DLL update period (s) 0:02 Position update rate

PLL update period (s) 0:02 Velocity update rate

Discriminator type Atan2 Cross product (CP)

4.2. Urban multipath model

L1/E1 code delay tracking

Carrier phase/frequency tracking

Table 1. Tracking loop parameters.

GPS L1 chip spacing kð Þ <sup>C</sup>�L1 chip 0.5 GAL E1 chip spacing kð Þ <sup>C</sup>�E1 chip 0.2

Figure 4. The reference car trajectory.

where the first entry refers to the pseudo-range error variance terms for the tracked GPS and Galileo satellites, while the second one is a common term for the pseudo-range rate error variance for all tracked satellites [12].

#### 4. Description of the test setup

Within the scope of this research, a realistic dual-constellation dual-frequency GNSS signal emulator, capable of simulating the GNSS signal reception at the correlator output level and including the navigation module, has been developed. The developed signal emulator is a powerful tool for flexible and reliable GNSS receiver testing, for which all the processing blocks from the GNSS signals' correlation function, passing through the channels' tracking module and up to the different navigation algorithms, are all designed in a modular manner [12].

Two different GNSS receiver architectures are herein analyzed with the scope of performance comparison:


#### 4.1. Test scenario

The urban navigation test is herein performed on a car trajectory in Toulouse city center based on the collected data from the real test campaign in Toulouse urban area, by employing a NovAtel's ProPak receiver mounted on the car. The recorded trajectory of 600 s duration is presented in Figure 4.

The simulated signal reception conditions are that of a complete urban multipath model included to the receiver processing blocks with a maximum of 13 simultaneously tracked GPS L1 and Galileo E1 channels during the whole trajectory.

The receiver tracking parameters employed in the test scenario, defining the scalar (ST) and the vector tracking (VT) algorithms, are summarized in Table 1.

Figure 4. The reference car trajectory.

• ε\_ ð Þi

main diagonal:

40 Accuracy of GNSS Methods

comparison:

4.1. Test scenario

presented in Figure 4.

range rate measurements.

variance for all tracked satellites [12].

4. Description of the test setup

n,GPS=Galð Þk denotes the receiver's thermal noise effect on the GPS and Galileo pseudo-

Code\_Discri,j for j ¼ 1⋯N

(16)

Carr�Discri,j for j <sup>¼</sup> <sup>1</sup>⋯<sup>N</sup>

The measurement noise vector vk is modeled as a zero-mean uncorrelated Gaussian noise process with the measurement noise covariance matrix Rk that has the following entries in the

where the first entry refers to the pseudo-range error variance terms for the tracked GPS and Galileo satellites, while the second one is a common term for the pseudo-range rate error

Within the scope of this research, a realistic dual-constellation dual-frequency GNSS signal emulator, capable of simulating the GNSS signal reception at the correlator output level and including the navigation module, has been developed. The developed signal emulator is a powerful tool for flexible and reliable GNSS receiver testing, for which all the processing blocks from the GNSS signals' correlation function, passing through the channels' tracking module and up to the different navigation algorithms, are all designed in a modular manner [12].

Two different GNSS receiver architectures are herein analyzed with the scope of performance

• The proposed L1/E1 VDFLL EKF architecture working at ΔT ¼ 20 ms integration time and

• The classic scalar tracking architecture employing a third-order loop PLL and a DLL, with an EKF positioning module for the navigation solution computation operating at the same

The urban navigation test is herein performed on a car trajectory in Toulouse city center based on the collected data from the real test campaign in Toulouse urban area, by employing a NovAtel's ProPak receiver mounted on the car. The recorded trajectory of 600 s duration is

The simulated signal reception conditions are that of a complete urban multipath model included to the receiver processing blocks with a maximum of 13 simultaneously tracked GPS

The receiver tracking parameters employed in the test scenario, defining the scalar (ST) and the

Rjj <sup>¼</sup> <sup>σ</sup><sup>2</sup>

thus providing 50 Hz code and carrier frequency updates

rate as for the VDFLL EKF case (50 Hz)

L1 and Galileo E1 channels during the whole trajectory.

vector tracking (VT) algorithms, are summarized in Table 1.

(

σ2

The navigation performance assessment of the proposed vectorized architecture with respect to the classic receiver configuration is performed in degraded signal reception conditions.

#### 4.2. Urban multipath model

In this work, a widely used urban propagation channel model has been used to generate a representative of urban environment signal's reception conditions. This model, known as the DLR land mobile multipath channel model, was developed thanks to an extensive measurement campaign conducted by DLR in Munich urban and suburban areas in 2002. This model is


Table 1. Tracking loop parameters.

a wideband propagation channel model where each LOS and multipath echo are individually considered [13].

Moreover, the DLR model is a hybrid statistic/deterministic mathematical propagation channel model. The statistical part refers to the generation of a random urban scenario from a given set of channel-defining parameters, as depicted in Figure 5. Afterward, the LOS and NLOS echo information, provided as the DLR model output, is fed in the tracking stage at the correlator output level per tracked satellite.

#### 4.3. Performance comparison results

The position error comparison between the scalar tracking receiver and the VDFLL algorithm is presented in Figure 6, presenting the EKF estimation errors along the entire trajectory in the navigation frame expressed in the along- and cross-track coordinates, in blue the VDFLL and in red the KF with scalar tracking. Moreover, the blue- and red-dotted curves denote the 95 ð Þ % or two σ covariance bounds, where σ is the estimation error standard deviation estimated by the Kalman filters for the two architectures, respectively.

The position error plots in the vehicle frame (along- and cross-track coordinates), illustrated in Figure 6(a) and (b), demonstrate a clear superiority of the VDFLL algorithm, observed in terms of the low-position error variations along the trajectory that is an evident indicator of the VDFLL capability in coping with the multipath conditions. Larger position errors are observed for both architectures in the cross-track coordinate in Figure 6(b) that is related to the higher multipath-induced bias on the lateral projection. A significant position bias of approximately 30 m is seen for the scalar tracking receiver (in red) in the cross-track coordinate from the 70th to the 100th epoch, which coincides with strong satellite outage event and thus limited satellite

measurements. Furthermore, the ST + EKF covariance bounds are significantly increased during this period due to the higher position estimation uncertainty since only four "good" measurements from the four locked LOS satellites are used for the navigation solution computation. On the contrary, the proposed VDFLL algorithm assures a positioning stability and much tighter confidence bounds related to the interchannel-aiding capability exhibited by the VDFLL EKF filter. Finally, it can be seen that the vector architecture better assesses the confi-

Figure 6. Position error comparison between the scalar tracking receiver (in red) and the VDFLL algorithm (in blue) for

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412 43

dence on the computed position.

the (a) along-track error [m] and (b) cross-track error [m].

Figure 5. Artificial urban scenario generated by the DLR urban propagation channel model [13].

a wideband propagation channel model where each LOS and multipath echo are individually

Moreover, the DLR model is a hybrid statistic/deterministic mathematical propagation channel model. The statistical part refers to the generation of a random urban scenario from a given set of channel-defining parameters, as depicted in Figure 5. Afterward, the LOS and NLOS echo information, provided as the DLR model output, is fed in the tracking stage at the correlator

The position error comparison between the scalar tracking receiver and the VDFLL algorithm is presented in Figure 6, presenting the EKF estimation errors along the entire trajectory in the navigation frame expressed in the along- and cross-track coordinates, in blue the VDFLL and in red the KF with scalar tracking. Moreover, the blue- and red-dotted curves denote the 95 ð Þ % or two σ covariance bounds, where σ is the estimation error standard deviation estimated by

The position error plots in the vehicle frame (along- and cross-track coordinates), illustrated in Figure 6(a) and (b), demonstrate a clear superiority of the VDFLL algorithm, observed in terms of the low-position error variations along the trajectory that is an evident indicator of the VDFLL capability in coping with the multipath conditions. Larger position errors are observed for both architectures in the cross-track coordinate in Figure 6(b) that is related to the higher multipath-induced bias on the lateral projection. A significant position bias of approximately 30 m is seen for the scalar tracking receiver (in red) in the cross-track coordinate from the 70th to the 100th epoch, which coincides with strong satellite outage event and thus limited satellite

Figure 5. Artificial urban scenario generated by the DLR urban propagation channel model [13].

considered [13].

42 Accuracy of GNSS Methods

output level per tracked satellite.

4.3. Performance comparison results

the Kalman filters for the two architectures, respectively.

Figure 6. Position error comparison between the scalar tracking receiver (in red) and the VDFLL algorithm (in blue) for the (a) along-track error [m] and (b) cross-track error [m].

measurements. Furthermore, the ST + EKF covariance bounds are significantly increased during this period due to the higher position estimation uncertainty since only four "good" measurements from the four locked LOS satellites are used for the navigation solution computation. On the contrary, the proposed VDFLL algorithm assures a positioning stability and much tighter confidence bounds related to the interchannel-aiding capability exhibited by the VDFLL EKF filter. Finally, it can be seen that the vector architecture better assesses the confidence on the computed position.

#### 5. Conclusions

The chapter was written in the context of the GNSS use in urban environment that is particularly challenging to the GNSS signal reception due to multipath and direct signal blockages, which significantly affect the signal processing and further degrade the position accuracy and availability. For this matter, this work was focused on the design of a dual-constellation GPS/ Galileo and single-frequency L1/E1 band vector tracking architecture for automotive usage in urban environment. This architecture ensures a better receiver's dynamic estimation due to the joint code delay and Doppler carrier frequency tracking for all the satellites in view performed by the common navigation EKF filter. The detailed flowchart of the proposed vector tracking algorithm and the relation between the state vector and observation model were also exposed. DLL delay lock loop

EMLP early-minus-late power

EKF extended Kalman filter

IF intermediate frequency

LNA low-noise amplifier

NCO numerical control oscillator

PVT position velocity and time

VDFLL vector delay/frequency-locked loop

Address all correspondence to: enik.shytermeja@altran.com

WLS weighted least squares

GNSS global navigation satellite systems

Robust GNSS Positioning in Urban Environment http://dx.doi.org/10.5772/intechopen.80412 45

FLL frequency lock loop

DP dot product

E early

I in phase

L late

KF Kalman filter

LS least squares

PLL phase lock loop

Q quadrature phase

SiS signal in space ST scalar tracking VT vector tracking

Author details

Enik Shytermeja

Altran Technologies, France

P prompt

The generation of the urban environment multipath conditions was detailed in the second part of Section 4. In this work, the wideband propagation model referred to as the DLR land mobile multipath channel model was employed. Herein, the urban environment conditions were generated separately for each GPS- and Galileo-tracked satellite by feeding their elevation/azimuth angles and the reference car trajectory to the DLR urban channel. The generated channel model samples were stored and directly fed to the signal emulator at the correlator level.

Furthermore, the dynamic car trajectory along with the test parameters related to the scalar (ST) and vector tracking (VT) loop design was introduced. The emphasis of this work was dedicated to the performance analysis of the two architectures under study in the navigation level, expressed by the position estimation errors in the vehicle navigation frame. The VDFLL superiority was observed in the navigation domain, especially when referring to the position estimation accuracies. Nearly twice lower position estimation error variations were observed for the VDFLL architecture w.r.t the scalar receiver configuration. Furthermore, the VDFLL robustness and reactivity were noted especially during the satellite outage intervals that induce a reduced number of measurements fed to the navigation processor. During these intervals, stable and accurate navigation solution estimations are assured by the VDFLL filter thanks to the code/carrier NCO updates steered from the navigation solution estimations.

#### Acknowledgements

This work was financially supported by the EU FP7 Marie Curie Initial Training Network MULTI-POS (multi-technology positioning professionals) under grant no. 316528 and with the funding provided from Altran Research.

#### Acronyms and abbreviations



#### Author details

5. Conclusions

44 Accuracy of GNSS Methods

Acknowledgements

the funding provided from Altran Research.

ADC analog-to-digital converter

AGC automated gate control

Acronyms and abbreviations

The chapter was written in the context of the GNSS use in urban environment that is particularly challenging to the GNSS signal reception due to multipath and direct signal blockages, which significantly affect the signal processing and further degrade the position accuracy and availability. For this matter, this work was focused on the design of a dual-constellation GPS/ Galileo and single-frequency L1/E1 band vector tracking architecture for automotive usage in urban environment. This architecture ensures a better receiver's dynamic estimation due to the joint code delay and Doppler carrier frequency tracking for all the satellites in view performed by the common navigation EKF filter. The detailed flowchart of the proposed vector tracking algorithm and the relation between the state vector and observation model were also exposed. The generation of the urban environment multipath conditions was detailed in the second part of Section 4. In this work, the wideband propagation model referred to as the DLR land mobile multipath channel model was employed. Herein, the urban environment conditions were generated separately for each GPS- and Galileo-tracked satellite by feeding their elevation/azimuth angles and the reference car trajectory to the DLR urban channel. The generated channel model

samples were stored and directly fed to the signal emulator at the correlator level.

Furthermore, the dynamic car trajectory along with the test parameters related to the scalar (ST) and vector tracking (VT) loop design was introduced. The emphasis of this work was dedicated to the performance analysis of the two architectures under study in the navigation level, expressed by the position estimation errors in the vehicle navigation frame. The VDFLL superiority was observed in the navigation domain, especially when referring to the position estimation accuracies. Nearly twice lower position estimation error variations were observed for the VDFLL architecture w.r.t the scalar receiver configuration. Furthermore, the VDFLL robustness and reactivity were noted especially during the satellite outage intervals that induce a reduced number of measurements fed to the navigation processor. During these intervals, stable and accurate navigation solution estimations are assured by the VDFLL filter thanks to the code/carrier NCO updates steered from the navigation solution estimations.

This work was financially supported by the EU FP7 Marie Curie Initial Training Network MULTI-POS (multi-technology positioning professionals) under grant no. 316528 and with

Enik Shytermeja

Address all correspondence to: enik.shytermeja@altran.com

Altran Technologies, France

#### References

[1] Dovis F, Mulassano P. Introduction to Global Navigation Satellite Systems. Politecnico di Torino; 2009

**Chapter 4**

**Provisional chapter**

**GPS Scintillations and Total Electron Content**

**GPS Scintillations and Total Electron Content** 

DOI: 10.5772/intechopen.79218

The radio communication and navigation systems can be strongly affected by the ionospheric conditions, which are controlled by solar phenomena associated with radiation variations and solar wind disturbances. These phenomena can generate ionospheric large-scale plasma redistribution and irregularities with scale sizes varying from centimeters to hundred kilometers. These ionospheric irregularities can produce rapid fluctuations in the amplitude and phase of global navigation satellite system (GNSS) signals, degrading the accuracy of GNSS measurements. Here we give a short review of the ionospheric variations associated with solar phenomena, and the actual state of art in the investigations of long-term (seasonal and solar cycle scales) TEC variations and climatology of scintillations, with focus on the southern American sector. It also presented a new

**Keywords:** ionospheric irregularities, scintillation, total electron content, climatology,

Nowadays, the global navigation satellite systems (GNSSs) are widely used in many human activities, particularly for geodetic positioning and navigation, as well for atmospheric monitoring in scientific research. The GNSS systems have been used to obtain the ionospheric total electron content (TEC) often in near real-time and in global scale because the networks groundbased receivers cover large geographic areas. In the last decades, TEC information has given a

TEC calibration procedure when applied to single-frequency PPP.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Climatology in the Southern American Sector**

**Climatology in the Southern American Sector**

Emília Correia, Marcio Tadeu de Assis Honorato Muella,

Marcio Tadeu de Assis Honorato Muella, Lucilla Alfonsi, Fabricio dos Santos Prol and

Lucilla Alfonsi, Fabricio dos Santos Prol and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Emília Correia,

**Abstract**

**1. Introduction**

Paulo de Oliveira Camargo

Paulo de Oliveira Camargo

http://dx.doi.org/10.5772/intechopen.79218

South America, single-frequency PPP


#### **GPS Scintillations and Total Electron Content Climatology in the Southern American Sector GPS Scintillations and Total Electron Content Climatology in the Southern American Sector**

DOI: 10.5772/intechopen.79218

Emília Correia, Marcio Tadeu de Assis Honorato Muella, Lucilla Alfonsi, Fabricio dos Santos Prol and Paulo de Oliveira Camargo Emília Correia, Marcio Tadeu de Assis Honorato Muella, Lucilla Alfonsi, Fabricio dos Santos Prol and Paulo de Oliveira Camargo

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79218

#### **Abstract**

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The radio communication and navigation systems can be strongly affected by the ionospheric conditions, which are controlled by solar phenomena associated with radiation variations and solar wind disturbances. These phenomena can generate ionospheric large-scale plasma redistribution and irregularities with scale sizes varying from centimeters to hundred kilometers. These ionospheric irregularities can produce rapid fluctuations in the amplitude and phase of global navigation satellite system (GNSS) signals, degrading the accuracy of GNSS measurements. Here we give a short review of the ionospheric variations associated with solar phenomena, and the actual state of art in the investigations of long-term (seasonal and solar cycle scales) TEC variations and climatology of scintillations, with focus on the southern American sector. It also presented a new TEC calibration procedure when applied to single-frequency PPP.

**Keywords:** ionospheric irregularities, scintillation, total electron content, climatology, South America, single-frequency PPP

#### **1. Introduction**

Nowadays, the global navigation satellite systems (GNSSs) are widely used in many human activities, particularly for geodetic positioning and navigation, as well for atmospheric monitoring in scientific research. The GNSS systems have been used to obtain the ionospheric total electron content (TEC) often in near real-time and in global scale because the networks groundbased receivers cover large geographic areas. In the last decades, TEC information has given a

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

great advance in the understanding of the ionospheric structuring and improving our forecasting capacity, which has revolutionized the ionospheric studies. Particularly, the behavior of the ionosphere during geomagnetic disturbed periods has been extensively investigated, showing that F-region response to geomagnetic storms is very complex in space and time, but a general morphology and physical processes have been defined (e.g., [1–13]; and references therein).

(EUV) forms the ionosphere. The physical processes in the thermosphere are primarily driven by solar and magnetic disturbances [42], which influence the ionospheric production and recombination, as well transport and frictional heating. The ionospheric conditions have been studied for decades, and particularly there is a good understanding of F-region conditions associated with seasonal, solar cycle, and level of magnetic activity variations. Despite that the predictive capability of its condition is still very poor because the variations appear over a wide range of timescales going from minutes to several days and also depend on the magnetic local time and geographic location. Even during quiet times, that is, under undisturbed geomagnetic conditions, significant ionospheric variability is observed. The low latitude ionosphere is controlled by electrodynamic plasma (**E × B**) drifts driven by thermospheric neutral winds (e.g., [43–45]). The zonal electric fields drive strong daytime E-region eastward currents in the equatorial region, which form two narrow latitudinal bands centered at the dip equator that are called equatorial electrojet (e.g., [46]). The zonal electric fields drive equatorial E and F region vertical plasma drifts (e.g., [47]) that lift the ionospheric plasma at the dip equator, which goes down following the magnetic field lines leading density enhance-

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49

followed by their diffusion along the geomagnetic field lines and the formation of the two density maxima away from the equator, is called "fountain effect," and the denser regions are called the crests of the equatorial ionospheric (or ionization) anomaly (EIA) [48]. The thermospheric winds are highly variable because they are driven by changes in the global tidal forcing, and effects of irregular winds, planetary and gravity waves. The planetary waves and tides have been identified as relevant factors affecting the electrodynamics of the lower

The ionospheric F-region often becomes turbulent and develops electron density irregularities during post-sunset hours [56]. During the day, the electrical field is eastward and it reverses to the west after sunset, but during sunset an enhanced eastward electric field develops, the so-called pre-reversal enhancement (PRE) [44, 57, 58]. The PRE drives an upward vertical plasma drift at magnetic equatorial region, and the bottom of the F-region becomes unstable to the Rayleigh-Taylor instability [59], developing large-scale plasma depletions (plasma bubbles). These bubbles ascend upwards over the magnetic equator, causing a redistribution of ionization similar to the fountain effect. The latitudinal extension of the plasma bubbles is defined by the upper height limit they reach in their rise up above the magnetic equator [60] and can intersect the crests of the EIA, where the steeper density gradients on the edges of the plasma bubbles favor the generation of smaller scale irregularities [56, 61, 62]. The plasma bubbles practically disappear after local midnight and are most intense during the equinoctial months and during the solar maximum years [63, 64]. These conditions favor the scintillations to occur most frequent and severe around the EIA crests, in particular after sunset due to the generation of irregularities caused by the intersection of the plasma bubbles with the regions of larger background electron density.

The ionosphere can be strongly disturbed during geomagnetic storm-time periods. These storms are terrestrial magnetospheric perturbations caused by the impact of interplanetary coronal mass ejections (ICMEs), and corotating interaction regions associated with high-speed streams (HSS), which are the most geo-effective solar wind phenomena. The coupling process involving the solar wind, the interplanetary magnetic field (IMF) and the magnetosphere strongly affects the high latitude ionospheric electrodynamics. The magnetosphere compression during geomagnetic

from the magnetic equator. The overall process, the plasma lifting

ments located at ~±10–20**°**

thermosphere (e.g., [49–55]).

The ionospheric knowledge has been used to improve the GNSS positional accuracy, which can be strongly degraded under severe atmospheric disturbances because they can suddenly change the satellite geometry that is essential for geodetic position, in particular for kinematic precise point position (PPP), and are a limiting factor to achieve centimeter accuracy (e.g., [14–16]). The main atmospheric disturbances that affect the GNSS quality signals are the ionospheric steep density gradients, signatures of irregularities of the electron density distribution. Special attention has been given to the ionospheric irregularities investigation, which can vary on a wide range of scale sizes, from centimeters to hundreds of kilometers. The formation and the temporal/spatial evolution of these irregularities affect the propagation of radio signals, causing cycle slips and loss of lock on GNSS receivers and degrading the performance of radio communication and navigation systems [17, 18]. At L-band, amplitude scintillations are due to irregularities with a scale size from hundreds of meters down to tens of meters (according to Fresnel's filtering mechanism), while phase scintillations are caused by structures from a few hundred meters to several kilometers (see, e.g., [18]). In addition, in your way down to the ground, the radio signals could interfere with itself due small changes in their way along the scattered ray paths, resulting in a sort of "space multipath" [19]. The overall of these atmospheric influences can produce rapid fluctuations in the amplitude and phase of GNSS signals, which are known as ionospheric scintillations.

The investigation of scintillations has shown that their activity is stronger at latitudes within the equatorial ionization anomaly (EIA), particularly during post-sunset hours when plasma bubbles are formed in the equatorial F-region driven by the Rayleigh-Taylor instability [20, 21]. Recently, the formation of ionospheric irregularities and plasma bubbles at equatorial region also have shown that they can be driven by gravity waves [22, 23]. The scintillations have been extensively studied at different longitudinal sectors and latitudes, showing a strong dependence on magnetic local time, season, magnetic activity, solar cycle, and geographic location (e.g., [6, 8–13, 19, 24–36]; and references therein).

This chapter provides the characterization of ionospheric scintillations observed with GNSS networks in the South American sector (e.g., [34, 35, 37–40]). The chapter is organized as follows: Section 2 presents the ionospheric variability, Section 3 presents the ionospheric scintillation indices and climatology in South American sector, Section 4 presents the impact of scintillations in a new method for high accurate single frequency precise point positioning (PPP), and finally a discussion section.

#### **2. Ionospheric variability**

The solar heating throughout the atmosphere causes large-scale variations associated with diurnal and semidiurnal tides in the thermosphere [41], while the extreme ultraviolet radiation (EUV) forms the ionosphere. The physical processes in the thermosphere are primarily driven by solar and magnetic disturbances [42], which influence the ionospheric production and recombination, as well transport and frictional heating. The ionospheric conditions have been studied for decades, and particularly there is a good understanding of F-region conditions associated with seasonal, solar cycle, and level of magnetic activity variations. Despite that the predictive capability of its condition is still very poor because the variations appear over a wide range of timescales going from minutes to several days and also depend on the magnetic local time and geographic location. Even during quiet times, that is, under undisturbed geomagnetic conditions, significant ionospheric variability is observed. The low latitude ionosphere is controlled by electrodynamic plasma (**E × B**) drifts driven by thermospheric neutral winds (e.g., [43–45]). The zonal electric fields drive strong daytime E-region eastward currents in the equatorial region, which form two narrow latitudinal bands centered at the dip equator that are called equatorial electrojet (e.g., [46]). The zonal electric fields drive equatorial E and F region vertical plasma drifts (e.g., [47]) that lift the ionospheric plasma at the dip equator, which goes down following the magnetic field lines leading density enhancements located at ~±10–20**°** from the magnetic equator. The overall process, the plasma lifting followed by their diffusion along the geomagnetic field lines and the formation of the two density maxima away from the equator, is called "fountain effect," and the denser regions are called the crests of the equatorial ionospheric (or ionization) anomaly (EIA) [48]. The thermospheric winds are highly variable because they are driven by changes in the global tidal forcing, and effects of irregular winds, planetary and gravity waves. The planetary waves and tides have been identified as relevant factors affecting the electrodynamics of the lower thermosphere (e.g., [49–55]).

great advance in the understanding of the ionospheric structuring and improving our forecasting capacity, which has revolutionized the ionospheric studies. Particularly, the behavior of the ionosphere during geomagnetic disturbed periods has been extensively investigated, showing that F-region response to geomagnetic storms is very complex in space and time, but a general morphology and physical processes have been defined (e.g., [1–13]; and references therein).

The ionospheric knowledge has been used to improve the GNSS positional accuracy, which can be strongly degraded under severe atmospheric disturbances because they can suddenly change the satellite geometry that is essential for geodetic position, in particular for kinematic precise point position (PPP), and are a limiting factor to achieve centimeter accuracy (e.g., [14–16]). The main atmospheric disturbances that affect the GNSS quality signals are the ionospheric steep density gradients, signatures of irregularities of the electron density distribution. Special attention has been given to the ionospheric irregularities investigation, which can vary on a wide range of scale sizes, from centimeters to hundreds of kilometers. The formation and the temporal/spatial evolution of these irregularities affect the propagation of radio signals, causing cycle slips and loss of lock on GNSS receivers and degrading the performance of radio communication and navigation systems [17, 18]. At L-band, amplitude scintillations are due to irregularities with a scale size from hundreds of meters down to tens of meters (according to Fresnel's filtering mechanism), while phase scintillations are caused by structures from a few hundred meters to several kilometers (see, e.g., [18]). In addition, in your way down to the ground, the radio signals could interfere with itself due small changes in their way along the scattered ray paths, resulting in a sort of "space multipath" [19]. The overall of these atmospheric influences can produce rapid fluctuations in the amplitude and

The investigation of scintillations has shown that their activity is stronger at latitudes within the equatorial ionization anomaly (EIA), particularly during post-sunset hours when plasma bubbles are formed in the equatorial F-region driven by the Rayleigh-Taylor instability [20, 21]. Recently, the formation of ionospheric irregularities and plasma bubbles at equatorial region also have shown that they can be driven by gravity waves [22, 23]. The scintillations have been extensively studied at different longitudinal sectors and latitudes, showing a strong dependence on magnetic local time, season, magnetic activity, solar cycle, and geographic location

This chapter provides the characterization of ionospheric scintillations observed with GNSS networks in the South American sector (e.g., [34, 35, 37–40]). The chapter is organized as follows: Section 2 presents the ionospheric variability, Section 3 presents the ionospheric scintillation indices and climatology in South American sector, Section 4 presents the impact of scintillations in a new method for high accurate single frequency precise point positioning

The solar heating throughout the atmosphere causes large-scale variations associated with diurnal and semidiurnal tides in the thermosphere [41], while the extreme ultraviolet radiation

phase of GNSS signals, which are known as ionospheric scintillations.

(e.g., [6, 8–13, 19, 24–36]; and references therein).

(PPP), and finally a discussion section.

**2. Ionospheric variability**

48 Accuracy of GNSS Methods

The ionospheric F-region often becomes turbulent and develops electron density irregularities during post-sunset hours [56]. During the day, the electrical field is eastward and it reverses to the west after sunset, but during sunset an enhanced eastward electric field develops, the so-called pre-reversal enhancement (PRE) [44, 57, 58]. The PRE drives an upward vertical plasma drift at magnetic equatorial region, and the bottom of the F-region becomes unstable to the Rayleigh-Taylor instability [59], developing large-scale plasma depletions (plasma bubbles). These bubbles ascend upwards over the magnetic equator, causing a redistribution of ionization similar to the fountain effect. The latitudinal extension of the plasma bubbles is defined by the upper height limit they reach in their rise up above the magnetic equator [60] and can intersect the crests of the EIA, where the steeper density gradients on the edges of the plasma bubbles favor the generation of smaller scale irregularities [56, 61, 62]. The plasma bubbles practically disappear after local midnight and are most intense during the equinoctial months and during the solar maximum years [63, 64]. These conditions favor the scintillations to occur most frequent and severe around the EIA crests, in particular after sunset due to the generation of irregularities caused by the intersection of the plasma bubbles with the regions of larger background electron density.

The ionosphere can be strongly disturbed during geomagnetic storm-time periods. These storms are terrestrial magnetospheric perturbations caused by the impact of interplanetary coronal mass ejections (ICMEs), and corotating interaction regions associated with high-speed streams (HSS), which are the most geo-effective solar wind phenomena. The coupling process involving the solar wind, the interplanetary magnetic field (IMF) and the magnetosphere strongly affects the high latitude ionospheric electrodynamics. The magnetosphere compression during geomagnetic storms induces intense electric fields and increases its convection. During these processes, the interplanetary electric field (IEF) is mapped along the magnetic field lines to the high latitude ionosphere, but can also propagate across them and promptly appears in the low latitude ionosphere, when it is called of prompt penetration electric field (PPEF). The effect of PPEF at the equatorial ionosphere has been observed during the first hours of the main phase of geomagnetic storms, suggesting a long-duration penetration of interplanetary electric field to the low-latitude ionosphere without shielding (e.g., [5, 65–68]). The equatorial ionosphere under the effect of the PPEFs is convected upward in the dayside and downward in the night side [66]. The PPEFs are stronger than the fields associated with the normal fountain effect resulting in a higher elevation of the equatorial plasma [5], and consequently the crests of the EIA departs more from magnetic equator and can reach middle latitudes (~±20–30**°** ). At high latitudes, the precipitation of energetic particles enhances ionospheric conductivities and generates intense electrical currents in the auroral zone [3]. The dissipation of these currents by the Joule effect heats the local plasma that expands, changing the lower thermospheric composition and driving large-scale neutral winds [3, 4, 42]. Thus, major geomagnetic storms results in a large-scale ionospheric thermal plasma redistribution involving all latitudes from the equatorial through the polar region. Particularly F2-region shows very complicated spatial and temporal behavior (e.g., [9]), but a general morphology and physical processes have been established (e.g., [1–4, 7, 9]). F2-region variations during geomagnetic disturbed periods are called ionospheric storms and are detected as an increase (positive) or depletion (negative) of electron density associated with electrodynamics processes or neutral composition changes (e.g., [4]), respectively. Their morphology is a function of the amount of energy inputted in the high latitude during the main phase of geomagnetic storm [69], as well of the station latitude and longitude, local time of storm onset, storm time and season.

where <> denotes 60 s average, I is the signal intensity and ∅ the signal phase at GPS L1

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51

The S4 and Phi60 indices are used to classify ionospheric scintillation severity, which can be separated in three categories: strong, moderate and weak scintillations, for example, as shown

The morphology of the Earth magnetic field favors the occurrence of strong scintillations at

[20, 72]. Particularly in the South American sector, the F-region irregularities present peculiarities due to the large longitudinal variation in the magnetic declination angle [38, 73, 74], as well by the influence of the South American Magnetic Anomaly (SAMA). The SAMA is the region on the Earth where the magnetic field has the lowest intensity values, allowing enhancement of energetic particle precipitation into the atmosphere [75]. The enhanced ionization in the SAMA region produced by the particle precipitation is a regular feature, which modifies the quiet ionospheric physical conditions increasing the F-layer vertical drift over the eastern sector as compared to the western sector of South America, which can be drastically modified during magnetospheric disturbances (e.g., [75]; and references therein).

The investigation in the South America sector has been improved in the last decades after using GNSS receivers networks dedicated to monitor ionospheric scintillations. Today, there are three GNSS networks, the GPS Low-Latitude Ionospheric Sensor Network (LISN) that is operating since November 2011 with an array of 45 receivers [76], 15 of them over the Brazilian territory, where they are complimented with one array of 12 GPS Ionospheric Scintillation Monitoring Receivers (ISMR) of the GPS Scintillation Monitors network (SCINTMON) [38] and other with 10 ISMR of the Concept for Ionospheric Scintillation Mitigation for Professional GNSS in Latin America and Countering GNSS high Accuracy applications Limitations due to Ionospheric disturbances in Brazil (CIGALA/CALIBRA) project [77]. At high latitude, these networks are complimented with GPS ionospheric scintillation and total electron content (TEC) monitor receivers (GISTM) that covers a large area from sub-equatorial Latin America

Ionospheric irregularities commonly appear in the regions of enhanced or depleted electron density. These regions are associated with the crests of the EIA anomaly located at latitudes

from the magnetic equator, where strong scintillations have been observed particularly

N and 20°

S magnetic latitudes

frequency (1.575 GHz) sampled at 20 ms (50 Hz).

**Table 1.** Classification of the ionospheric scintillation severity.

**Class Index value**

Strong S4 > 0.7 or Phi60 > 0.7

**3.2. Ionospheric scintillation climatology in south American sector**

Weak 0.1 < S4 < 0.25 or 0.1 < Phi60 < 0.25 Moderate 0.25 < S4 < 0.7 or 0.25 < Phi60 < 0.7

high latitudes, and intense at equatorial region between about 20°

in **Table 1**.

to the South Pole [71].

~15–20°

*3.2.1. Quiet geomagnetic conditions*

#### **3. Ionospheric scintillations**

#### **3.1. Scintillation indices**

Scintillations are rapid fluctuations in the amplitude and phase of GNSS signals produced by the ionospheric irregularities, which are responsible by the refraction and diffraction of trans-ionospheric signals [20, 70].

The ionospheric scintillations are evaluated from 60 s amplitude (S4) and phase scintillation (Phi60) indices, which give information about intermediate (around hundreds of meters) and large (above hundreds of meters)-scale size irregularities, respectively. The scintillation indices are obtained by using GNSS dual-frequency receivers recording data at a high data sampling rate of 50 Hz, which also compute the total electron content values.

The S4 index can be interpreted as the standard deviation of the received power (C/NO) normalized by its mean value and the Phi60 index is the standard deviation (in radians) of the carrier phase computed over 60 s time interval. The indices are obtained as Eqs. (1) and (2) [71].

$$\text{S4} = \sqrt{\frac{\zeta I^2 > \overline{-\zeta I^2}}{\zeta I^2}}\tag{1}$$

$$\text{Phi60} = \sqrt{\text{°C} \text{°C} - \text{°C} \text{°C}^2},\tag{2}$$


**Table 1.** Classification of the ionospheric scintillation severity.

storms induces intense electric fields and increases its convection. During these processes, the interplanetary electric field (IEF) is mapped along the magnetic field lines to the high latitude ionosphere, but can also propagate across them and promptly appears in the low latitude ionosphere, when it is called of prompt penetration electric field (PPEF). The effect of PPEF at the equatorial ionosphere has been observed during the first hours of the main phase of geomagnetic storms, suggesting a long-duration penetration of interplanetary electric field to the low-latitude ionosphere without shielding (e.g., [5, 65–68]). The equatorial ionosphere under the effect of the PPEFs is convected upward in the dayside and downward in the night side [66]. The PPEFs are stronger than the fields associated with the normal fountain effect resulting in a higher elevation of the equatorial plasma [5], and consequently the crests of the EIA departs more from magnetic

particles enhances ionospheric conductivities and generates intense electrical currents in the auroral zone [3]. The dissipation of these currents by the Joule effect heats the local plasma that expands, changing the lower thermospheric composition and driving large-scale neutral winds [3, 4, 42]. Thus, major geomagnetic storms results in a large-scale ionospheric thermal plasma redistribution involving all latitudes from the equatorial through the polar region. Particularly F2-region shows very complicated spatial and temporal behavior (e.g., [9]), but a general morphology and physical processes have been established (e.g., [1–4, 7, 9]). F2-region variations during geomagnetic disturbed periods are called ionospheric storms and are detected as an increase (positive) or depletion (negative) of electron density associated with electrodynamics processes or neutral composition changes (e.g., [4]), respectively. Their morphology is a function of the amount of energy inputted in the high latitude during the main phase of geomagnetic storm [69], as well of the station latitude and longitude, local time of storm onset, storm time and season.

Scintillations are rapid fluctuations in the amplitude and phase of GNSS signals produced by the ionospheric irregularities, which are responsible by the refraction and diffraction of

The ionospheric scintillations are evaluated from 60 s amplitude (S4) and phase scintillation (Phi60) indices, which give information about intermediate (around hundreds of meters) and large (above hundreds of meters)-scale size irregularities, respectively. The scintillation indices are obtained by using GNSS dual-frequency receivers recording data at a high data

The S4 index can be interpreted as the standard deviation of the received power (C/NO) normalized by its mean value and the Phi60 index is the standard deviation (in radians) of the carrier phase computed over 60 s time interval. The indices are obtained as Eqs. (1) and (2) [71].

> \_\_\_\_\_\_\_\_\_\_\_\_\_\_ < *I*<sup>2</sup> > − < *I* >2 \_\_\_\_\_\_\_\_\_\_\_\_\_\_

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

sampling rate of 50 Hz, which also compute the total electron content values.

). At high latitudes, the precipitation of energetic

<sup>&</sup>lt; *<sup>I</sup>* >2 , (1)

<sup>&</sup>lt; <sup>∅</sup> 2 <sup>&</sup>gt; <sup>−</sup> <sup>&</sup>lt; <sup>∅</sup> >2, (2)

equator and can reach middle latitudes (~±20–30**°**

**3. Ionospheric scintillations**

trans-ionospheric signals [20, 70].

*<sup>S</sup>*<sup>4</sup> <sup>=</sup> <sup>√</sup>

*Phi*60 = √

**3.1. Scintillation indices**

50 Accuracy of GNSS Methods

where <> denotes 60 s average, I is the signal intensity and ∅ the signal phase at GPS L1 frequency (1.575 GHz) sampled at 20 ms (50 Hz).

The S4 and Phi60 indices are used to classify ionospheric scintillation severity, which can be separated in three categories: strong, moderate and weak scintillations, for example, as shown in **Table 1**.

#### **3.2. Ionospheric scintillation climatology in south American sector**

The morphology of the Earth magnetic field favors the occurrence of strong scintillations at high latitudes, and intense at equatorial region between about 20° N and 20° S magnetic latitudes [20, 72]. Particularly in the South American sector, the F-region irregularities present peculiarities due to the large longitudinal variation in the magnetic declination angle [38, 73, 74], as well by the influence of the South American Magnetic Anomaly (SAMA). The SAMA is the region on the Earth where the magnetic field has the lowest intensity values, allowing enhancement of energetic particle precipitation into the atmosphere [75]. The enhanced ionization in the SAMA region produced by the particle precipitation is a regular feature, which modifies the quiet ionospheric physical conditions increasing the F-layer vertical drift over the eastern sector as compared to the western sector of South America, which can be drastically modified during magnetospheric disturbances (e.g., [75]; and references therein).

The investigation in the South America sector has been improved in the last decades after using GNSS receivers networks dedicated to monitor ionospheric scintillations. Today, there are three GNSS networks, the GPS Low-Latitude Ionospheric Sensor Network (LISN) that is operating since November 2011 with an array of 45 receivers [76], 15 of them over the Brazilian territory, where they are complimented with one array of 12 GPS Ionospheric Scintillation Monitoring Receivers (ISMR) of the GPS Scintillation Monitors network (SCINTMON) [38] and other with 10 ISMR of the Concept for Ionospheric Scintillation Mitigation for Professional GNSS in Latin America and Countering GNSS high Accuracy applications Limitations due to Ionospheric disturbances in Brazil (CIGALA/CALIBRA) project [77]. At high latitude, these networks are complimented with GPS ionospheric scintillation and total electron content (TEC) monitor receivers (GISTM) that covers a large area from sub-equatorial Latin America to the South Pole [71].

#### *3.2.1. Quiet geomagnetic conditions*

Ionospheric irregularities commonly appear in the regions of enhanced or depleted electron density. These regions are associated with the crests of the EIA anomaly located at latitudes ~15–20° from the magnetic equator, where strong scintillations have been observed particularly during sunset hours. Before GNSS era, Aarons [20] using ionosondes and VHF systems showed the scintillation intensities, produced by smaller scale ionospheric irregularities, were stronger in the EIA crests after sunset hours under the influence of plasma bubbles. A comprehensive study of the occurrence of irregularities over the south EIA crest in Brazil during two decades was reported by Sobral et al. [21], which shows the plasma bubbles occurrence has a broad maximum around summer months (from September to April), with a significant increase from low to high solar activity levels during the equinoctial months of March-April and September-October. De Paula et al. [38], using GPS L1-band receivers in the Brazilian territory, reported the characteristics of small-scale irregularities that produced strong scintillations in the post-sunset equatorial ionosphere from 1997 to 2002, the ascending phase of the solar cycle 23. They reported that the ionospheric irregularities are stronger in the southern crest of the EIA, and present a seasonal variation occurring predominantly from September to March during magnetic quiet periods, being more intense during December (local summer). They also show a large longitudinal variation in the South American sector showing that the irregularities are most intense in the EIA crest in Brazilian sector than over Argentinean sector, which is attributed to the large longitudinal variation of magnetic declination in this sector. During quiet magnetic periods, the irregularities occur in the sunset-midnight local time sector while during magnetic storms their occurrence can extend to the midnight-sunrise sector. Akala et al. [39] using a chain of GPS receivers along the western longitude sector of South America, during different levels of solar activity, also shows the scintillations occur predominantly at post-sunset hours and decay before or around local midnight, with stronger activity and longer durations in the months of March and January, which means in the March Equinox and December solstice; and in particular the station near northern crest of the EIA recorded the highest occurrences of scintillation especially during periods of high solar activity.

and summer months [38]. At high latitude the two main hot spots identified as CUSP and PATC show enhancements at equinoxes that are attributed to direct particle precipitation.

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Muella et al. [34] investigated the scintillation occurrence from 2002 to 2006, during the descending phase of the 23rd solar cycle, at two sites located in the inner regions of the northern and southern crests of the equatorial ionization anomaly in the Brazilian sector. They showed that the scintillation occurrences during sunset hours present a north-south asymmetry, being ~10% higher over the southern EIA crest than over northern one during solar maximum. This asymmetry was considered to be a possible influence of the SAMA on the scintillation activity. The scintillation occurrence also showed a broad minimum in June and maximum in December over both crests. On a recent investigation of scintillation occurrence at Cachoeira Paulista near the south EIA crest, covering almost the two last solar cycles (1998–2014), Muella et al. [37] showed that the maximum occurrence of scintillations observed during the peak of 23rd solar cycle was 20% higher than that one observed for the 24th, which was the weakest cycle in the last century. This behavior can be attributed to the scintillation intensity dependence on the electron density gradients and the thickness of irregularity layer, which are driven by the intensity of the solar extreme ultraviolet radiation (EUV). In addition, the fewer occurrences of scintillation in the maximum of the 24th solar cycle at Cachoeira Paulista could also be associated with the secular variation in the dip latitude, which changed

 in south direction from 1997 to 2014.These results on the long-term trend analysis and climatology of scintillations at the EIA region are shown in **Figure 1**. The colored contours in the upper panel of **Figure 1** show the nocturnal occurrence statistics of scintillation from 1998 to 2014 for S4 > 0.2 as function of universal time (UT = LT + 3 h) and the mean F10.7 cm solar flux index. For the type of the GPS receiver used to measure scintillations, the threshold of S<sup>4</sup>

0.2 can be considered above the level of multipath and noise effects, which may produce very

of occurrence used in the plots of scintillation statistics. The monthly mean variation of the F10.7 cm solar flux is shown in the lower panel and depicts its changes from the ascending phase of solar cycle 23rd to the maximum of solar cycle 24th. **Figure 1** reveals that the patches of larger occurrence of scintillations are observed from 23:00 to 04:00 UT between the months

The climatology of the onset time of ionospheric scintillations near the southern crest of EIA over Brazilian territory, covering a period between solar cycles 23 and 24, showed that their start time is about 40 min earlier in the months of November and December when compared to January and February, suggesting an association with the ionospheric pre-reversal vertical

An investigation of the equatorial scintillations over São Luis (2.33°S, 44.21°W, dip latitude 1.3°S) was done by Muella et al. [35] during different solar activity levels of the 23rd solar cycle (1999–2006). The study showed the scintillations occurred more frequently during the years of high solar activity, but strong scintillation variability was also observed during the descending phase of the solar cycle. The scintillations occurred predominantly during pre-midnight hours with a broad maximum in the summer. They observed a weak level of scintillations all

of September and March and mainly around the solar maximum years.

< 0.2). The middle panel shows the occurrence for the strongest levels

> 0.5), whereas the color scale bar indicates the percentage

>

53

~3°

weak scintillations (S4

of scintillations (threshold of S4

drift (PRVD) magnitude and time [79].

Spogli et al. [24], using GISTM receivers located between South America, South Atlantic Ocean and Antarctica, defined crucial areas in the ionosphere where the probability of scintillation occurrences is higher. These areas were called ionospheric scintillation "hot-spots" and were defined using a climatological representation given by the Ground Based Scintillation Climatology (GBSC) technique [19]. They showed that there are two main hot-spots over South America, first one associated with the post-sunset (POST) hours at low latitudes located in the magnetic latitude (MLAT) range 15–25° S and magnetic local time (MLT) between 20 and 24 h, and another one associated with particle precipitation region (SAMA) nearby SAMA region located in the MLAT range 22–24° S and MLT between 0 and 24 h. At high latitudes, they identified three scintillation hot spots, one associated with particle precipitation region in the polar cusp (CUSP, MLAT: 74–82° S and MLT: 10–14 h), other associated with place where the irregularities are induced by reconnection from the magnetotail (MLAT: 68–82° S, MLT: 20–4 h), and other one associated with polar cap patches (PATC, MLAT: 82–90° S, MLT: 0–24 h). The POST hot spot shows scintillation intensifications in March and November, in agreement with the intensification of pre-reversal at equinoxes (e.g., [78]). The hot-spot intensification is stronger in November probably due to the superposition effects associated with the spring equinox and the local summer. The SAMA hot spot also shows one stronger enhancement in November similarly the observed at POST hot spot. They also confirm that in the Brazilian longitudes, the irregularities are more intense in the September (spring) equinox and summer months [38]. At high latitude the two main hot spots identified as CUSP and PATC show enhancements at equinoxes that are attributed to direct particle precipitation.

during sunset hours. Before GNSS era, Aarons [20] using ionosondes and VHF systems showed the scintillation intensities, produced by smaller scale ionospheric irregularities, were stronger in the EIA crests after sunset hours under the influence of plasma bubbles. A comprehensive study of the occurrence of irregularities over the south EIA crest in Brazil during two decades was reported by Sobral et al. [21], which shows the plasma bubbles occurrence has a broad maximum around summer months (from September to April), with a significant increase from low to high solar activity levels during the equinoctial months of March-April and September-October. De Paula et al. [38], using GPS L1-band receivers in the Brazilian territory, reported the characteristics of small-scale irregularities that produced strong scintillations in the post-sunset equatorial ionosphere from 1997 to 2002, the ascending phase of the solar cycle 23. They reported that the ionospheric irregularities are stronger in the southern crest of the EIA, and present a seasonal variation occurring predominantly from September to March during magnetic quiet periods, being more intense during December (local summer). They also show a large longitudinal variation in the South American sector showing that the irregularities are most intense in the EIA crest in Brazilian sector than over Argentinean sector, which is attributed to the large longitudinal variation of magnetic declination in this sector. During quiet magnetic periods, the irregularities occur in the sunset-midnight local time sector while during magnetic storms their occurrence can extend to the midnight-sunrise sector. Akala et al. [39] using a chain of GPS receivers along the western longitude sector of South America, during different levels of solar activity, also shows the scintillations occur predominantly at post-sunset hours and decay before or around local midnight, with stronger activity and longer durations in the months of March and January, which means in the March Equinox and December solstice; and in particular the station near northern crest of the EIA recorded the

highest occurrences of scintillation especially during periods of high solar activity.

in the magnetic latitude (MLAT) range 15–25°

region located in the MLAT range 22–24°

52 Accuracy of GNSS Methods

in the polar cusp (CUSP, MLAT: 74–82°

Spogli et al. [24], using GISTM receivers located between South America, South Atlantic Ocean and Antarctica, defined crucial areas in the ionosphere where the probability of scintillation occurrences is higher. These areas were called ionospheric scintillation "hot-spots" and were defined using a climatological representation given by the Ground Based Scintillation Climatology (GBSC) technique [19]. They showed that there are two main hot-spots over South America, first one associated with the post-sunset (POST) hours at low latitudes located

24 h, and another one associated with particle precipitation region (SAMA) nearby SAMA

they identified three scintillation hot spots, one associated with particle precipitation region

where the irregularities are induced by reconnection from the magnetotail (MLAT: 68–82°

0–24 h). The POST hot spot shows scintillation intensifications in March and November, in agreement with the intensification of pre-reversal at equinoxes (e.g., [78]). The hot-spot intensification is stronger in November probably due to the superposition effects associated with the spring equinox and the local summer. The SAMA hot spot also shows one stronger enhancement in November similarly the observed at POST hot spot. They also confirm that in the Brazilian longitudes, the irregularities are more intense in the September (spring) equinox

MLT: 20–4 h), and other one associated with polar cap patches (PATC, MLAT: 82–90°

S and magnetic local time (MLT) between 20 and

S and MLT between 0 and 24 h. At high latitudes,

S and MLT: 10–14 h), other associated with place

S,

S, MLT:

Muella et al. [34] investigated the scintillation occurrence from 2002 to 2006, during the descending phase of the 23rd solar cycle, at two sites located in the inner regions of the northern and southern crests of the equatorial ionization anomaly in the Brazilian sector. They showed that the scintillation occurrences during sunset hours present a north-south asymmetry, being ~10% higher over the southern EIA crest than over northern one during solar maximum. This asymmetry was considered to be a possible influence of the SAMA on the scintillation activity. The scintillation occurrence also showed a broad minimum in June and maximum in December over both crests. On a recent investigation of scintillation occurrence at Cachoeira Paulista near the south EIA crest, covering almost the two last solar cycles (1998–2014), Muella et al. [37] showed that the maximum occurrence of scintillations observed during the peak of 23rd solar cycle was 20% higher than that one observed for the 24th, which was the weakest cycle in the last century. This behavior can be attributed to the scintillation intensity dependence on the electron density gradients and the thickness of irregularity layer, which are driven by the intensity of the solar extreme ultraviolet radiation (EUV). In addition, the fewer occurrences of scintillation in the maximum of the 24th solar cycle at Cachoeira Paulista could also be associated with the secular variation in the dip latitude, which changed ~3° in south direction from 1997 to 2014.These results on the long-term trend analysis and climatology of scintillations at the EIA region are shown in **Figure 1**. The colored contours in the upper panel of **Figure 1** show the nocturnal occurrence statistics of scintillation from 1998 to 2014 for S4 > 0.2 as function of universal time (UT = LT + 3 h) and the mean F10.7 cm solar flux index. For the type of the GPS receiver used to measure scintillations, the threshold of S<sup>4</sup> > 0.2 can be considered above the level of multipath and noise effects, which may produce very weak scintillations (S4 < 0.2). The middle panel shows the occurrence for the strongest levels of scintillations (threshold of S4 > 0.5), whereas the color scale bar indicates the percentage of occurrence used in the plots of scintillation statistics. The monthly mean variation of the F10.7 cm solar flux is shown in the lower panel and depicts its changes from the ascending phase of solar cycle 23rd to the maximum of solar cycle 24th. **Figure 1** reveals that the patches of larger occurrence of scintillations are observed from 23:00 to 04:00 UT between the months of September and March and mainly around the solar maximum years.

The climatology of the onset time of ionospheric scintillations near the southern crest of EIA over Brazilian territory, covering a period between solar cycles 23 and 24, showed that their start time is about 40 min earlier in the months of November and December when compared to January and February, suggesting an association with the ionospheric pre-reversal vertical drift (PRVD) magnitude and time [79].

An investigation of the equatorial scintillations over São Luis (2.33°S, 44.21°W, dip latitude 1.3°S) was done by Muella et al. [35] during different solar activity levels of the 23rd solar cycle (1999–2006). The study showed the scintillations occurred more frequently during the years of high solar activity, but strong scintillation variability was also observed during the descending phase of the solar cycle. The scintillations occurred predominantly during pre-midnight hours with a broad maximum in the summer. They observed a weak level of scintillations all

which can be produced by the fact that in years of higher solar activity, the thermospheric zonal

GPS Scintillations and Total Electron Content Climatology in the Southern American Sector

http://dx.doi.org/10.5772/intechopen.79218

55

The ionospheric electrodynamics conditions depend on magnetosphere-ionospherethermosphere system, which can be strongly disturbed during geomagnetic storms. During geomagnetic storms, the magnetosphere is compressed inducing intense electric fields and increasing the magnetospheric convection. The strongest geomagnetic storms are mainly produced by the impact of solar wind disturbances associated with geoeffective solar coronal mass ejections (CMEs) and coronal hole solar high speed streams (HSS) on the magnetosphere, which results in a highly inhomogeneous ionosphere, producing steep electron density gradients and irregularities. The ionospheric electron density distribution changes as a function of the solar wind input energy in the high latitude upper atmosphere, which occurs

The spatial and temporal variations of F2-region during geomagnetic storms are called ionospheric storms, and their morphology depends on the site location, local time of geomagnetic storm onset, storm time and season. Despite the very complex ionospheric behavior during disturbed periods, there is a general understanding about its morphology and physical processes (e.g., [1–4, 7, 9]). The negative phase of ionospheric storm is attributed to changes in the thermosphere at middle and high latitudes due to the heating in the auroral zone, mainly by Joule dissipation [87], occurring at all seasons but in winter. In contrast, the positive phase occurs at middle and low latitudes mainly in winter season and involves more complex physical processes associated with uplifting due vertical drift, plasma fluxes from the plasma sphere, and downwelling produced by storm-induced thermosphere circulation at low latitudes (e.g., [3, 7, 9]). The vertical drift during daytime is controlled by equatorward winds at middle latitudes during the winter, and at equatorial region is driven by the EIA anomaly in association with prompt penetration electric field effect (PPEF) [5], resulting in an enhancement of the electron concentration because the photoionization is still operating (e.g., [3, 88]). At middle latitudes, TEC enhancements are observed during the main phase of geomagnetic storms in the dusk sector, which are called storm-enhanced density (SED), and have been associated with large-scale redistribution of ionospheric plasma, covering a large extension from equatorial to polar region [89]. This phenomenon has been observed during the first hours of the main phase storm when the fountain effect at the equatorial region is reinforced by the PPEF, moving EIA crests from low to middle latitudes. The middle latitude EIA crest at dusk sector, under electrodynamic processes, has its plasma redistributed in longitude and latitude generating plumes of SED [90], which can be transported into dayside cusp where enter the polar cap and form the called tongue of ionization (TOI; [8, 10–13, 24, 89]; and references there in) at polar region. The ionospheric plasma redistribution during geomagnetic storms is a function of their intensity, magnetic local time, storm time, latitude and season. The ionospheric regions affected by impact of geomagnetic storms show a strong intensification of scintillation occurrence. At high and middle latitudes, these regions are the night side auroral oval due to the particle precipitation events [12, 91, 92], the cusp on the dayside

wind velocities are higher enhancing the solar thermal tide [86].

during the main phase of the geomagnetic storms [69].

*3.2.2. Disturbed geomagnetic conditions*

**Figure 1.** Occurrence climatology of the GPS L1-frequency scintillation (1998–2014) at Cachoeira Paulista for two threshold levels of the S4 amplitude scintillation index as function of universal time (UT = LT + 3 h) and the mean solar radio flux in 10.7 cm (F10.7 index). The upper and middle panels denote the nocturnal occurrence climatology for the levels of S4 > 0.2 and S4 > 0.5, respectively. The colored bar indicates the percentage of scintillation occurrence used in the plots. The monthly mean variation of the F10.7 cm solar flux is shown in the bottom panel to depict the changes in the solar cycles. [after Muella et al. [37]. Reproduced with permission of the Copernicus publications on behalf of the European geoscience union].

over the year, however, during the winter months near the years of solar maximum, some stronger levels of scintillations were observed at comparable rate with the weak scintillations.

The ionospheric scintillations are driven by zonal drift of the irregularities, so the investigation of the spatial and temporal variations of the irregularities have been done in the last decades. The study of the zonal drift driven scintillations in the South American sector has shown that: a latitudinal gradient in the irregularity zonal velocities is associated with the vertical shear of the zonal drift in the topside equatorial ionosphere [80]; at two magnetic conjugate sites over Brazilian territory, the magnitude of the zonal velocities in the site inside the SAMA region was ~12% larger than in the conjugate one [81]; during nighttime, there is a strong correlation between neutral winds and scintillation drifts near magnetic equator [82]; the irregularity of the zonal drifts shows a negative gradient with increasing geomagnetic latitude [83]; and that the magnitude of the zonal velocities might be reduced at the inner regions of the EIA due to the latitudinal variation in the ion drag force [35]. The nighttime zonal drift velocities of the ionospheric irregularities increase in association with increasing EUV solar radiation [37, 84, 85], which can be produced by the fact that in years of higher solar activity, the thermospheric zonal wind velocities are higher enhancing the solar thermal tide [86].

#### *3.2.2. Disturbed geomagnetic conditions*

over the year, however, during the winter months near the years of solar maximum, some stronger levels of scintillations were observed at comparable rate with the weak scintillations. The ionospheric scintillations are driven by zonal drift of the irregularities, so the investigation of the spatial and temporal variations of the irregularities have been done in the last decades. The study of the zonal drift driven scintillations in the South American sector has shown that: a latitudinal gradient in the irregularity zonal velocities is associated with the vertical shear of the zonal drift in the topside equatorial ionosphere [80]; at two magnetic conjugate sites over Brazilian territory, the magnitude of the zonal velocities in the site inside the SAMA region was ~12% larger than in the conjugate one [81]; during nighttime, there is a strong correlation between neutral winds and scintillation drifts near magnetic equator [82]; the irregularity of the zonal drifts shows a negative gradient with increasing geomagnetic latitude [83]; and that the magnitude of the zonal velocities might be reduced at the inner regions of the EIA due to the latitudinal variation in the ion drag force [35]. The nighttime zonal drift velocities of the ionospheric irregularities increase in association with increasing EUV solar radiation [37, 84, 85],

**Figure 1.** Occurrence climatology of the GPS L1-frequency scintillation (1998–2014) at Cachoeira Paulista for two

radio flux in 10.7 cm (F10.7 index). The upper and middle panels denote the nocturnal occurrence climatology for the levels of S4 > 0.2 and S4 > 0.5, respectively. The colored bar indicates the percentage of scintillation occurrence used in the plots. The monthly mean variation of the F10.7 cm solar flux is shown in the bottom panel to depict the changes in the solar cycles. [after Muella et al. [37]. Reproduced with permission of the Copernicus publications on behalf of the

amplitude scintillation index as function of universal time (UT = LT + 3 h) and the mean solar

threshold levels of the S4

54 Accuracy of GNSS Methods

European geoscience union].

The ionospheric electrodynamics conditions depend on magnetosphere-ionospherethermosphere system, which can be strongly disturbed during geomagnetic storms. During geomagnetic storms, the magnetosphere is compressed inducing intense electric fields and increasing the magnetospheric convection. The strongest geomagnetic storms are mainly produced by the impact of solar wind disturbances associated with geoeffective solar coronal mass ejections (CMEs) and coronal hole solar high speed streams (HSS) on the magnetosphere, which results in a highly inhomogeneous ionosphere, producing steep electron density gradients and irregularities. The ionospheric electron density distribution changes as a function of the solar wind input energy in the high latitude upper atmosphere, which occurs during the main phase of the geomagnetic storms [69].

The spatial and temporal variations of F2-region during geomagnetic storms are called ionospheric storms, and their morphology depends on the site location, local time of geomagnetic storm onset, storm time and season. Despite the very complex ionospheric behavior during disturbed periods, there is a general understanding about its morphology and physical processes (e.g., [1–4, 7, 9]). The negative phase of ionospheric storm is attributed to changes in the thermosphere at middle and high latitudes due to the heating in the auroral zone, mainly by Joule dissipation [87], occurring at all seasons but in winter. In contrast, the positive phase occurs at middle and low latitudes mainly in winter season and involves more complex physical processes associated with uplifting due vertical drift, plasma fluxes from the plasma sphere, and downwelling produced by storm-induced thermosphere circulation at low latitudes (e.g., [3, 7, 9]). The vertical drift during daytime is controlled by equatorward winds at middle latitudes during the winter, and at equatorial region is driven by the EIA anomaly in association with prompt penetration electric field effect (PPEF) [5], resulting in an enhancement of the electron concentration because the photoionization is still operating (e.g., [3, 88]).

At middle latitudes, TEC enhancements are observed during the main phase of geomagnetic storms in the dusk sector, which are called storm-enhanced density (SED), and have been associated with large-scale redistribution of ionospheric plasma, covering a large extension from equatorial to polar region [89]. This phenomenon has been observed during the first hours of the main phase storm when the fountain effect at the equatorial region is reinforced by the PPEF, moving EIA crests from low to middle latitudes. The middle latitude EIA crest at dusk sector, under electrodynamic processes, has its plasma redistributed in longitude and latitude generating plumes of SED [90], which can be transported into dayside cusp where enter the polar cap and form the called tongue of ionization (TOI; [8, 10–13, 24, 89]; and references there in) at polar region. The ionospheric plasma redistribution during geomagnetic storms is a function of their intensity, magnetic local time, storm time, latitude and season.

The ionospheric regions affected by impact of geomagnetic storms show a strong intensification of scintillation occurrence. At high and middle latitudes, these regions are the night side auroral oval due to the particle precipitation events [12, 91, 92], the cusp on the dayside in association with SED, and the polar cap in association with TOI, while at equatorial latitudes the scintillations are associated with regions under the influence of the EIA anomaly. Similarly, the ionospheric storms, the occurrence of scintillations during geomagnetic disturbed periods also are function of magnetic local time, season, magnetic activity, solar cycle, and geographic location [12, 13, 19, 25, 26]. The ionospheric irregularities can be inhibited during magnetic storms with main phase occurring during daylight hours, but can be intensified during any season when main phase storm coincides with the hours of the pre-reversal electric field is maximum (e.g., [75]). De Paula et al. [38] from an investigation of small scale irregularities (~400 m) at equatorial and low latitudes over Brazilian territory obtained that during geomagnetic storms they can occur at any epoch of the year, present largest intensities in the south EIA crest, could extend from sunset-midnight to midnight-sunrise sector during some storms, are enhanced during PPEF occurring during post sunset hours, and can be suppressed during daytime main phase storm under the disturbance dynamo effect. In association with geomagnetic storms, the large-scale irregularities (few km) have shown a seasonal variability [93]. On the other hand, an investigation of the F-region under the impact of the geomagnetic storm occurred on June 2013, from equatorial to middle latitudes in both hemispheres over American sector, showed that the ionospheric irregularities were observed confined in the equatorial region before and during the storm, which shows this storm did not affect the generation or suppression of irregularities [94].

TEC can be expressed as the integral of the electron density *ne*

being the ionospheric delay given by the following relation with TEC:

where *I* represents the ionospheric delay and *f* the signal frequency.

*r* and *d t s*

GPS frequencies (L1 and L2) in a unique arc of data is calculated through:

. It can be written as:

*TEC* =

*<sup>I</sup>* <sup>=</sup> \_\_\_\_ 40, <sup>3</sup>

*PL* = *ρ* + *c*(*d t*

*λ<sup>L</sup> φ<sup>L</sup>* = *ρ* + *c*(*d t*

speed of the light in vacuum, *d t*

guity and the satellite DCB (*Δ b*

*<sup>c</sup> br* <sup>=</sup> \_\_\_\_\_\_\_ <sup>1</sup>

*<sup>F</sup>* <sup>=</sup> *<sup>f</sup>*

with

and the following equation for the carrier phase:

the tropospheric delay, *dm* is the multipath, *NL*

represents the noise in code (*P*) and phase (*φ*).

*<sup>N</sup>* <sup>=</sup> (*λ*<sup>1</sup> *<sup>N</sup>*<sup>1</sup> <sup>−</sup> *<sup>λ</sup>*<sup>2</sup> *<sup>N</sup>*2) <sup>=</sup> \_\_\_1

by the daily weighted mean of the phase difference (*λ*<sup>1</sup> *<sup>φ</sup>*1*<sup>j</sup>*

∑*i*=1 *narc* ∑ *j*=1 *nobs wij* <sup>∑</sup>*<sup>i</sup>*=1 *narc* ∑ *j*=1 *nobs*

*s*

lent to 1 m2

code:

GNSS satellite (*s*) and the receiving antenna (*r*), in a column whose cross sectional is equiva-

GPS Scintillations and Total Electron Content Climatology in the Southern American Sector

∫

*f*

The ionospheric delay is related to the GNSS observations by the following equation for the

where the frequency-dependent terms are referred by *L*, *ρ* is the geometric distance, *c* is the

The method to estimate TEC (Eq. (3)) using GNSS observations (Eqs. (5) and (6)), is performed in three steps. In the first step, a phase leveling estimation based on the code information provides the ambiguity terms. In this regard, the difference between ambiguities (*N*) of two

where only arcs with a minimum of 5 min of continuous data are used. Once the *N* term is

*wij*[(*λ*<sup>1</sup> *φ*1*<sup>j</sup>* − *λ*<sup>2</sup> *φ*2*<sup>j</sup>*) −

) and *wij* <sup>=</sup> \_\_\_\_\_\_\_\_\_\_ <sup>1</sup> (*TE Cij*

− *λ*<sup>2</sup> *φ*2*<sup>j</sup>*

). The receiver DCB is derived by the following weighted mean:

*TE Cij gim* \_\_\_\_\_\_

*gim*/*F*)

*nobs* ∑ *j*=1 *nobs*

obtained for all arcs of a specific day, the receiver DCB (Differential Code Bias - *Δ b*

1 2 *f* 2 2 \_\_\_\_\_\_\_\_ 40.3(*f* 1 <sup>2</sup> − *f* 2 2

*<sup>r</sup>* − *d ts* ) + *I*

*<sup>r</sup>* − *d ts* ) − *I*

r *s* along the path between the

57

http://dx.doi.org/10.5772/intechopen.79218

*ne ds*, (3)

<sup>2</sup> *TEC*, (4)

*<sup>L</sup>* + *T* + *d mL* + ϵ*P*, (5)

*<sup>L</sup>* + *T* + *d mL* + *λ<sup>L</sup> NL* + ϵ*φ*, (6)

are the receiver and satellite clock errors, *T* refers to

is an ambiguity term, *λ* is the wavelength and ϵ

[(*P*2*<sup>j</sup>* − *P*1*<sup>j</sup>*) − (*λ*<sup>1</sup> *φ*1*<sup>j</sup>* − *λ*<sup>2</sup> *φ*2*<sup>j</sup>*)], (7)

*r*

), the initial TEC, the leveling ambi-

*<sup>F</sup>* − *N* − *Δ bsi*], (8)

2, (9)

) is obtained

An investigation of the 26–27 September 2011 moderately intense geomagnetic storm impact in the ionosphere at middle and high latitudes in the South American sector showed that during its dayside main phase two SEDs were observed at middle latitudes [13]. These SEDs were attributed to a combination of processes, including the PPEF effect from low latitudes during a couple of hours just after the storm onset, and dominated by the disturbance dynamo effect from high latitudes during its evolution. The plumes of these SEDs were located near the dayside cusp and result in TOI formations observed in nightside polar cap region. In association with the middle latitude SEDs and polar cap TOIs were observed strong ionospheric scintillations.

#### **4. The impact of ionospheric scintillations in a new single-frequency PPP method**

New analysis about the GNSS positioning was performed by Prol et al. [95] in order to evaluate the ionospheric delay retrieved by a new method for TEC calibration when this method was applied to correct the single-frequency PPP. The results revealed the possibility of performing the single-frequency PPP corrected by a TEC calibration and obtaining a similar accuracy to the double-frequency PPP. It suggested that almost all of the first-order ionospheric effect was eliminated by the TEC calibration method. Additionally, the single-frequency PPP corrected by the new method was very sensitive to the impact of the ionospheric scintillations. In fact, the proposed single-frequency PPP appeared to be even more sensitive to ionospheric scintillation in comparison with the single-frequency PPP corrected by traditional ionospheric models and the double-frequency PPP. In order to present the impact of the ionospheric scintillations in the proposed single-frequency PPP, this section describes the developed method for TEC calibration and some experiments and results.

TEC can be expressed as the integral of the electron density *ne* along the path between the GNSS satellite (*s*) and the receiving antenna (*r*), in a column whose cross sectional is equivalent to 1 m2 . It can be written as:

$$\text{TEC} = \int\_{\epsilon}^{\epsilon} n\_{\epsilon} \, ds\_{\epsilon} \tag{3}$$

being the ionospheric delay given by the following relation with TEC:

$$I = \frac{40,3}{f^2} \,\text{TEC},\tag{4}$$

where *I* represents the ionospheric delay and *f* the signal frequency.

The ionospheric delay is related to the GNSS observations by the following equation for the code:

$$P\_{\perp} = \rho + c(d \, t\_r - d \, t^\*) + I\_{\perp} + T + d \, m\_{\perp} + \varepsilon\_{pr} \tag{5}$$

and the following equation for the carrier phase:

$$
\lambda\_{\perp} \phi\_{\perp} = \rho + c \{ d \, t\_r - d \, t^{\circ} \} - I\_{\perp} + T + d \, m\_{\perp} + \lambda\_{\perp} \, N\_{\perp} + \mathbf{e}\_{\phi^{\prime}} \tag{6}
$$

where the frequency-dependent terms are referred by *L*, *ρ* is the geometric distance, *c* is the speed of the light in vacuum, *d t r* and *d t s* are the receiver and satellite clock errors, *T* refers to the tropospheric delay, *dm* is the multipath, *NL* is an ambiguity term, *λ* is the wavelength and ϵ represents the noise in code (*P*) and phase (*φ*).

The method to estimate TEC (Eq. (3)) using GNSS observations (Eqs. (5) and (6)), is performed in three steps. In the first step, a phase leveling estimation based on the code information provides the ambiguity terms. In this regard, the difference between ambiguities (*N*) of two GPS frequencies (L1 and L2) in a unique arc of data is calculated through:

$$
\Delta \mathbf{V} = \left\langle \lambda\_1 \mathbf{N}\_1 - \lambda\_2 \mathbf{N}\_2 \right\rangle = \frac{1}{n\_{\text{obs}}} \sum\_{j=1}^{n\_{\text{obs}}} \left[ \left( P\_{2j} - P\_{1j} \right) - \left( \lambda\_1 \phi\_{1j} - \lambda\_2 \phi\_{2j} \right) \right] \tag{7}
$$

where only arcs with a minimum of 5 min of continuous data are used. Once the *N* term is obtained for all arcs of a specific day, the receiver DCB (Differential Code Bias - *Δ b r* ) is obtained by the daily weighted mean of the phase difference (*λ*<sup>1</sup> *<sup>φ</sup>*1*<sup>j</sup>* − *λ*<sup>2</sup> *φ*2*<sup>j</sup>* ), the initial TEC, the leveling ambiguity and the satellite DCB (*Δ b s* ). The receiver DCB is derived by the following weighted mean:

$$c\Delta b\_{r} = \frac{1}{\sum\_{i=1}^{n}\sum\_{j=1}^{n} w\_{ij}} \sum\_{i=1}^{n\_{ir}} \sum\_{j=1}^{n\_{\alpha}} w\_{ij} \left[ \left(\lambda\_{1}\phi\_{1j} - \lambda\_{2}\phi\_{2j}\right) - \frac{TE\_{\eta}C\_{\eta}^{in}}{F} - \Delta \mathcal{N} - \Delta \left. \partial\_{s} \right|\_{s} \right] \tag{8}$$

with

in association with SED, and the polar cap in association with TOI, while at equatorial latitudes the scintillations are associated with regions under the influence of the EIA anomaly. Similarly, the ionospheric storms, the occurrence of scintillations during geomagnetic disturbed periods also are function of magnetic local time, season, magnetic activity, solar cycle, and geographic location [12, 13, 19, 25, 26]. The ionospheric irregularities can be inhibited during magnetic storms with main phase occurring during daylight hours, but can be intensified during any season when main phase storm coincides with the hours of the pre-reversal electric field is maximum (e.g., [75]). De Paula et al. [38] from an investigation of small scale irregularities (~400 m) at equatorial and low latitudes over Brazilian territory obtained that during geomagnetic storms they can occur at any epoch of the year, present largest intensities in the south EIA crest, could extend from sunset-midnight to midnight-sunrise sector during some storms, are enhanced during PPEF occurring during post sunset hours, and can be suppressed during daytime main phase storm under the disturbance dynamo effect. In association with geomagnetic storms, the large-scale irregularities (few km) have shown a seasonal variability [93]. On the other hand, an investigation of the F-region under the impact of the geomagnetic storm occurred on June 2013, from equatorial to middle latitudes in both hemispheres over American sector, showed that the ionospheric irregularities were observed confined in the equatorial region before and during the storm, which shows this storm did not

An investigation of the 26–27 September 2011 moderately intense geomagnetic storm impact in the ionosphere at middle and high latitudes in the South American sector showed that during its dayside main phase two SEDs were observed at middle latitudes [13]. These SEDs were attributed to a combination of processes, including the PPEF effect from low latitudes during a couple of hours just after the storm onset, and dominated by the disturbance dynamo effect from high latitudes during its evolution. The plumes of these SEDs were located near the dayside cusp and result in TOI formations observed in nightside polar cap region. In association with the middle latitude SEDs and polar cap TOIs were observed

**4. The impact of ionospheric scintillations in a new single-frequency** 

New analysis about the GNSS positioning was performed by Prol et al. [95] in order to evaluate the ionospheric delay retrieved by a new method for TEC calibration when this method was applied to correct the single-frequency PPP. The results revealed the possibility of performing the single-frequency PPP corrected by a TEC calibration and obtaining a similar accuracy to the double-frequency PPP. It suggested that almost all of the first-order ionospheric effect was eliminated by the TEC calibration method. Additionally, the single-frequency PPP corrected by the new method was very sensitive to the impact of the ionospheric scintillations. In fact, the proposed single-frequency PPP appeared to be even more sensitive to ionospheric scintillation in comparison with the single-frequency PPP corrected by traditional ionospheric models and the double-frequency PPP. In order to present the impact of the ionospheric scintillations in the proposed single-frequency PPP, this section describes the developed method

affect the generation or suppression of irregularities [94].

for TEC calibration and some experiments and results.

strong ionospheric scintillations.

**PPP method**

56 Accuracy of GNSS Methods

$$F = \frac{f\_1^2 f\_2^2}{40.3 \langle f\_1^2 - f\_2^2 \rangle} \text{ and } w\_\psi = \frac{1}{\left(\sigma \text{TE } \mathbb{C}\_\eta^{\text{in}}/F\right)^{2\nu}} \tag{9}$$

being *TE Cij gim* the standard deviation of the initial TEC, which is derived from the Global Ionospheric Maps (GIMs) of the International GNSS Service (IGS) and their root-mean-square (RMS) maps. In addition, the satellite DCB *Δ b si* is obtained from GIMs. Therefore, as the satellite DCB and the initial TEC are obtained from GIMs, it is expected that the estimated receiver DCB is related to the DCB referential frame defined by IGS.

Once the ambiguity leveling (first step) and the receiver DCB estimation (second step) are done, the third step consists in the TEC estimation. TEC is directly calculated along the path of the GNSS signal with the following equation:

$$TEC = F\left[\left(\lambda\_1 \phi\_1 - \lambda\_2 \phi\_2\right) - \Delta N - c\left(\Delta \left. b\right|\_\ast + \Delta \left. b\right)\right],\tag{10}$$

scintillation not so clearing TEC. However, the impact of the ionospheric scintillations is much

**Figure 2.** TEC estimation with the proposed procedure at RIOD station on 2013 for DOY 005 during the summer (top panel) and DOY 191 during the winter (bottom panel). Each colored line represents the slant TEC calculated for a distinct

GPS Scintillations and Total Electron Content Climatology in the Southern American Sector

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59

RTKLIB is adapted for the use of the calibrated TEC during the single-frequency PPP. Among the PPP configurations, it is used the kinematic mode, a combined solution obtained by forward and backward filters, a cut-off angle of 10°, Earth tides corrections, the estimation of tropospheric delay during PPP, IGS precise ephemerides, satellite clock corrections with a 30 s rate (clk\_30s), global positioning system constellation, correction of the phase center variation of the antenna, phase wind up corrections, no strategy for ambiguity solution and corrections of the differential instrumental bias between the civil and precise codes (C1-P1) when P1 was not available. In general, three modes of PPP are analyzed: (1) using the ion-free observation (PPP/if); (2) using L1 and the ionospheric delay from GIMs from UQRG (UPC Quarter an hour Rapid GIM), identified as PPP/uqrg; and (3) using L1 and the calibrated TEC through the proposed method (PPP/tec). Indeed, the PPP/if solutions are obtained using the ion-free observation of the carrier phase, which means that a linear combination is carried out with the L1 and L2 frequencies to eliminate the first-order effect in the ionospheric delay. In the case of PPP/uqrg, the observation used in the PPP Kalman Filter is related to the L1

more easily seen when looking to the single-frequency PPP performance.

GPS satellite.

where the TEC is derived for each GNSS observation, that is, TEC is estimated with the same time resolution as the phase and code collection rate.

Two close GNSS stations located at Rio de Janeiro in Brazil have been selected to make the experiments. The TEC estimation procedure was performed in the station RIOD (lat. Mag. 36.47° S), and the ionospheric delay correction was applied in the station ONRJ, which is located 12 km away. Using the configuration of short distances apart, it is possible to mitigate the problems of spatial gradients of the ionosphere. In addition, the receivers and antennas are from different brands in order to avoid possible correlations between clock and ambiguities of the stations. In this way, it has been as much as possible to isolate the degradation of the ionospheric scintillations in the PPP results.

Prol et al. [95] evaluated the analysis of the performance of the new TEC calibration procedure when applied to PPP for 120 days with six distinct configurations of base and rover stations, and the TEC performance is assessed by applying the estimated TEC from the base station to correct the ionospheric delay in a nearby rover receiver. Just to show the potentiality of the new procedure, here are shown the results of the analysis for two specific days with and without ionospheric scintillations.

**Figure 2** shows an example of the calibrated TEC in RIOD during epochs with and without evidences of ionospheric scintillations. Each colored line represents the slant TEC calculated for a distinct satellite, that is, one colored line refers to the slant TEC of one GPS satellite. The Day Of Year (DOY) 005 of 2013 is shown in the top panel, which refers to the summer solstice in the south crest of EIA. On the other hand, DOY 191 of 2013 is referred to the winter. As it can be seen, the maximum of TEC in the summer solstice reaches around 150 TECU in the slant direction during the daytime. The magnitude of the TEC in daytime is reduced in the winter for up to 100 TECU, mainly due to the reduced intensity of the solar irradiation. However, TEC variability in the daytime is similar. In contrast, the nighttime between 22 and 04 LT presents a significant difference in terms of the TEC variability. The maximum TEC in the nighttime is reduced from 60 TECU in the solstice up to 30 TECU in the winter. Additionally, the high TEC variability evidenced between 22 and 04 LT is associated to the plasma depletions propagating trough the Brazilian region. In fact, the high magnitude of the TEC observations in comparison with the TEC variability makes the impact of the ionospheric GPS Scintillations and Total Electron Content Climatology in the Southern American Sector http://dx.doi.org/10.5772/intechopen.79218 59

being *TE Cij*

58 Accuracy of GNSS Methods

(RMS) maps. In addition, the satellite DCB *Δ b*

of the GNSS signal with the following equation:

time resolution as the phase and code collection rate.

the ionospheric scintillations in the PPP results.

without ionospheric scintillations.

DCB is related to the DCB referential frame defined by IGS.

*gim* the standard deviation of the initial TEC, which is derived from the Global

is obtained from GIMs. Therefore, as the satel-

Ionospheric Maps (GIMs) of the International GNSS Service (IGS) and their root-mean-square

lite DCB and the initial TEC are obtained from GIMs, it is expected that the estimated receiver

Once the ambiguity leveling (first step) and the receiver DCB estimation (second step) are done, the third step consists in the TEC estimation. TEC is directly calculated along the path

*TEC* = *F*[(*λ*<sup>1</sup> *φ*<sup>1</sup> − <sup>2</sup> *φ*2) − Δ*N* − *c*(Δ *bs* + Δ *br*)], (10)

where the TEC is derived for each GNSS observation, that is, TEC is estimated with the same

Two close GNSS stations located at Rio de Janeiro in Brazil have been selected to make the experiments. The TEC estimation procedure was performed in the station RIOD (lat. Mag. 36.47° S), and the ionospheric delay correction was applied in the station ONRJ, which is located 12 km away. Using the configuration of short distances apart, it is possible to mitigate the problems of spatial gradients of the ionosphere. In addition, the receivers and antennas are from different brands in order to avoid possible correlations between clock and ambiguities of the stations. In this way, it has been as much as possible to isolate the degradation of

Prol et al. [95] evaluated the analysis of the performance of the new TEC calibration procedure when applied to PPP for 120 days with six distinct configurations of base and rover stations, and the TEC performance is assessed by applying the estimated TEC from the base station to correct the ionospheric delay in a nearby rover receiver. Just to show the potentiality of the new procedure, here are shown the results of the analysis for two specific days with and

**Figure 2** shows an example of the calibrated TEC in RIOD during epochs with and without evidences of ionospheric scintillations. Each colored line represents the slant TEC calculated for a distinct satellite, that is, one colored line refers to the slant TEC of one GPS satellite. The Day Of Year (DOY) 005 of 2013 is shown in the top panel, which refers to the summer solstice in the south crest of EIA. On the other hand, DOY 191 of 2013 is referred to the winter. As it can be seen, the maximum of TEC in the summer solstice reaches around 150 TECU in the slant direction during the daytime. The magnitude of the TEC in daytime is reduced in the winter for up to 100 TECU, mainly due to the reduced intensity of the solar irradiation. However, TEC variability in the daytime is similar. In contrast, the nighttime between 22 and 04 LT presents a significant difference in terms of the TEC variability. The maximum TEC in the nighttime is reduced from 60 TECU in the solstice up to 30 TECU in the winter. Additionally, the high TEC variability evidenced between 22 and 04 LT is associated to the plasma depletions propagating trough the Brazilian region. In fact, the high magnitude of the TEC observations in comparison with the TEC variability makes the impact of the ionospheric

*si*

**Figure 2.** TEC estimation with the proposed procedure at RIOD station on 2013 for DOY 005 during the summer (top panel) and DOY 191 during the winter (bottom panel). Each colored line represents the slant TEC calculated for a distinct GPS satellite.

scintillation not so clearing TEC. However, the impact of the ionospheric scintillations is much more easily seen when looking to the single-frequency PPP performance.

RTKLIB is adapted for the use of the calibrated TEC during the single-frequency PPP. Among the PPP configurations, it is used the kinematic mode, a combined solution obtained by forward and backward filters, a cut-off angle of 10°, Earth tides corrections, the estimation of tropospheric delay during PPP, IGS precise ephemerides, satellite clock corrections with a 30 s rate (clk\_30s), global positioning system constellation, correction of the phase center variation of the antenna, phase wind up corrections, no strategy for ambiguity solution and corrections of the differential instrumental bias between the civil and precise codes (C1-P1) when P1 was not available. In general, three modes of PPP are analyzed: (1) using the ion-free observation (PPP/if); (2) using L1 and the ionospheric delay from GIMs from UQRG (UPC Quarter an hour Rapid GIM), identified as PPP/uqrg; and (3) using L1 and the calibrated TEC through the proposed method (PPP/tec). Indeed, the PPP/if solutions are obtained using the ion-free observation of the carrier phase, which means that a linear combination is carried out with the L1 and L2 frequencies to eliminate the first-order effect in the ionospheric delay. In the case of PPP/uqrg, the observation used in the PPP Kalman Filter is related to the L1 frequency but corrected from the ionospheric delay derived from UQRG GIMs. The PPP/tec is similar to PPP/uqrg, but the ionospheric delay is derived directly from Eq. (10). The reference coordinates of ONRJ has been obtained from the Sistema de Referencia Geocéntrico para las Américas (SIRGAS) final solutions at epoch 2013, where a time update was performed to make the coordinates consistent with the PPP solutions.

was 0.19 m with a standard deviation of 0.05 m and the RMSE of PPP/uqrg was 0.70 m with a standard deviation of 0.66 m. By itself, this is an outstanding result, since many researchers have already used single-frequency receivers and ionospheric corrections to obtain, in general, an absolute accuracy of 0.5 m in the horizontal and 1 m in vertical for the kinematic PPP [96–98]. Now, we are showing the possibility of obtaining the single-frequency PPP accuracy similar to that from dual-frequency PPP. The horizontal accuracy in the experiment for PPP/tec was 0.12 m in DOY 005 and 0.05 m in DOY 191 and the vertical accuracy was 0.15 m in DOY 005 and 0.07 m in DOY 191. These accuracies are compatible to the double-frequency solutions. Therefore, the unique consideration for a high accuracy in single-frequency PPP is that TEC needs to be sufficient precise, which was not realistic in some epochs of DOY 005 due to the ionospheric scintillations.

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61

A noticeable degradation of the PPP solution occurs between 00 and 04 hours LT in the summer solstice due to the high TEC variability. This PPP degradation is related to the ionospheric irregularities that impact GPS observations more effectively. At such instances, the uplifted ionosphere due to the pre-reversal drift produces high vertical gradients. It is believed that these gradients set the preconditions for plasma instability, controlling the generation of ionospheric irregularities. Therefore, the change of the GPS signal phase and amplitude imposed by ionospheric irregularities degrades the PPP solution. It is interesting to note that the PPP/if is sensitive, but not too much, to the ionospheric scintillations. In case of PPP/uqrg, it is hard to see the impact because of the high standard deviation in the PPP solution at other epochs. However, the impact of the scintillations is very evident in PPP/tec. This mainly happens because the estimated TEC was set to be very precise during the PPP, so that TEC was included with small values for standard deviation in the PPP Kalman filter. At epochs where only the first-order ionospheric delay is supposed to affect the GPS observations, the PPP/tec solution is very accurate. At epochs where the high-orders terms of the ionosphere delay impact the GPS signal, the

The ionospheric conditions are affected by electrodynamic processes that are driven by solar phenomena. During quiet geomagnetic periods, the effects are clearly associated with the seasonal variation of the solar illumination and with the 11-year solar radiation variation. These conditions can be strongly disturbed under the impact of CMEs (coronal mass ejections) and HSS (high-speed streams) in the magnetosphere producing the geomagnetic storms, which result in steeper electron density gradients and stronger irregularities. These irregularities are responsible for fluctuations in the amplitude and phase of GNSS signals, which can degrade the accuracy of the measurements. Therefore, the climatology of these irregularities is very

The investigation of ionospheric scintillations over South America has shown that they can occur at all longitudinal sectors during quiet geomagnetic periods, but they are stronger at post-sunset hours in the crest regions of the EIA (equatorial ionospheric anomaly), and seems to be more intense in the southern EIA crest, which is under the effect of the SAMA (South American Magnetic Anomaly) [24, 37, 81]. The scintillation occurrences strongly enhance with the increase of the solar activity [20, 21, 35, 37, 99], and during geomagnetic disturbed

important to define its spatial distribution and time of occurrence.

PPP degradation becomes evident.

**5. Conclusions**

periods [13, 38, 75, 93, 94].

**Figure 3** shows the performance of PPP/if, PPP/tec and PPP/uqrg in terms of the threedimensional (3D) error of the estimated coordinates. Each point represents the error of the PPP solution calculated in each processing epoch in kinematic mode. Since it was used a combined filter of forward and backward solution, there is no need for time convergence in the solution. Consequently, the remaining errors are related to the terms not efficiently mitigated and, as can be seen, the PPP/tec (blue points) was obtained with a high accuracy in many hours, except to the hours when is typically observed ionospheric scintillations.

In general, the proposed method allowed having the single-frequency PPP with a similar accuracy than the double-frequency PPP. The root mean square error (RMSE) obtained for PPP/if in DOY 191 was 0.04 m with a standard of 0.04 m, the RMSE of PPP/tec was 0.09 m with a standard deviation of 0.04 m and the RMSE of PPP/uqrg was 0.47 m with a standard deviation of 0.65 m. In the case of DOY 005, the RMSE of PPP/if was 0.04 m with a standard of 0.04 m, the RMSE of PPP/tec

**Figure 3.** 3D error of PPP at ONRJ station on 2013 for DOY 005 during summer (top panel) and DOY 191 during winter (bottom panel).

was 0.19 m with a standard deviation of 0.05 m and the RMSE of PPP/uqrg was 0.70 m with a standard deviation of 0.66 m. By itself, this is an outstanding result, since many researchers have already used single-frequency receivers and ionospheric corrections to obtain, in general, an absolute accuracy of 0.5 m in the horizontal and 1 m in vertical for the kinematic PPP [96–98]. Now, we are showing the possibility of obtaining the single-frequency PPP accuracy similar to that from dual-frequency PPP. The horizontal accuracy in the experiment for PPP/tec was 0.12 m in DOY 005 and 0.05 m in DOY 191 and the vertical accuracy was 0.15 m in DOY 005 and 0.07 m in DOY 191. These accuracies are compatible to the double-frequency solutions. Therefore, the unique consideration for a high accuracy in single-frequency PPP is that TEC needs to be sufficient precise, which was not realistic in some epochs of DOY 005 due to the ionospheric scintillations.

A noticeable degradation of the PPP solution occurs between 00 and 04 hours LT in the summer solstice due to the high TEC variability. This PPP degradation is related to the ionospheric irregularities that impact GPS observations more effectively. At such instances, the uplifted ionosphere due to the pre-reversal drift produces high vertical gradients. It is believed that these gradients set the preconditions for plasma instability, controlling the generation of ionospheric irregularities. Therefore, the change of the GPS signal phase and amplitude imposed by ionospheric irregularities degrades the PPP solution. It is interesting to note that the PPP/if is sensitive, but not too much, to the ionospheric scintillations. In case of PPP/uqrg, it is hard to see the impact because of the high standard deviation in the PPP solution at other epochs. However, the impact of the scintillations is very evident in PPP/tec. This mainly happens because the estimated TEC was set to be very precise during the PPP, so that TEC was included with small values for standard deviation in the PPP Kalman filter. At epochs where only the first-order ionospheric delay is supposed to affect the GPS observations, the PPP/tec solution is very accurate. At epochs where the high-orders terms of the ionosphere delay impact the GPS signal, the PPP degradation becomes evident.

#### **5. Conclusions**

frequency but corrected from the ionospheric delay derived from UQRG GIMs. The PPP/tec is similar to PPP/uqrg, but the ionospheric delay is derived directly from Eq. (10). The reference coordinates of ONRJ has been obtained from the Sistema de Referencia Geocéntrico para las Américas (SIRGAS) final solutions at epoch 2013, where a time update was performed to

**Figure 3** shows the performance of PPP/if, PPP/tec and PPP/uqrg in terms of the threedimensional (3D) error of the estimated coordinates. Each point represents the error of the PPP solution calculated in each processing epoch in kinematic mode. Since it was used a combined filter of forward and backward solution, there is no need for time convergence in the solution. Consequently, the remaining errors are related to the terms not efficiently mitigated and, as can be seen, the PPP/tec (blue points) was obtained with a high accuracy in many hours, except to the hours when is typically observed ionospheric scintillations.

In general, the proposed method allowed having the single-frequency PPP with a similar accuracy than the double-frequency PPP. The root mean square error (RMSE) obtained for PPP/if in DOY 191 was 0.04 m with a standard of 0.04 m, the RMSE of PPP/tec was 0.09 m with a standard deviation of 0.04 m and the RMSE of PPP/uqrg was 0.47 m with a standard deviation of 0.65 m. In the case of DOY 005, the RMSE of PPP/if was 0.04 m with a standard of 0.04 m, the RMSE of PPP/tec

**Figure 3.** 3D error of PPP at ONRJ station on 2013 for DOY 005 during summer (top panel) and DOY 191 during winter

(bottom panel).

make the coordinates consistent with the PPP solutions.

60 Accuracy of GNSS Methods

The ionospheric conditions are affected by electrodynamic processes that are driven by solar phenomena. During quiet geomagnetic periods, the effects are clearly associated with the seasonal variation of the solar illumination and with the 11-year solar radiation variation. These conditions can be strongly disturbed under the impact of CMEs (coronal mass ejections) and HSS (high-speed streams) in the magnetosphere producing the geomagnetic storms, which result in steeper electron density gradients and stronger irregularities. These irregularities are responsible for fluctuations in the amplitude and phase of GNSS signals, which can degrade the accuracy of the measurements. Therefore, the climatology of these irregularities is very important to define its spatial distribution and time of occurrence.

The investigation of ionospheric scintillations over South America has shown that they can occur at all longitudinal sectors during quiet geomagnetic periods, but they are stronger at post-sunset hours in the crest regions of the EIA (equatorial ionospheric anomaly), and seems to be more intense in the southern EIA crest, which is under the effect of the SAMA (South American Magnetic Anomaly) [24, 37, 81]. The scintillation occurrences strongly enhance with the increase of the solar activity [20, 21, 35, 37, 99], and during geomagnetic disturbed periods [13, 38, 75, 93, 94].

It was presented the potentiality of a new procedure for TEC calibration, showing a useful tool to correct the first-order ionospheric delay that improves the traditional single-frequency PPP solutions. Additionally, the results show a high-sensitive solution of PPP/tec to the ionospheric scintillations, even more sensitive in comparison with the impact of the ionospheric scintillation in the TEC level, which indicates that this kind of procedures are emerging as having potential for a wide range of applications for those measuring and predicting the ionospheric scintillations.

[2] Prolss GW. Ionospheric storms at mid-latitude: A short review. In: Kintner PM Jr, Coster AJ, Fuller-Rowell T, Mannucci AJ, Mendillo M, Heelis R, editors. Midlatitude Ionospheric Dynamics and Disturbances, Geophysical Monograph Series. Vol. 181. Washington, D.C:

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[13] Correia E, Spogli L, Alfonsi L, Cesaroni C, Gulisano AM, Thomas EG, Ramirez RFH, Rodel AA. Ionospheric F-region response to the 26 September 2011 geomagnetic storm in the Antarctica American and Australian sectors. Annales Geophysicae. 2017;**35**:1113-

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#### **Acknowledgements**

EC thanks the National Council for Research and Development (CNPq) for individual research support (processes nos. 556872/2009-6, 406690/2013-8, 303299/2016-9) and the National Institute for Space Research (INPE/MCTI). MTAHM thanks the support from CNPq through grant no. 429885/2016-4. FSP and POC are grateful to CNPq (grant no. 309924/2013-8), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP grant no. 2015/15027-7) and to Faculdade de Ciências e Tecnologia of UNESP (FCT/UNESP).

#### **Conflict of interest**

The authors declare that they have no conflict of interest.

#### **Author details**

Emília Correia1,2\*, Marcio Tadeu de Assis Honorato Muella3 , Lucilla Alfonsi4 , Fabricio dos Santos Prol5 and Paulo de Oliveira Camargo5


#### **References**

[1] Prolss GW.Ionospheric F-region storms. In: Volland H, editor. Handbook of Atmospheric Electrodynamics. Florida: CRC Press; 1995. pp. 195-248

[2] Prolss GW. Ionospheric storms at mid-latitude: A short review. In: Kintner PM Jr, Coster AJ, Fuller-Rowell T, Mannucci AJ, Mendillo M, Heelis R, editors. Midlatitude Ionospheric Dynamics and Disturbances, Geophysical Monograph Series. Vol. 181. Washington, D.C: AGU; 2008. pp. 9-24. DOI: 10.1029/181GM03

It was presented the potentiality of a new procedure for TEC calibration, showing a useful tool to correct the first-order ionospheric delay that improves the traditional single-frequency PPP solutions. Additionally, the results show a high-sensitive solution of PPP/tec to the ionospheric scintillations, even more sensitive in comparison with the impact of the ionospheric scintillation in the TEC level, which indicates that this kind of procedures are emerging as having potential for a wide range of applications for those measuring and predicting the

EC thanks the National Council for Research and Development (CNPq) for individual research support (processes nos. 556872/2009-6, 406690/2013-8, 303299/2016-9) and the National Institute for Space Research (INPE/MCTI). MTAHM thanks the support from CNPq through grant no. 429885/2016-4. FSP and POC are grateful to CNPq (grant no. 309924/2013-8), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP grant no. 2015/15027-7)

, Lucilla Alfonsi4

,

and to Faculdade de Ciências e Tecnologia of UNESP (FCT/UNESP).

The authors declare that they have no conflict of interest.

Emília Correia1,2\*, Marcio Tadeu de Assis Honorato Muella3

\*Address all correspondence to: ecorreia@craam.mackenzie.br

2 CRAAM-Presbiterian Mackenzie University, São Paulo, Brazil

and Paulo de Oliveira Camargo5

[1] Prolss GW.Ionospheric F-region storms. In: Volland H, editor. Handbook of Atmospheric

1 National Institute for Space Research - INPE, São José dos Campos, Brazil

3 University of Vale do Paraíba - UNIVAP, São José dos Campos, Brazil 4 National Institute of Geophysics and Vulcanology - INGV, Rome, Italy

5 Universidade Estadual Paulista-UNESP, Presidente Prudente, Brazil

Electrodynamics. Florida: CRC Press; 1995. pp. 195-248

ionospheric scintillations.

62 Accuracy of GNSS Methods

**Acknowledgements**

**Conflict of interest**

**Author details**

**References**

Fabricio dos Santos Prol5


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**Chapter 5**

**Provisional chapter**

**Evaluation of GNSS Data with Internet Based Services:**

**Evaluation of GNSS Data with Internet Based Services:** 

Nowadays, as the Internet services are developed, it becomes possible to offer services for many applications in the engineering field online via the Internet. One of these services is the evaluation of online GPS data. The most important feature of Internet-based applications is that these services are free and easy to use. In this study, the data of Global Navigation Satellite Systems (GNSS) of different periods belonging to newly established HRUH permanent GNSS station in Harran University were evaluated through Internetbased services. The evaluation strategy of GNSS data was conducted in 1-, 2-, 6-, 12-, and 24-h campaigns, and the results were compared between different Internet site solution results. When the results obtained are examined, it can be said that the accuracy of the data obtained from these services can be used in many applications requiring precision

**Keywords:** PPP, GNSS, RINEX, internet-based GNSS evaluation services, positioning

Recently, web-based GNSS positioning services have begun to be developed as an additional option to classical evaluation methods. Such services produce solutions automatically by using some of the GNSSS observations loaded via the web interface over the Internet. GNSS observations collected in the field are recorded in standard data formats such as Receiver INdependent EXchange (RINEX) and then uploaded to web-based positioning services, allowing location coordinates of observation points to be obtained in short time and free of

in centimeter levels and is capable of satisfying the expectancies.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.79064

**The Case of HRUH Station**

**The Case of HRUH Station**

http://dx.doi.org/10.5772/intechopen.79064

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Mustafa Ulukavak

Mustafa Ulukavak

**Abstract**

accuracy

**1. Introduction**

charge [1–3].

#### **Evaluation of GNSS Data with Internet Based Services: The Case of HRUH Station Evaluation of GNSS Data with Internet Based Services: The Case of HRUH Station**

DOI: 10.5772/intechopen.79064

#### Mustafa Ulukavak Mustafa Ulukavak

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79064

#### **Abstract**

Nowadays, as the Internet services are developed, it becomes possible to offer services for many applications in the engineering field online via the Internet. One of these services is the evaluation of online GPS data. The most important feature of Internet-based applications is that these services are free and easy to use. In this study, the data of Global Navigation Satellite Systems (GNSS) of different periods belonging to newly established HRUH permanent GNSS station in Harran University were evaluated through Internetbased services. The evaluation strategy of GNSS data was conducted in 1-, 2-, 6-, 12-, and 24-h campaigns, and the results were compared between different Internet site solution results. When the results obtained are examined, it can be said that the accuracy of the data obtained from these services can be used in many applications requiring precision in centimeter levels and is capable of satisfying the expectancies.

**Keywords:** PPP, GNSS, RINEX, internet-based GNSS evaluation services, positioning accuracy

#### **1. Introduction**

Recently, web-based GNSS positioning services have begun to be developed as an additional option to classical evaluation methods. Such services produce solutions automatically by using some of the GNSSS observations loaded via the web interface over the Internet. GNSS observations collected in the field are recorded in standard data formats such as Receiver INdependent EXchange (RINEX) and then uploaded to web-based positioning services, allowing location coordinates of observation points to be obtained in short time and free of charge [1–3].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Web-based positioning services have been considered as an alternative to scientific or commercial software for 15 years. Wherever the Internet access is available, it is easier to evaluate RINEX data using such services. Another reliable aspect of preferring web-based GNSS software is the use of reliable scientific software (Bernese, Gamit, GIPSY/OASIS II, etc.) running in the background of these systems. These services also provide many advantages to the user by reducing the cost of many software, hardware, tools, personnel and transportation services. The results of evaluations of GNSS observations uploaded to these services also provide many advantages such as the possibility of downloading results from the web interface or sending the results to the users via e-mail. The results from these services are in the form of a summary or detailed report. The standard deviation values of these points are sent together with the estimated point coordinates in the incoming reports. Some services send out summary reports in the form of short summary information, while some services provide detailed reports with detailed and graphical presentations. Many of these services are free and some of them require free membership for accessing with a user name and password while using. In general, these services use the data and products of the high accurate and precise International GNSS Service (IGS). IGS provides these products with high precision of GPS/GLONASS ephemeris, satellite and station clocks, earth orientation parameters (ERP), IGS stations coordinates and velocities, and atmospheric parameters to users. These services provided by IGS have led to the emergence of new approaches and new evaluation methods in positioning with the accuracy increase in data processing, orbit determination, and acquisition of clock information in satellite geodesy [4].

1-, 2-, 6-, 12-, and 24-h GNSS observations of the HRUH permanent GNSS station which is established on the roof of the GNSS Laboratory of Harran University Geomatics Engineering Department are evaluated for each web-based positioning service. Then, the same GNSS observations of this station are compared with the analysis results (coordinates and standard deviations) with the scientific GNSS-Inferred Positioning System and Orbit Analysis

Evaluation of GNSS Data with Internet Based Services: The Case of HRUH Station

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75

The widespread use of satellite and space techniques has become an indispensable tool in satellite positioning. Nowadays, by using developed techniques and methods, highly accurate position information is obtained with the help of positioning algorithms. These techniques often differ according to the data collection method. Absolute and relative positioning methods from the earliest times of use of positioning systems are the most preferred techniques for application purposes. The relative positioning technique requires at least two receivers to be used by simultaneous GNSS observations. However, PPP is a method that can be applied by removing this necessity. The PPP technique is based on the evaluation of the code and phase measurements collected from a single receiver. In this technique, the receiver position is directly determined by using precise orbits and clock corrections issued by IGS and similar organizations [5, 6]. The success of the positioning with the PPP technique depends largely on the determination of precise orbit changes of GPS satellites. Therefore, in PPP solutions, it is important to obtain precise orbit (ultra-rapid, rapid, and final) and satellite clock information instead of orbital information broadcast from satellites. Accuracy, broadcast latency, update and sample interval for accurate GPS satellite orbits and clock corrections published by IGS

Nowadays, as the accuracy of precise satellite orbits and clock products published by organizations such as IGS, CODE, and JPL advances, the use of PPP technique is gradually increas-

The ionosphere-independent observation equations of pseudorange and carrier phase measurements include receiver location, clock offset, tropospheric delay, carrier phase unknown

*<sup>r</sup>* + *ε<sup>p</sup>*

are the ionosphere-independent combination of the code and phase measure-

is the ionospheric signal delay between the satellite and the receiver; *λ* is

*<sup>r</sup>* + *εϕ*

(1)

is the tropospheric

*<sup>p</sup>* = *ρ* + *c*(*dt* − *dT*) + *Tr* + *I*

*<sup>N</sup>* is the integer ambiguity of the ionosphere-independent carrier phase; *Tr*

 *<sup>l</sup> <sup>ϕ</sup>* = *ρ* + *c*(*dt* − *dT*) + *N* + *Tr* + *I*

ments, respectively; *dt* is the receiver clock offset which is the difference between receiver time (receiver clock) and system time (GPS); *dT* is the satellite clock offset which is the difference between satellite time (satellite clock) and system time (GPS); *c* is the speed of light in space;

Simulation Software (GIPSY/OASIS II) developed by NASA's JPL laboratory.

**2. Precise point positioning (PPP)**

are given in **Table 1**.

where *l p* and *l ϕ*

signal delay, and *I*

ing in determining the point positions.

parameters, and observation errors:

*r*

*l*

Web-based positioning services have introduced two different types of solutions. The first is the relative positioning approach and the second is the precise point positioning (PPP) solution approach. In this study, web-based precise point positioning solution will be mentioned. The services that are mainly used for the PPP solution approach use only GPS or GPS + GLONASS products such as orbits and clock corrections. The data flow for both webbased positioning services is shown in **Figure 1**.

In this study, four different web-based PPP services, which are most well known and widely used, general properties of services, accessing addresses and analysis results are examined.

**Figure 1.** Schematic presentation of web-based positioning services.

1-, 2-, 6-, 12-, and 24-h GNSS observations of the HRUH permanent GNSS station which is established on the roof of the GNSS Laboratory of Harran University Geomatics Engineering Department are evaluated for each web-based positioning service. Then, the same GNSS observations of this station are compared with the analysis results (coordinates and standard deviations) with the scientific GNSS-Inferred Positioning System and Orbit Analysis Simulation Software (GIPSY/OASIS II) developed by NASA's JPL laboratory.

#### **2. Precise point positioning (PPP)**

Web-based positioning services have been considered as an alternative to scientific or commercial software for 15 years. Wherever the Internet access is available, it is easier to evaluate RINEX data using such services. Another reliable aspect of preferring web-based GNSS software is the use of reliable scientific software (Bernese, Gamit, GIPSY/OASIS II, etc.) running in the background of these systems. These services also provide many advantages to the user by reducing the cost of many software, hardware, tools, personnel and transportation services. The results of evaluations of GNSS observations uploaded to these services also provide many advantages such as the possibility of downloading results from the web interface or sending the results to the users via e-mail. The results from these services are in the form of a summary or detailed report. The standard deviation values of these points are sent together with the estimated point coordinates in the incoming reports. Some services send out summary reports in the form of short summary information, while some services provide detailed reports with detailed and graphical presentations. Many of these services are free and some of them require free membership for accessing with a user name and password while using. In general, these services use the data and products of the high accurate and precise International GNSS Service (IGS). IGS provides these products with high precision of GPS/GLONASS ephemeris, satellite and station clocks, earth orientation parameters (ERP), IGS stations coordinates and velocities, and atmospheric parameters to users. These services provided by IGS have led to the emergence of new approaches and new evaluation methods in positioning with the accuracy increase in data processing, orbit determination, and acquisition of clock information in satellite geodesy [4]. Web-based positioning services have introduced two different types of solutions. The first is the relative positioning approach and the second is the precise point positioning (PPP) solution approach. In this study, web-based precise point positioning solution will be mentioned. The services that are mainly used for the PPP solution approach use only GPS or GPS + GLONASS products such as orbits and clock corrections. The data flow for both web-

In this study, four different web-based PPP services, which are most well known and widely used, general properties of services, accessing addresses and analysis results are examined.

based positioning services is shown in **Figure 1**.

74 Accuracy of GNSS Methods

**Figure 1.** Schematic presentation of web-based positioning services.

The widespread use of satellite and space techniques has become an indispensable tool in satellite positioning. Nowadays, by using developed techniques and methods, highly accurate position information is obtained with the help of positioning algorithms. These techniques often differ according to the data collection method. Absolute and relative positioning methods from the earliest times of use of positioning systems are the most preferred techniques for application purposes. The relative positioning technique requires at least two receivers to be used by simultaneous GNSS observations. However, PPP is a method that can be applied by removing this necessity. The PPP technique is based on the evaluation of the code and phase measurements collected from a single receiver. In this technique, the receiver position is directly determined by using precise orbits and clock corrections issued by IGS and similar organizations [5, 6]. The success of the positioning with the PPP technique depends largely on the determination of precise orbit changes of GPS satellites. Therefore, in PPP solutions, it is important to obtain precise orbit (ultra-rapid, rapid, and final) and satellite clock information instead of orbital information broadcast from satellites. Accuracy, broadcast latency, update and sample interval for accurate GPS satellite orbits and clock corrections published by IGS are given in **Table 1**.

Nowadays, as the accuracy of precise satellite orbits and clock products published by organizations such as IGS, CODE, and JPL advances, the use of PPP technique is gradually increasing in determining the point positions.

The ionosphere-independent observation equations of pseudorange and carrier phase measurements include receiver location, clock offset, tropospheric delay, carrier phase unknown parameters, and observation errors:

$$\begin{aligned} \text{errors:}\\ l\_p &= \rho + c(dt - dT) + T\_r + I\_r + \varepsilon\_p\\ l\_q &= \rho + c(dt - dT) + N\lambda + T\_r + I\_r + \varepsilon\_q \end{aligned} \tag{1}$$

where *l p* and *l ϕ* are the ionosphere-independent combination of the code and phase measurements, respectively; *dt* is the receiver clock offset which is the difference between receiver time (receiver clock) and system time (GPS); *dT* is the satellite clock offset which is the difference between satellite time (satellite clock) and system time (GPS); *c* is the speed of light in space; *<sup>N</sup>* is the integer ambiguity of the ionosphere-independent carrier phase; *Tr* is the tropospheric signal delay, and *I r* is the ionospheric signal delay between the satellite and the receiver; *λ* is


**Table 1.** Accurate GPS satellite orbits and clock corrections issued by IGS.

the wavelength; *ε<sup>p</sup>* and *εϕ* are the noise components including the signal reflection [5, 6]. The geometric distance between satellite (*X<sup>S</sup>* , *Y<sup>S</sup>* , *Z<sup>S</sup>* ) and receiver (*XR* , *YR* , *ZR* ) is defined as: (*XS* <sup>−</sup> *XR*)<sup>2</sup> <sup>+</sup> (*YS* <sup>−</sup> *YR*)<sup>2</sup> <sup>+</sup> (*ZS* <sup>−</sup> *ZR*)<sup>2</sup> (2)

$$\rho = \sqrt{(X^{\mathbb{S}} - \overline{X\_{\mathbb{R}}})^2 + \left(Y^{\mathbb{S}} - \overline{Y\_{\mathbb{R}}}\right)^2 + \left(Z^{\mathbb{S}} - \overline{Z\_{\mathbb{R}}}\right)^2} \tag{2}$$

more training-, information-, and experience-related requirements. In such software, different parameters used in the evaluation can provide a different significance in the results. A third type of software that can process GNSS observations is web-based positioning services. In this service, it is necessary to have only one GNSS receiver and an Internet connection in order to be able to generate the point position information if the observations in the GNSS receiver are aggregated in whatever manner the observations are aggregated in static or kinematic methods. There is no need for any additional financing or equipment other than these equipment. Web-based GNSS services are simple to use and require no additional software knowledge. The data in the RINEX format obtained from the GNSS receivers are processed by uploading them to the web interface of web-based positioning services. Depending on the service to be used, some services require additional information such as the receiving antenna brand and antenna height. At the end of the evaluation process initiated after the uploading process of the GNSS observations, the final report of the relevant GNSS observations is presented to the user via e-mail or a link that can be downloaded from the web interface. The Internet addresses of the web-based positioning services that can process GNSS observations accord-

php?locale=en

https://webapp.geod.nrcan.gc.ca/geod/tools-outils/ppp.

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http://gaps.gge.unb.ca/submitadvanced.php

http://apps.gdgps.net/apps\_file\_upload.php

https://magicgnss.gmv.com/user/ppp

All of the services mentioned in **Table 2** have limited use. However, they use scientific and academic software in the background to determine the station coordinates. These services present the resultant product using the commonly accepted parameters of the data processing methods for coordinate production from GNSS observations in the literature. The web-based

Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP) is a web-based GPS observations processing service provided by the Natural Resources Canada (NRCAN). This service works with a membership system that has the ability to process GNSS observations

ing to the PPP method and provide them to the users are given in **Table 2**.

**PPP service name Organizations Web pages (March, 2018)**

Natural Resources Canada (NRC)

University of New Brunswick (UNB)

NASA- Jet Propulsion Laboratory (JPL)

**Table 2.** Online services using PPP solution approach.

GMV Aerospace and Defence S.A.U.

CSRS-PPP: Canadian Spatial Reference System- Precise Point Positioning

GAPS: GPS Analysis and Positioning Software

APPS: Automatic Precise Positioning Service

magicGNSS: magic Precise Point Positioning

Solution

**3.1. CSRS-PPP: Canadian spatial reference system-precise point positioning**

positioning services used in this study are:

PPP technology has different software options such as Bernese, Gamit, GIPSY/OASIS II to determine the position.

#### **3. GNSS measurements processing software**

Today, we can classify software that can evaluate GNSS measurements in three different groups. The first of these is commercial software. Commercial software is a software that is bundled with the GNSS set, which is often used in practical engineering applications and is usually purchased by customer companies. These are the more preferred software by institutions and organizations that best determine the solutions offered by the company in order to avoid any problems from the users. Other software that can process GNSS measurements are scientific software. Scientific software has been fully developed at research centers and universities for use in academic and scientific studies. The use of scientific software is more complex than commercial software and web-based data processing services. For this reason, there are


**Table 2.** Online services using PPP solution approach.

the wavelength; *ε<sup>p</sup>*

76 Accuracy of GNSS Methods

determine the position.

and *εϕ*

Sat. and Stn. clocks

Sat. and Stn. clocks

**Table 1.** Accurate GPS satellite orbits and clock corrections issued by IGS.

**3. GNSS measurements processing software**

geometric distance between satellite (*X<sup>S</sup>*

*ρ* = √

are the noise components including the signal reflection [5, 6]. The

, *YR* , *ZR*

(*XS* <sup>−</sup> *XR*)<sup>2</sup> <sup>+</sup> (*YS* <sup>−</sup> *YR*)<sup>2</sup> <sup>+</sup> (*ZS* <sup>−</sup> *ZR*)<sup>2</sup> (2)

) is defined as:

**interval**

5 min

Sat.: 30s Stn.:5 min

) and receiver (*XR*

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

PPP technology has different software options such as Bernese, Gamit, GIPSY/OASIS II to

Today, we can classify software that can evaluate GNSS measurements in three different groups. The first of these is commercial software. Commercial software is a software that is bundled with the GNSS set, which is often used in practical engineering applications and is usually purchased by customer companies. These are the more preferred software by institutions and organizations that best determine the solutions offered by the company in order to avoid any problems from the users. Other software that can process GNSS measurements are scientific software. Scientific software has been fully developed at research centers and universities for use in academic and scientific studies. The use of scientific software is more complex than commercial software and web-based data processing services. For this reason, there are

, *Y<sup>S</sup>* , *Z<sup>S</sup>*

**Type Accuracy Latency Updates Sample** 

Broadcast Orbits ~100 cm Real time --- Daily

~2.5 ns SDev Ultra-rapid (predicted) Orbits ~5 cm Real time At 03, 09, 15, 21 UTC 15 min

~1.5 ns SDev Ultra-rapid (observed) Orbits ~3 cm 3–9 h At 03, 09, 15, 21 UTC 15 min

~50 ps SDev Rapid Orbits ~2.5 cm 17–41 h At 17 UTC daily 15 min

> ~75 ps RMS ~25 ps SDev

> ~75 ps RMS ~20 ps SDev

Final Orbits ~2.5 cm 12–18 days Every Thursday 15 min

Sat. clocks ~5 ns RMS

Sat. clocks ~3 ns RMS

Sat. clocks ~150 ps RMS

more training-, information-, and experience-related requirements. In such software, different parameters used in the evaluation can provide a different significance in the results. A third type of software that can process GNSS observations is web-based positioning services. In this service, it is necessary to have only one GNSS receiver and an Internet connection in order to be able to generate the point position information if the observations in the GNSS receiver are aggregated in whatever manner the observations are aggregated in static or kinematic methods. There is no need for any additional financing or equipment other than these equipment. Web-based GNSS services are simple to use and require no additional software knowledge. The data in the RINEX format obtained from the GNSS receivers are processed by uploading them to the web interface of web-based positioning services. Depending on the service to be used, some services require additional information such as the receiving antenna brand and antenna height. At the end of the evaluation process initiated after the uploading process of the GNSS observations, the final report of the relevant GNSS observations is presented to the user via e-mail or a link that can be downloaded from the web interface. The Internet addresses of the web-based positioning services that can process GNSS observations according to the PPP method and provide them to the users are given in **Table 2**.

All of the services mentioned in **Table 2** have limited use. However, they use scientific and academic software in the background to determine the station coordinates. These services present the resultant product using the commonly accepted parameters of the data processing methods for coordinate production from GNSS observations in the literature. The web-based positioning services used in this study are:

#### **3.1. CSRS-PPP: Canadian spatial reference system-precise point positioning**

Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP) is a web-based GPS observations processing service provided by the Natural Resources Canada (NRCAN). This service works with a membership system that has the ability to process GNSS observations from single- or dual-frequency receivers based on static or PPP techniques. CSRS-PPP uses precise GPS orbit and clock products provided by the IGS. The solutions of PPP coordinates are represented in both NAD83 and ITRF14 data with detailed graphical analysis reports. This service has actively processed GLONASS data from October 4, 2011 and accepted userprovided ocean tidal loading (OTL) correction files from February 14, 2012.

#### **3.2. GAPS: GPS analysis and positioning software**

GPS analysis and positioning software (GAPS) is a web-based processing service for GPS observations provided by the University of New Brunswick (UNB). It is a service that does not require membership registration. This service uses IGS's rapid and final orbit and clock products during the process of GPS observations. GAPS is a service that delivers GNSS solutions to users via e-mail. The coordinate solutions of GAPS are represented in ITRF14 datum.

#### **3.3. APPS: automatic precise positioning service**

Automatic precise positioning service (APPS) is a web-based GPS evaluation service operated by NASA Jet Propulsion Laboratory (JPL) and the California Institute of Technology. In the background of this service, the scientific software GIPSY/OASIS II developed in this institution is also run. The system also uses real-time, daily and weekly GPS orbit and clock products produced by JPL. The results of the evaluation can be obtained shortly after the options in the service interface (antenna height, antenna type, e-mail address, etc.) are checked and the GNSS observations are loaded. The solutions of PPP coordinates are represented in ITRF08 datum with detailed analysis reports. APPS is a web-based positioning service that requires membership and offers the use of ftp services for industrial users.

was selected for the accuracy analysis. The GPS data segmented into 1-, 2-, 6-, 12-, and 24-h sessions were collected by HRUH station in static mode on April 18, 2018 (DOY 108). The data sampling interval of the GNSS receiver was 30 s. As a result of this study, we have compared the analysis results obtained by using CSRS-PPP, GAPS, APPS, MagicGNSS services, and scientific software (GIPSY/OASIS II) which produce solutions based on PPP technique. All services including GIPSY/OASIS II scientific software (except APPS) use coordinate solutions at ITRF14 datum. In order to be able to compare the analysis results of all services in the same datum, APPS coordinate solutions in ITRF08 datum have been converted to the coordinates of ITRF14 datum with the help of URL [7]. **Table 3** gives the coordinates and standard deviation results in the Cartesian coordinate system according to the 1-, 2-, 6-, 12-, and 24-h GPS

*X(m) Y(m) Z(m) σX*(*m*) *σY*(*m*) *σZ*(*m*)

Evaluation of GNSS Data with Internet Based Services: The Case of HRUH Station

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79

0.0460 0.0386 0.0347

0.0065 0.0065 0.0060

0.0035 0.0031 0.0031

0.0025 0.0022 0.0023

0.0018 0.0015 0.0016

1 h 3,954,667.2472 3,202,680.8771 3,833,020.8337

2 h 3,954,667.2465 3,202,680.8640 3,833,020.8351

6 h 3,954,667.2430 3,202,680.8621 3,833,020.8269

12 h 3,954,667.2426 3,202,680.8609 3,833,020.8263

24 h 3,954,667.2418 3,202,680.8605 3,833,020.8310

**Table 3.** HRUH station hourly coordinates and standard deviations.

The aim of the study was to determine how consistent results from web-based positioning services are. GPS observations for 1-, 2-, 6,- 12-, and 24-h on the same day (DOY 108) belonging to the same station were separated and loaded into each individual web-based positioning system and results were obtained. Apart from the results obtained during the 1-h observation period, the best coordinate precision and accuracy are understood from the results of the APPS service. The consistency between the GIPSY/OASIS II scientific software and the solutions of the GAPS web-based positioning systems is close together. MagicGNSS service provides only the coordinate points, the related standard deviations are not added to the figures. **Figures 2**–**6** show the results of the coordinates and standard deviation values of the Cartesian coordinate system for 1-, 2-, 6-, 12-, and 24-h GPS observations of the HRUH

When the solutions of 1-h GPS observations of the HRUH station in **Figure 2** are examined, the standard deviation values for the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.01 to 0.1 m. Standard deviation values of the coordinate components

observations of the HRUH station with GIPSY/OASIS II scientific software.

**HRUH GNSS station Observation duration**

station produced by the web-based positioning services, respectively.

#### **3.4. MagicGNSS: magic precise point positioning solution**

Magic Precise Point Positioning Solution is an Internet service created by Spanish GMV Company. MagicGNSS is a positioning service that uses accurate positioning detection technology. The most important advantage of the service is that it can analyze GPS and GLONASS observations together. This system can process both static and kinematic observations. The PPP module of this service uses accurate clock and precise orbit products which are provided by the IGS. The system supports RINEX and all compressed observation formats and offers free 1-GB disk space for member users. The service provides users with a detailed graphical analysis report along with positioning solutions. The solutions of PPP methods are represented in both ETRS89 and ITRF14 data. The service works by downloading or e-mailing the result files from the service's Internet interface.

#### **4. Experimental study**

This study provides the accuracy analysis of the web-based online services using PPP solution approaches. For this purpose, HRUH permanent reference station which located on top of the roof of Geomatics Engineering Department's GNSS Laboratory in Harran University Evaluation of GNSS Data with Internet Based Services: The Case of HRUH Station http://dx.doi.org/10.5772/intechopen.79064 79


**Table 3.** HRUH station hourly coordinates and standard deviations.

from single- or dual-frequency receivers based on static or PPP techniques. CSRS-PPP uses precise GPS orbit and clock products provided by the IGS. The solutions of PPP coordinates are represented in both NAD83 and ITRF14 data with detailed graphical analysis reports. This service has actively processed GLONASS data from October 4, 2011 and accepted user-

GPS analysis and positioning software (GAPS) is a web-based processing service for GPS observations provided by the University of New Brunswick (UNB). It is a service that does not require membership registration. This service uses IGS's rapid and final orbit and clock products during the process of GPS observations. GAPS is a service that delivers GNSS solutions to users via e-mail. The coordinate solutions of GAPS are represented in ITRF14 datum.

Automatic precise positioning service (APPS) is a web-based GPS evaluation service operated by NASA Jet Propulsion Laboratory (JPL) and the California Institute of Technology. In the background of this service, the scientific software GIPSY/OASIS II developed in this institution is also run. The system also uses real-time, daily and weekly GPS orbit and clock products produced by JPL. The results of the evaluation can be obtained shortly after the options in the service interface (antenna height, antenna type, e-mail address, etc.) are checked and the GNSS observations are loaded. The solutions of PPP coordinates are represented in ITRF08 datum with detailed analysis reports. APPS is a web-based positioning service that requires

Magic Precise Point Positioning Solution is an Internet service created by Spanish GMV Company. MagicGNSS is a positioning service that uses accurate positioning detection technology. The most important advantage of the service is that it can analyze GPS and GLONASS observations together. This system can process both static and kinematic observations. The PPP module of this service uses accurate clock and precise orbit products which are provided by the IGS. The system supports RINEX and all compressed observation formats and offers free 1-GB disk space for member users. The service provides users with a detailed graphical analysis report along with positioning solutions. The solutions of PPP methods are represented in both ETRS89 and ITRF14 data. The service works by downloading or e-mailing the

This study provides the accuracy analysis of the web-based online services using PPP solution approaches. For this purpose, HRUH permanent reference station which located on top of the roof of Geomatics Engineering Department's GNSS Laboratory in Harran University

provided ocean tidal loading (OTL) correction files from February 14, 2012.

**3.2. GAPS: GPS analysis and positioning software**

78 Accuracy of GNSS Methods

**3.3. APPS: automatic precise positioning service**

membership and offers the use of ftp services for industrial users.

**3.4. MagicGNSS: magic precise point positioning solution**

result files from the service's Internet interface.

**4. Experimental study**

was selected for the accuracy analysis. The GPS data segmented into 1-, 2-, 6-, 12-, and 24-h sessions were collected by HRUH station in static mode on April 18, 2018 (DOY 108). The data sampling interval of the GNSS receiver was 30 s. As a result of this study, we have compared the analysis results obtained by using CSRS-PPP, GAPS, APPS, MagicGNSS services, and scientific software (GIPSY/OASIS II) which produce solutions based on PPP technique. All services including GIPSY/OASIS II scientific software (except APPS) use coordinate solutions at ITRF14 datum. In order to be able to compare the analysis results of all services in the same datum, APPS coordinate solutions in ITRF08 datum have been converted to the coordinates of ITRF14 datum with the help of URL [7]. **Table 3** gives the coordinates and standard deviation results in the Cartesian coordinate system according to the 1-, 2-, 6-, 12-, and 24-h GPS observations of the HRUH station with GIPSY/OASIS II scientific software.

The aim of the study was to determine how consistent results from web-based positioning services are. GPS observations for 1-, 2-, 6,- 12-, and 24-h on the same day (DOY 108) belonging to the same station were separated and loaded into each individual web-based positioning system and results were obtained. Apart from the results obtained during the 1-h observation period, the best coordinate precision and accuracy are understood from the results of the APPS service. The consistency between the GIPSY/OASIS II scientific software and the solutions of the GAPS web-based positioning systems is close together. MagicGNSS service provides only the coordinate points, the related standard deviations are not added to the figures. **Figures 2**–**6** show the results of the coordinates and standard deviation values of the Cartesian coordinate system for 1-, 2-, 6-, 12-, and 24-h GPS observations of the HRUH station produced by the web-based positioning services, respectively.

When the solutions of 1-h GPS observations of the HRUH station in **Figure 2** are examined, the standard deviation values for the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.01 to 0.1 m. Standard deviation values of the coordinate components

**Figure 2.** Standard deviations of HRUH station coordinates (1 h).

obtained from the CSRS-PPP service were determined as σx = ±0.092 m, σ<sup>y</sup> = ±0.079 m, and σ<sup>z</sup> = ±0.071 m, respectively. Standard deviation values of the coordinate components obtained from the GAPS service are σx = ±0.021 m, σ<sup>y</sup> = ±0.033 m, and σ<sup>z</sup> = ±0.026 m, respectively, and the standard deviation values of the coordinate components obtained from the APPS service are σx = ±0.038 m, σ<sup>y</sup> = ±0.033 m, and σ<sup>z</sup> = ±0.026 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software are calculated as σx = ±0.046 m, σ<sup>y</sup> = ±0.038 m, and σ<sup>z</sup> = ±0.034 m, respectively.

When the solutions of the 2-h GPS observations of the HRUH station in **Figure 3** are examined, the standard deviation values of the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.005 to 0.056 m. Standard deviation values of the coordinate components obtained from the CSRS-PPP service were determined as σx = ±0.056 m, σ<sup>y</sup> = ±0.035 m, and σ<sup>z</sup> = ±0.037 m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.014 m, σ<sup>y</sup> = ±0.006 m, and σ<sup>z</sup> = ±0.008 m, respectively and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.005 m, σ<sup>y</sup> = ±0.005 m, and σ<sup>z</sup> = ±0.005 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software were calculated as σx = ±0.006 m, σ<sup>y</sup> = ±0.006 m, and σ<sup>z</sup> = ±0.006 m, respectively.

When the solutions of the 6-h GPS observations of the HRUH station in **Figure 4** are examined, the standard deviation values for the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.002 to 0.027 m. Standard deviation values of the coordinate components obtained from CSRS-PPP service were determined as σx = ±0.027m, σ<sup>y</sup> = ±0.017m, and σ<sup>z</sup> = ±0.018m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.005 m, σ<sup>y</sup> = ±0.003 m, and σ<sup>z</sup> = ±0.003 m, respectively, and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.003 m, σ<sup>y</sup> = ±0.003 m, and σ<sup>z</sup> = ±0.003 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software were calculated as σx = ±0.003 m, σ<sup>y</sup> = ±0.003 m, and σ<sup>z</sup> = ±0.003 m, respectively.

When the solutions of the 12-h GPS observations of the HRUH station are examined in **Figure 5**, the standard deviation values of the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.002 to 0.015 m. Standard deviation values of the coordinate components obtained from the CSRS-PPP service were determined as σx = ±0.0147 m, σ<sup>y</sup> = ±0.0128 m, and σ<sup>z</sup> = ±0.0125 m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.0026 m, σ<sup>y</sup> = ±0.0024 m, and σ<sup>z</sup> = ±0.0021 m,

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**Figure 3.** Standard deviations of HRUH station coordinates (2 h).

**Figure 4.** Standard deviations of HRUH station coordinates (6 h).

Evaluation of GNSS Data with Internet Based Services: The Case of HRUH Station http://dx.doi.org/10.5772/intechopen.79064 81

**Figure 3.** Standard deviations of HRUH station coordinates (2 h).

obtained from the CSRS-PPP service were determined as σx = ±0.092 m, σ<sup>y</sup> = ±0.079 m, and σ<sup>z</sup> = ±0.071 m, respectively. Standard deviation values of the coordinate components obtained from the GAPS service are σx = ±0.021 m, σ<sup>y</sup> = ±0.033 m, and σ<sup>z</sup> = ±0.026 m, respectively, and the standard deviation values of the coordinate components obtained from the APPS service are σx = ±0.038 m, σ<sup>y</sup> = ±0.033 m, and σ<sup>z</sup> = ±0.026 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software are calculated as σx = ±0.046 m,

When the solutions of the 2-h GPS observations of the HRUH station in **Figure 3** are examined, the standard deviation values of the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.005 to 0.056 m. Standard deviation values of the coordinate components obtained from the CSRS-PPP service were determined as σx = ±0.056 m, σ<sup>y</sup> = ±0.035 m, and σ<sup>z</sup> = ±0.037 m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.014 m, σ<sup>y</sup> = ±0.006 m, and σ<sup>z</sup> = ±0.008 m, respectively and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.005 m, σ<sup>y</sup> = ±0.005 m, and σ<sup>z</sup> = ±0.005 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software were calculated as σx = ±0.006 m,

When the solutions of the 6-h GPS observations of the HRUH station in **Figure 4** are examined, the standard deviation values for the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.002 to 0.027 m. Standard deviation values of the coordinate components obtained from CSRS-PPP service were determined as σx = ±0.027m, σ<sup>y</sup> = ±0.017m, and σ<sup>z</sup> = ±0.018m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.005 m, σ<sup>y</sup> = ±0.003 m, and σ<sup>z</sup> = ±0.003 m, respectively, and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.003 m, σ<sup>y</sup> = ±0.003 m, and σ<sup>z</sup> = ±0.003 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software were calculated as σx = ±0.003 m, σ<sup>y</sup> = ±0.003 m, and σ<sup>z</sup> = ±0.003 m, respectively.

σ<sup>y</sup> = ±0.038 m, and σ<sup>z</sup> = ±0.034 m, respectively.

**Figure 2.** Standard deviations of HRUH station coordinates (1 h).

80 Accuracy of GNSS Methods

σ<sup>y</sup> = ±0.006 m, and σ<sup>z</sup> = ±0.006 m, respectively.

**Figure 4.** Standard deviations of HRUH station coordinates (6 h).

When the solutions of the 12-h GPS observations of the HRUH station are examined in **Figure 5**, the standard deviation values of the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.002 to 0.015 m. Standard deviation values of the coordinate components obtained from the CSRS-PPP service were determined as σx = ±0.0147 m, σ<sup>y</sup> = ±0.0128 m, and σ<sup>z</sup> = ±0.0125 m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.0026 m, σ<sup>y</sup> = ±0.0024 m, and σ<sup>z</sup> = ±0.0021 m,

**Figure 5.** Standard deviations of HRUH station coordinates (12 h).

respectively, and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.0022 m, σ<sup>y</sup> = ±0.0019 m, and σ<sup>z</sup> = ±0.0019 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software are calculated as σx = ±0.0025 m, σ<sup>y</sup> = ±0.0022 m, and σ<sup>z</sup> = ±0.0023 m, respectively.

When the solutions of the 24-h GPS observations of the HRUH station are examined in **Figure 6**, the standard deviation values of the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.001 to 0.009 m. Standard deviation values of the coordinate components obtained from CSRS-PPP service were determined as σx = ±0.0096 m, σ<sup>y</sup> = ±0.0086 m, and σ<sup>z</sup> = ±0.0084 m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.0017 m, σ<sup>y</sup> = ±0.0015 m, and σ<sup>z</sup> = ±0.0015 m, respectively, and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.0015 m, σ<sup>y</sup> = ±0.0013 m, and σ<sup>z</sup> = ±0.0014 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software are calculated as σx = ±0.0018 m, σ<sup>y</sup> = ±0.0015 m, and σ<sup>z</sup> = ±0.0016 m, respectively.

If the result in **Figures 2**–**6** will be interpreted graphically, the most sensitive results for the results of different observation periods of each coordinate component evaluated in the webbased positioning services are GAPS service for 1 h observation period; APPS service for 2-, 6-, 12-, and 24-h observation periods. The CSRS-PPP service was at the forefront of all evaluations.

After obtaining the standard deviations of each coordinate component in the Cartesian coordinate system of the web-based positioning services, the obtained coordinates were compared with the coordinates obtained in GIPSY/OASIS II scientific software. The calculated web-based coordinate results were subtracted from the coordinates obtained from GIPSY/ OASIS II scientific software and classified according to web-based positioning services and GPS observation times (**Figures 7**–**10**).

In **Figure 7**, the differences between the CSRS-PPP web-based positioning service and the coordinate solutions of different GPS observation times obtained by the GIPSY/OASIS II scientific software are calculated. The differences of the coordinate solutions of 1 h GPS observation time are calculated as ΔX = 0.039 m, ΔY = 0.095 m, and ΔZ = 0.115 m. The differences of the coordinate solutions of the 2-h GPS observation time were calculated as ΔX = −0.020 m, ΔY = 0.091 m, and ΔZ = 0.058 m. The differences of the coordinate solutions of the 6-h GPS observation

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**Figure 7.** Coordinate differences between CSRS-PPP solution and GIPSY/OASIS II solution.

**Figure 6.** Standard deviations of HRUH station coordinates (24 h).

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**Figure 6.** Standard deviations of HRUH station coordinates (24 h).

respectively, and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.0022 m, σ<sup>y</sup> = ±0.0019 m, and σ<sup>z</sup> = ±0.0019 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software are calculated

When the solutions of the 24-h GPS observations of the HRUH station are examined in **Figure 6**, the standard deviation values of the CSRS-PPP, GAPS, APPS, and GIPSY/OASIS II coordinate solutions range from 0.001 to 0.009 m. Standard deviation values of the coordinate components obtained from CSRS-PPP service were determined as σx = ±0.0096 m, σ<sup>y</sup> = ±0.0086 m, and σ<sup>z</sup> = ±0.0084 m, respectively. Standard deviation values of coordinate components obtained from GAPS service are σx = ±0.0017 m, σ<sup>y</sup> = ±0.0015 m, and σ<sup>z</sup> = ±0.0015 m, respectively, and the standard deviation values of coordinate components obtained from APPS service are σx = ±0.0015 m, σ<sup>y</sup> = ±0.0013 m, and σ<sup>z</sup> = ±0.0014 m. Standard deviation values of the coordinate components obtained by GIPSY/OASIS II scientific software are calculated

If the result in **Figures 2**–**6** will be interpreted graphically, the most sensitive results for the results of different observation periods of each coordinate component evaluated in the webbased positioning services are GAPS service for 1 h observation period; APPS service for 2-, 6-, 12-, and 24-h observation periods. The CSRS-PPP service was at the forefront of all evaluations. After obtaining the standard deviations of each coordinate component in the Cartesian coordinate system of the web-based positioning services, the obtained coordinates were compared with the coordinates obtained in GIPSY/OASIS II scientific software. The calculated web-based coordinate results were subtracted from the coordinates obtained from GIPSY/ OASIS II scientific software and classified according to web-based positioning services and

as σx = ±0.0025 m, σ<sup>y</sup> = ±0.0022 m, and σ<sup>z</sup> = ±0.0023 m, respectively.

**Figure 5.** Standard deviations of HRUH station coordinates (12 h).

82 Accuracy of GNSS Methods

as σx = ±0.0018 m, σ<sup>y</sup> = ±0.0015 m, and σ<sup>z</sup> = ±0.0016 m, respectively.

GPS observation times (**Figures 7**–**10**).

**Figure 7.** Coordinate differences between CSRS-PPP solution and GIPSY/OASIS II solution.

In **Figure 7**, the differences between the CSRS-PPP web-based positioning service and the coordinate solutions of different GPS observation times obtained by the GIPSY/OASIS II scientific software are calculated. The differences of the coordinate solutions of 1 h GPS observation time are calculated as ΔX = 0.039 m, ΔY = 0.095 m, and ΔZ = 0.115 m. The differences of the coordinate solutions of the 2-h GPS observation time were calculated as ΔX = −0.020 m, ΔY = 0.091 m, and ΔZ = 0.058 m. The differences of the coordinate solutions of the 6-h GPS observation

**Figure 8.** Coordinate differences between GAPS solution and GIPSY/OASIS II solution.

period were calculated as ΔX = −0.001 m, ΔY = 0.074 m, and ΔZ = 0.049 m. The differences of the coordinate solutions of the 12-h GPS observation period were calculated as ΔX = 0.031 m, ΔY = 0.058 m, and ΔZ = 0.058 m. The differences of the coordinate solutions for the 24-h GPS observation period were calculated as ΔX = 0.042 m, ΔY = 0.052 m, and ΔZ = 0.053 m.

In **Figure 8**, the differences between the GAPS web-based positioning service and the coordinate solutions of different GPS observation times obtained by the GIPSY/OASIS II scientific software are calculated. The differences of the coordinate solutions of the 1 h GPS observation period were calculated as ΔX = 0.033 m, ΔY = 0.019 m, and ΔZ = 0.045 m. The differences in coordinate solutions for the 2-h GPS observation period were calculated as ΔX = 0.058 m, ΔY = 0.034 m, and ΔZ = 0.064 m. The differences of the coordinate solutions of the 6-h GPS observation period were calculated as ΔX = 0.037 m, ΔY = 0.032 m, and ΔZ = 0.057 m. The differences of the coordinate solutions of the 12-h GPS observation period were calculated as ΔX = 0.033 m, ΔY = 0.030 m, and ΔZ = 0.053 m. The differences of coordinate solutions for the 24-h GPS observation period were calculated as ΔX = 0.039 m, ΔY = 0.039 m, and ΔZ = 0.053 m.

In **Figure 9**, the differences between the coordinate solutions of different GPS observation times obtained by the APPS web-based positioning service and GIPSY/OASIS II scientific software are calculated. The differences of the coordinate solutions of 1 h GPS observation time are calculated as ΔX = 0.050 m, ΔY = 0.008 m, and ΔZ = 0.039 m. The differences of the coordinate solutions of the 2-h GPS observation period were calculated as ΔX = 0.054 m, ΔY = 0.040 m, and ΔZ = 0.055 m. The differences of the coordinate solutions of the 6-h GPS observation period were calculated as ΔX = 0.052 m, ΔY = 0.042 m, and ΔZ = 0.054 m. The differences of the coordinate solutions for the 12-h GPS observation period were calculated as ΔX = 0.048 m, ΔY = 0.039 m, and ΔZ = 0.052 m. The differences in the coordinate solutions of the 24-h GPS observation period were calculated as ΔX = 0.048 m, ΔY = 0.040 m, and ΔZ = 0.053 m.

In **Figure 10** the differences between the coordinate solutions of different GPS observation times obtained by the MagicGNSS web-based positioning service and GIPSY-OASIS scientific software are calculated. The differences of the coordinate solutions of 1 h GPS observation time are calculated as ΔX = 0.026 m, ΔY = 0.033 m, and ΔZ = 0.013 m. The differences of coordinate solutions for the 2-h GPS observation time are calculated as ΔX = 0.035 m, ΔY = 0.026 m,

**Figure 10.** Coordinate differences between MagicGNSS solution and GIPSY/OASIS II solution.

**Figure 9.** Coordinate differences between APPS solution and GIPSY/OASIS II solution.

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**Figure 9.** Coordinate differences between APPS solution and GIPSY/OASIS II solution.

**Figure 8.** Coordinate differences between GAPS solution and GIPSY/OASIS II solution.

84 Accuracy of GNSS Methods

period were calculated as ΔX = −0.001 m, ΔY = 0.074 m, and ΔZ = 0.049 m. The differences of the coordinate solutions of the 12-h GPS observation period were calculated as ΔX = 0.031 m, ΔY = 0.058 m, and ΔZ = 0.058 m. The differences of the coordinate solutions for the 24-h GPS

In **Figure 8**, the differences between the GAPS web-based positioning service and the coordinate solutions of different GPS observation times obtained by the GIPSY/OASIS II scientific software are calculated. The differences of the coordinate solutions of the 1 h GPS observation period were calculated as ΔX = 0.033 m, ΔY = 0.019 m, and ΔZ = 0.045 m. The differences in coordinate solutions for the 2-h GPS observation period were calculated as ΔX = 0.058 m, ΔY = 0.034 m, and ΔZ = 0.064 m. The differences of the coordinate solutions of the 6-h GPS observation period were calculated as ΔX = 0.037 m, ΔY = 0.032 m, and ΔZ = 0.057 m. The differences of the coordinate solutions of the 12-h GPS observation period were calculated as ΔX = 0.033 m, ΔY = 0.030 m, and ΔZ = 0.053 m. The differences of coordinate solutions for the 24-h GPS observation period were calculated as ΔX = 0.039 m, ΔY = 0.039 m, and ΔZ = 0.053 m. In **Figure 9**, the differences between the coordinate solutions of different GPS observation times obtained by the APPS web-based positioning service and GIPSY/OASIS II scientific software are calculated. The differences of the coordinate solutions of 1 h GPS observation time are calculated as ΔX = 0.050 m, ΔY = 0.008 m, and ΔZ = 0.039 m. The differences of the coordinate solutions of the 2-h GPS observation period were calculated as ΔX = 0.054 m, ΔY = 0.040 m, and ΔZ = 0.055 m. The differences of the coordinate solutions of the 6-h GPS observation period were calculated as ΔX = 0.052 m, ΔY = 0.042 m, and ΔZ = 0.054 m. The differences of the coordinate solutions for the 12-h GPS observation period were calculated as ΔX = 0.048 m, ΔY = 0.039 m, and ΔZ = 0.052 m. The differences in the coordinate solutions of the 24-h GPS

observation period were calculated as ΔX = 0.042 m, ΔY = 0.052 m, and ΔZ = 0.053 m.

observation period were calculated as ΔX = 0.048 m, ΔY = 0.040 m, and ΔZ = 0.053 m.

**Figure 10.** Coordinate differences between MagicGNSS solution and GIPSY/OASIS II solution.

In **Figure 10** the differences between the coordinate solutions of different GPS observation times obtained by the MagicGNSS web-based positioning service and GIPSY-OASIS scientific software are calculated. The differences of the coordinate solutions of 1 h GPS observation time are calculated as ΔX = 0.026 m, ΔY = 0.033 m, and ΔZ = 0.013 m. The differences of coordinate solutions for the 2-h GPS observation time are calculated as ΔX = 0.035 m, ΔY = 0.026 m, and ΔZ = 0.037 m. The differences of the coordinate solutions of the 6-h GPS observation period were calculated as ΔX = 0.036 m, ΔY = 0.026 m, and ΔZ = 0.045 m. The differences in coordinate solutions for the 12-h GPS observation period were calculated as ΔX = 0.035 m, ΔY = 0.028 m, and ΔZ = 0.045 m. The differences of the coordinate solutions of the 24-h GPS observation period were calculated as ΔX = 0.035 m, ΔY = 0.038 m, and ΔZ = 0.043 m.

evaluated according to the PPP technique is directly related to the accuracy of the IGS orbit

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In such systems, many outcome products can be obtained without the need for GNSS expertise other than basic level. When using web-based positioning services, choosing the solution parameters appropriate to the data structure and the measurement method can bring the coordinate accuracy to the highest level. Applications for scientific research should indicate that such services are not suitable for applications that require expertise, such as ionospheric and tropospheric models, deformation analysis studies, earth orienta-

The results from web-based location services show that there is not much difference between the results of software that solves with scientific PPP technique when there is enough observation period in GNSS sessions. This is rather obvious in the precision results given in **Figures 2**–**6**. In the application where PPP services are evaluated, it is seen that the results are directly related to the observation period. Accuracy is increased by increasing the observation time from 1 to 24 h, but the results are still at several centimeters. Precision results given in **Figures 2**–**6** are very similar to those published by the IGS. In order to be able to obtain accuracy results similar to those of precision results, one needs to adopt equal processing strategy for all software used here but unfortunately this was impossible

The user needs to select the observation period on the point according to the expected accuracy level. The results obtained from such services, which provide a great gain in terms of time and cost, are sufficient to give the position information for many engineering applications.

The author thanks to International GNSS Service (IGS) for product supports, and to organizations, which present web-based online services (CSRS-PPP, GAPS, APPS, MagicGNSS). Special thanks to Research Assistants Ali Hasan DOĞAN and Mustafa Fahri KARABULUT in Yildiz Technical University (YTU) for their help in assisting at the post processing stage of GPS observations by using GIPSY-OASIS II scientific software with PPP technique. NASA JPL's software GIPSY/OASIS II is licensed to Department of Geomatic Engineering of YTU.

and clock information.

tion parameters, and so on.

throughout this study.

**Acknowledgements**

**Author details**

Mustafa Ulukavak

Address all correspondence to: mulukavak@gmail.com

Harran University, Sanliurfa, Turkey

APPS uses GIPSY/OASIS II in the background. However, the difference in the results between GIPSY/OASIS II and APPS is slightly larger than the difference in results between GIPSY/ OASIS II and MagicGNSS. This can be ascribed to the fact that APPS results are based on the ITRF08 but not the ITRF14 on which both GIPSY/OASIS II and MagicGNSS rely.

In **Figures 7**–**10**, the differences between the coordinate values of the HRUH permanent GNSS station produced by the web-based positioning services for different GPS observation times and the coordinate solutions obtained by the GIPSY/OASIS II scientific software are examined.

In **Figure 7**, when the coordinate solutions obtained from the CSRS-PPP web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1- and 2-h observation periods are found to be around 10 cm, coordinate differences for 6- and 12-h observation periods are around 5 cm, and for 24-h observation periods, coordinate differences are less than 5 cm.

In **Figure 8**, when the coordinate solutions obtained from the GAPS web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1-h observation period is found to be less than 5 cm, coordinate differences for 2-, 6-, 12-, and 24-h observation periods are around 5 cm.

In **Figure 9**, when the coordinate solutions obtained from the APPS web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1-h observation period is found to be less than 5 cm, coordinate differences for 2-, 6-, 12-, and 24-h observation periods are around 5 cm.

In **Figure 10**, when the coordinate solutions obtained from the MagicGNSS web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1-, 2-, 6-, 12-, and 24-h observation period is found to be less than 5 cm.

#### **5. Conclusion**

Today, PPP technology is becoming increasingly important. With its many advantages, it poses a serious alternative to positioning methods. However, the use of web-based positioning services, which analyze using PPP technology, is becoming widespread. The PPP technique is feasible in the measurement and evaluation process with only one GNSS receiver, and providing these services to the user free of charge on the Internet makes these systems advantageous in many applications. It should not be forgotten that the reliability of the results evaluated according to the PPP technique is directly related to the accuracy of the IGS orbit and clock information.

In such systems, many outcome products can be obtained without the need for GNSS expertise other than basic level. When using web-based positioning services, choosing the solution parameters appropriate to the data structure and the measurement method can bring the coordinate accuracy to the highest level. Applications for scientific research should indicate that such services are not suitable for applications that require expertise, such as ionospheric and tropospheric models, deformation analysis studies, earth orientation parameters, and so on.

The results from web-based location services show that there is not much difference between the results of software that solves with scientific PPP technique when there is enough observation period in GNSS sessions. This is rather obvious in the precision results given in **Figures 2**–**6**. In the application where PPP services are evaluated, it is seen that the results are directly related to the observation period. Accuracy is increased by increasing the observation time from 1 to 24 h, but the results are still at several centimeters. Precision results given in **Figures 2**–**6** are very similar to those published by the IGS. In order to be able to obtain accuracy results similar to those of precision results, one needs to adopt equal processing strategy for all software used here but unfortunately this was impossible throughout this study.

The user needs to select the observation period on the point according to the expected accuracy level. The results obtained from such services, which provide a great gain in terms of time and cost, are sufficient to give the position information for many engineering applications.

#### **Acknowledgements**

and ΔZ = 0.037 m. The differences of the coordinate solutions of the 6-h GPS observation period were calculated as ΔX = 0.036 m, ΔY = 0.026 m, and ΔZ = 0.045 m. The differences in coordinate solutions for the 12-h GPS observation period were calculated as ΔX = 0.035 m, ΔY = 0.028 m, and ΔZ = 0.045 m. The differences of the coordinate solutions of the 24-h GPS

APPS uses GIPSY/OASIS II in the background. However, the difference in the results between GIPSY/OASIS II and APPS is slightly larger than the difference in results between GIPSY/ OASIS II and MagicGNSS. This can be ascribed to the fact that APPS results are based on the

In **Figures 7**–**10**, the differences between the coordinate values of the HRUH permanent GNSS station produced by the web-based positioning services for different GPS observation times and the coordinate solutions obtained by the GIPSY/OASIS II scientific software are examined. In **Figure 7**, when the coordinate solutions obtained from the CSRS-PPP web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1- and 2-h observation periods are found to be around 10 cm, coordinate differences for 6- and 12-h observation periods are around

In **Figure 8**, when the coordinate solutions obtained from the GAPS web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1-h observation period is found to be less than 5 cm, coordinate differences for 2-, 6-, 12-, and 24-h observation periods are around 5 cm. In **Figure 9**, when the coordinate solutions obtained from the APPS web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1-h observation period is found to be less than 5 cm, coordinate differences for 2-, 6-, 12-, and 24-h observation periods are around 5 cm. In **Figure 10**, when the coordinate solutions obtained from the MagicGNSS web-based positioning service are compared with the coordinate solutions obtained from the GIPSY/OASIS II scientific software, the coordinate differences between 1-, 2-, 6-, 12-, and 24-h observation

Today, PPP technology is becoming increasingly important. With its many advantages, it poses a serious alternative to positioning methods. However, the use of web-based positioning services, which analyze using PPP technology, is becoming widespread. The PPP technique is feasible in the measurement and evaluation process with only one GNSS receiver, and providing these services to the user free of charge on the Internet makes these systems advantageous in many applications. It should not be forgotten that the reliability of the results

observation period were calculated as ΔX = 0.035 m, ΔY = 0.038 m, and ΔZ = 0.043 m.

ITRF08 but not the ITRF14 on which both GIPSY/OASIS II and MagicGNSS rely.

5 cm, and for 24-h observation periods, coordinate differences are less than 5 cm.

period is found to be less than 5 cm.

**5. Conclusion**

86 Accuracy of GNSS Methods

The author thanks to International GNSS Service (IGS) for product supports, and to organizations, which present web-based online services (CSRS-PPP, GAPS, APPS, MagicGNSS). Special thanks to Research Assistants Ali Hasan DOĞAN and Mustafa Fahri KARABULUT in Yildiz Technical University (YTU) for their help in assisting at the post processing stage of GPS observations by using GIPSY-OASIS II scientific software with PPP technique. NASA JPL's software GIPSY/OASIS II is licensed to Department of Geomatic Engineering of YTU.

#### **Author details**

Mustafa Ulukavak Address all correspondence to: mulukavak@gmail.com Harran University, Sanliurfa, Turkey

### **References**

[1] Ghoddousi-Fard R, Dare P. Online GPS processing services: An initial study. GPS Solutions. 2006;**10**:12-20. DOI: 10.1007/s10291-005-0147-5

**Chapter 6**

Provisional chapter

**Comparative Study of Some Online GNSS Post-**

Comparative Study of Some Online GNSS Post-

Olalekan Adekunle Isioye, Mefe Moses and

Olalekan Adekunle Isioye, Mefe Moses

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79924

**in Nigeria**

in Nigeria

Lukman Abdulmumin

Abstract

accuracy

and Lukman Abdulmumin

**Processing Services at Selected Permanent GNSS Sites**

DOI: 10.5772/intechopen.79924

Many applications in surveying and mapping have been made simpler and more precise due to the advent of GNSS, and thus, the demand for using cutting-edge GNSS techniques in surveying and mapping applications has become indispensable. Online GNSS postprocessing services are now available to provide support for users in need of precise point positioning or conventional differential positioning services and without requiring a prior knowledge of GNSS processing software. This study evaluates the performance of some online GNSS facilities with emphasis on observation duration (i.e. 1hr, 2hr, 6hr 12hr and 24hr observations). Three of these online facilities (AUSPOS, GAPS and magic-GNSS) were chosen based on their mode of operation and were evaluated at the location of five permanent GNSS stations in Nigeria. The study cut across two epochs in the year 2014 (i.e. seven days each in the months of January and July). Results in this study indicate that users can expect reliable results from these online services and their accuracy is within allowable limits for mapping applications in Nigeria. The similarity of the results between all of the services used is amazing, thus further demonstrates the robustness of the

Keywords: Global Navigation Satellite System (GNSS), continuously operating reference stations (CORS), precise point positioning (PPP), GNSS online processing, positioning

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

algorithms and processes employed by the different online facilities.

Processing Services at Selected Permanent GNSS Sites


#### **Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria** Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

DOI: 10.5772/intechopen.79924

Olalekan Adekunle Isioye, Mefe Moses and Lukman Abdulmumin Olalekan Adekunle Isioye, Mefe Moses and Lukman Abdulmumin

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79924

#### Abstract

**References**

88 Accuracy of GNSS Methods

[1] Ghoddousi-Fard R, Dare P. Online GPS processing services: An initial study. GPS

[2] El-Mowafy A. Analysis of web-based GNSS post-processing services for static and kinematic positioning using short data spans. Survey Review. 2011;**43**:535-549. DOI: 10.1179

[3] Gakstatter E. A Comparison of Free GPS Online Post-Processing Services GPS World [Internet]. 2013. Available from: http://gpsworld.com/a-comparison-of-free-gps-online-

[4] Ocalan T, Erdogan B, Tunalioglu N. Analysis of web-based online services for GPS relative and precise point positioning techniques. Boletim de Ciências Geodésicas.

[5] Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH. Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of

[6] Dach R, Hugentobler U, Fridez P, Meindl M. Manual of bernese GPS Software Version

[7] Transformation Parameters from ITRF08 to ITRF2014 [Internet]. 2018. Available from: http://itrf.ign.fr/doc\_ITRF/Transfo-ITRF2014\_ITRFs.txt [Accessed: Apr 28, 2018]

Solutions. 2006;**10**:12-20. DOI: 10.1007/s10291-005-0147-5

post-processing-services/ [Accessed: Apr 19, 2018]

2013;**19**(2):191-207. DOI: 10.1590/S1982-21702013000200003

5.0. University of Bern: Astronomical Institute; 2007. 612 p

Geophysical Research. 1997;**102**(3):5005-5017. DOI: 10.1029/96JB03860

/003962611X13117748892074

Many applications in surveying and mapping have been made simpler and more precise due to the advent of GNSS, and thus, the demand for using cutting-edge GNSS techniques in surveying and mapping applications has become indispensable. Online GNSS postprocessing services are now available to provide support for users in need of precise point positioning or conventional differential positioning services and without requiring a prior knowledge of GNSS processing software. This study evaluates the performance of some online GNSS facilities with emphasis on observation duration (i.e. 1hr, 2hr, 6hr 12hr and 24hr observations). Three of these online facilities (AUSPOS, GAPS and magic-GNSS) were chosen based on their mode of operation and were evaluated at the location of five permanent GNSS stations in Nigeria. The study cut across two epochs in the year 2014 (i.e. seven days each in the months of January and July). Results in this study indicate that users can expect reliable results from these online services and their accuracy is within allowable limits for mapping applications in Nigeria. The similarity of the results between all of the services used is amazing, thus further demonstrates the robustness of the algorithms and processes employed by the different online facilities.

Keywords: Global Navigation Satellite System (GNSS), continuously operating reference stations (CORS), precise point positioning (PPP), GNSS online processing, positioning accuracy

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 1. Introduction

Global Navigation Satellite Systems (GNSS) is generic term for a composition of different satellite navigation technologies such as American GPS (Global Positioning System); its Russian equivalent, GLONASS (GLObal Navigation Satellite System); the Chinese system, BeiDou; the Japanese regional system, QZSS; the Indian regional system IRNSS (Indian Regional Navigation Satellite System); finally, is the European Galileo system. The GPS and GLONASS has since attained full operational status. The BeiDou, is expected to achieve completion for worldwide service in 2020, although a limited version of its signal has already been available since December 2012. The QZSS, is at present providing a limited service in the form of an augmented signal for GPS, but should be progressively upgraded and achieve full impartiality in 2023. The IRNSS, is at a final point operation as well. The Galileo system is expected to attain full operational capability in 2020 [1, 2].

GNSS processing services. These services provide GNSS processing results to the user free of charge and with unlimited access. The user sends a Receiver Independent Exchange Format (RINEX) file to the service and within a short period of time, the estimated position of the receiver used to collect the RINEX data is sent back to the user. Organisations that provide these free services include: Geohazards Division of Geoscience Australia, the Geodetic Survey Division (GSD) in Canada, the United States' National Geodetic Survey (NGS), Scripps Orbit and Permanent Array Center (SOPAC) at the University of California and the Jet Propulsion

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

http://dx.doi.org/10.5772/intechopen.79924

91

The only requirement for using these services is a computer having an internet connection and web browser. These services are designed to be as simple as possible for the user and with minimal input. Users of such systems have to perform uploading/sending of their collected data in RINEX format by using the web site of these services, e-mail or ftp sites to the system and selecting a few processing options. Some of these services process not only the GPS but also the data of other systems, particularly those of GLONASS, and provide resilience and a

Currently, there are several online GNSS post-processing services, and are best categorised base on their adopted approach of processing the RINEX files. Categorically, there are those that use the Precise Point Positioning (PPP) approach (see [11–13] for documentation). Those in this category include Canadian Spatial Reference System-Precise Point Positioning (CSRS-PPP), magicGNSS, (APPS) and GPS Analysis and Positioning Software (GAPS). PPP based services used the GNSS data collected with only a single receiver with precise satellite ephemerides and clock data by taking into account corrections like carrier phase wind-up, satellite antenna phase offset, solid and ocean tides. The category of the GNSS online processing services that adopted the conventional relative approach, where user's RINEX files are processed relative to other GNSS continuously operating reference stations (CORS). The Trimble RTX, Australian Surveying and Land Information Group Online GPS Processing Service (AUSPOS) and Online Positioning User Service (OPUS) are based on this approach [5].

The application/usage of these facilities are gaining global acceptance and numerous studies have evaluated the accuracy of different online GNSS processing in different part of the world (e.g. Australia, Egypt, etc.). The results of such studies have demonstrated inherent limitations, the accuracies, conveniences of online post processing of GNSS observations, and have also identified a wide range of uses within the surveying community (e.g., see [13–15]). This chapter is dedicated to the report on the accuracy of three online GNSS processing facilities (magic GNSS, GAPS, and AUSPOS) over the territory of Nigeria. The major objective of the study is to investigate the effects of the variation in the duration of GNSS observation sessions

The structure of the paper is as follows: first a general description and status of the different online GNSS post-processing services is presented in Section 2. Section 3 explains the methods used in the data acquisition, processing and evaluation of results. Section 4 describes the results. Lastly, the concluding remarks were presented and additionally, the paper gives

Laboratory (JPL) at National Aeronautics and Space Administration (NASA) [7].

higher accurate positioning service in certain cases to their users [5].

on the positional accuracy when using online processing facilities.

insight into possible future expansion of GNSS infrastructures in Nigeria.

Global Navigation Satellite System (GNSS) is one of the most innovative and practical technology developed in recent times. Since its inception it has grown to provide not only world-wide, all weather navigation, but precise position determination capabilities to all manner of users especially for surveying and geodetic applications. In surveying and mapping, this represents a revolutionary departure from conventional surveying procedures, which relied on observed angles and distances for determining point positions [3, 4].

Traditionally, it was necessary to obtain positioning with GNSS using at least two receivers, and the collected data processed for high accurate positioning using the GNSS data processing software whether scientific or commercial. However, the usage of such software is also quite difficult because they generally require deep knowledge of the GNSS, experience in the processing and they mostly need a licencing fee [4–7].

A remarkable volume of information and resources on GNSS are available on the internet including GNSS raw data, precise GNSS satellite orbit and clock files (which are provided by the international GNSS Service (IGS) and many other organisations, as well as some GNSS processing software (e.g., see [8]). This software vary in terms availability for use (cost), accuracy, and their mode of operation which are often dependant on the technical know-how of the users. Some of the very accurate but complex to use software are GAMIT/GLOBK (from Department of Earth Atmospheric and Planetary Sciences, MIT), GIPSY/OASIS-II (from Jet Propulsion Laboratory, JPL), PAGES (from United States National Geodetic Survey, NGS). The BERNESE software (from the Astronomisches Institut der Universitat Bern, Switzerland), is a state-of-the-art GNSS processing software similar to GIPSY and GAMIT but available only commercially at a very high cost. There are also numerous MATLAB based GNSS processing system which are freely available online (e.g., see [8, 9]), however, users require requisite skills to use them. Numerous studies have explore and put forward improvements in GNSS processing system that will aid users confronted with challenges enumerated herein [5, 6, 10].

Regarding the improvements in GNSS data processing methodology, many new opportunities have been offered to the users. In this respect, many organisations have developed online GNSS processing services. These services provide GNSS processing results to the user free of charge and with unlimited access. The user sends a Receiver Independent Exchange Format (RINEX) file to the service and within a short period of time, the estimated position of the receiver used to collect the RINEX data is sent back to the user. Organisations that provide these free services include: Geohazards Division of Geoscience Australia, the Geodetic Survey Division (GSD) in Canada, the United States' National Geodetic Survey (NGS), Scripps Orbit and Permanent Array Center (SOPAC) at the University of California and the Jet Propulsion Laboratory (JPL) at National Aeronautics and Space Administration (NASA) [7].

1. Introduction

90 Accuracy of GNSS Methods

capability in 2020 [1, 2].

Global Navigation Satellite Systems (GNSS) is generic term for a composition of different satellite navigation technologies such as American GPS (Global Positioning System); its Russian equivalent, GLONASS (GLObal Navigation Satellite System); the Chinese system, BeiDou; the Japanese regional system, QZSS; the Indian regional system IRNSS (Indian Regional Navigation Satellite System); finally, is the European Galileo system. The GPS and GLONASS has since attained full operational status. The BeiDou, is expected to achieve completion for worldwide service in 2020, although a limited version of its signal has already been available since December 2012. The QZSS, is at present providing a limited service in the form of an augmented signal for GPS, but should be progressively upgraded and achieve full impartiality in 2023. The IRNSS, is at a final point operation as well. The Galileo system is expected to attain full operational

Global Navigation Satellite System (GNSS) is one of the most innovative and practical technology developed in recent times. Since its inception it has grown to provide not only world-wide, all weather navigation, but precise position determination capabilities to all manner of users especially for surveying and geodetic applications. In surveying and mapping, this represents a revolutionary departure from conventional surveying procedures, which relied on observed

Traditionally, it was necessary to obtain positioning with GNSS using at least two receivers, and the collected data processed for high accurate positioning using the GNSS data processing software whether scientific or commercial. However, the usage of such software is also quite difficult because they generally require deep knowledge of the GNSS, experience in the

A remarkable volume of information and resources on GNSS are available on the internet including GNSS raw data, precise GNSS satellite orbit and clock files (which are provided by the international GNSS Service (IGS) and many other organisations, as well as some GNSS processing software (e.g., see [8]). This software vary in terms availability for use (cost), accuracy, and their mode of operation which are often dependant on the technical know-how of the users. Some of the very accurate but complex to use software are GAMIT/GLOBK (from Department of Earth Atmospheric and Planetary Sciences, MIT), GIPSY/OASIS-II (from Jet Propulsion Laboratory, JPL), PAGES (from United States National Geodetic Survey, NGS). The BERNESE software (from the Astronomisches Institut der Universitat Bern, Switzerland), is a state-of-the-art GNSS processing software similar to GIPSY and GAMIT but available only commercially at a very high cost. There are also numerous MATLAB based GNSS processing system which are freely available online (e.g., see [8, 9]), however, users require requisite skills to use them. Numerous studies have explore and put forward improvements in GNSS processing system that will aid users confronted with challenges enumerated herein [5, 6, 10].

Regarding the improvements in GNSS data processing methodology, many new opportunities have been offered to the users. In this respect, many organisations have developed online

angles and distances for determining point positions [3, 4].

processing and they mostly need a licencing fee [4–7].

The only requirement for using these services is a computer having an internet connection and web browser. These services are designed to be as simple as possible for the user and with minimal input. Users of such systems have to perform uploading/sending of their collected data in RINEX format by using the web site of these services, e-mail or ftp sites to the system and selecting a few processing options. Some of these services process not only the GPS but also the data of other systems, particularly those of GLONASS, and provide resilience and a higher accurate positioning service in certain cases to their users [5].

Currently, there are several online GNSS post-processing services, and are best categorised base on their adopted approach of processing the RINEX files. Categorically, there are those that use the Precise Point Positioning (PPP) approach (see [11–13] for documentation). Those in this category include Canadian Spatial Reference System-Precise Point Positioning (CSRS-PPP), magicGNSS, (APPS) and GPS Analysis and Positioning Software (GAPS). PPP based services used the GNSS data collected with only a single receiver with precise satellite ephemerides and clock data by taking into account corrections like carrier phase wind-up, satellite antenna phase offset, solid and ocean tides. The category of the GNSS online processing services that adopted the conventional relative approach, where user's RINEX files are processed relative to other GNSS continuously operating reference stations (CORS). The Trimble RTX, Australian Surveying and Land Information Group Online GPS Processing Service (AUSPOS) and Online Positioning User Service (OPUS) are based on this approach [5].

The application/usage of these facilities are gaining global acceptance and numerous studies have evaluated the accuracy of different online GNSS processing in different part of the world (e.g. Australia, Egypt, etc.). The results of such studies have demonstrated inherent limitations, the accuracies, conveniences of online post processing of GNSS observations, and have also identified a wide range of uses within the surveying community (e.g., see [13–15]). This chapter is dedicated to the report on the accuracy of three online GNSS processing facilities (magic GNSS, GAPS, and AUSPOS) over the territory of Nigeria. The major objective of the study is to investigate the effects of the variation in the duration of GNSS observation sessions on the positional accuracy when using online processing facilities.

The structure of the paper is as follows: first a general description and status of the different online GNSS post-processing services is presented in Section 2. Section 3 explains the methods used in the data acquisition, processing and evaluation of results. Section 4 describes the results. Lastly, the concluding remarks were presented and additionally, the paper gives insight into possible future expansion of GNSS infrastructures in Nigeria.

#### 2. Overview of GNSS data processing and online services

Currently, there exist several online facilities for GNSS post processing applications. The different facilities or services are provided by different organisations and thus their mode of processing, restrictions, processing options, and format/latency of results varies. Table 1 gives a summary of the comparison of the different facilities.

Each of the above-mentioned organisations have different technical specifications with respect to service features such as membership requirement, storage limitation of the GPS/GNSS RINEX data to be uploaded, process in static/kinematic modes, evaluation the data collected by single/dual or multi frequency receiver, GPS/GNSS antenna type selection, etc. The basic requirements that the user needs to take advantage of these different services are almost the same: access to the Internet and a valid email address. The user sends a Receiver Independent Exchange Format (RINEX) file to the service and within a short period of time, the estimated position of the receiver used to collect the RINEX data is sent back to the user. Solution quality from the various processing services depends on the availability, proximity and quality of base station data, and the availability of precise satellite orbits and clock corrections.

#### 3. Methodology

Three online GNSS processing software were selected for this study. The selection was based on their mode of processing. One out of the selected three used the relative solution approach (i.e. AUSPOS) and the remaining two utilises the PPP technique (i.e. magicGNSS and GAPS).

The study utilised data from the new Nigerian GNSS Network (NIGNET) [16, 17] for the evaluation of the selected online GNSS services. Daily GNSS data in Hatanaka-compressed ASCII format were downloaded from the NIGNET site at www.nignet.net. The files were uncompressed with the freely available CRX2RNX software. The GNSS data were downloaded at the location of five different stations in the NIGNET (see Figure 1) for the year 2014. These stations include: ABUZ (Zaria); BKFP (Birnin-Kebbi); CLBR (Calabar); FUTY (Yola); and UNEC (Enugu). The stations were selected based on the data available per day (data consistency) from each station as the NIGNET is often characterised by large data gaps [18].

The GNSS data were collected at two epochs corresponding to GPS weeks 1774 and 1800, respectively. The data were collected for all 7 days in each week, it cuts across two different seasons of the year (months of January and July). The reason for this was to identify possible seasonal variations in the estimated coordinates from the different online facilities. The daily (24 h) RINEX files (observation data files) at each station were then decimated into 2, 6 and 12 h using the TEQC analysis software. This was done in order to check the effect of the length of observation session on the output of the different online GNSS processing services. The 24 h files and the decimated files were submitted to the three GNSS online processing services (magicGNSS, GAPs, and AUSPOS). After submission, both the 24 h and decimated files were processed and all the results were received via e-mail.

Service

Organisation

Software

 Supported

Data transfer

Restrictions

length of GPS data

set

 of

Available options

Coordinates

Websites

(Datum)

ITFR2008, GDA

http://wwwb.

ga.gov.au/bin/

gps.pl

http://www.

geod.nrcan.

gc.ca/

online\_data\_e.

php

2020, GDA94

IGS 2014, ITRF

2008, NAD83

(CSRS)

constellations

method

short

/company

name

AUSPOS

 Geoscience

Bernese

 GPS

Web service

Minimum of 1 h.

Dual frequency, static

observations,

 DGPS only

Maximum of 7 days

(uploading),

anonymous

 FTP

of data

 via

Australia

USA

CSRS-PPP

Natural Resources

NRCanPPP

 GPS,

Web Service

No minimum

Single and dual frequency in static

and kinematic mode, uses velocity

grid

account for crustal motion, PPP

only

(NUVEL1-A

 model) to

Maximum 6-day

long Provided

uncompressed

RINEX file is less

than 100 MB

GLONASS

(uploading)

Canada

OPUS

 National

PAGES

 GPS

Web service

Minimum 2 h.

Dual frequency, static

ITRF 2008

 http://www. ngs.noaa.gov/

OPUS/

observations.

only to central and north America

 Services available

Maximum 24 h

(uploading)

Geodetic

Survey

GAPS

 University of

GAPS

GPS, Galileo,

Uploading

 via

Minimum 2 h

 Dual frequency carrier phase static and kinematic

observations,

mode of processing,

 basic and advance

 PPP only

pseudo-range

 and

ITRF 2008, ETRF

http://gaps.

gge.unb.ca/

2005 & earlier

solutions

BeiDou

web service (supports RINEX

2, 3, and raw

data)

v6.0.0 r587

New

Brunswick

APPS

 NASA Jet

AUTO-GIPSY 6.4

GPS, GLONASS,

Uploading,

email (RINEX 2,

GIPSY TDP files)

 FTP,

Process multiple

Dual and single frequency, four

processing mode(static, NRT, most accurate), user input

pressure correction, PPP and

DGNSS services

 kinematic,

ITRF 2008

 http://apps.

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

gdgps.net/

RINEX files in a

single session, multi-day RINEX

files

BeiDou

Propulsion

Laboratory

Magic-GNSS

GMV Innovating

Magic

GPS,

Uploading

 and E-

No restrictions

 Dual frequency, static and

kinematic

observations,

 PPP only

ITRF 2008

 http:// magicgnss.

gmv.com/ppp

GLONASS,

mail (RINEX-2,

PPP client

Solutions

Trimble

Trimble

Trimble

GPS,

Uploading

Minimum of 1 h

Dual frequency

carrier phase

observations,

 PPP

pseudo-range

observations,

 static

options for other

datum, option of

plate model

 and

ITRF 2014 with

http://www.

http://dx.doi.org/10.5772/intechopen.79924

trimblertx.

com/

UploadForm.

aspx

Maximum 24 h

GLONASS,

(RINEX 2, RINEX

Galileo,

3)

BeiDou, QZSS

RTX

Navigation

office

Limited

Table 1.

Overview of the structures,

requirements,

 and processing

 options of the different online GNSS

post-processing

 services. 93

(magicAPK)

Galileo,

RINEX-3, RTCM

10403.2)

BeiDou, QZSS


Table 1. Overview of the structures, requirements, and processing options of the different online GNSS post-processing services.

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria http://dx.doi.org/10.5772/intechopen.79924 93

2. Overview of GNSS data processing and online services

a summary of the comparison of the different facilities.

3. Methodology

92 Accuracy of GNSS Methods

Currently, there exist several online facilities for GNSS post processing applications. The different facilities or services are provided by different organisations and thus their mode of processing, restrictions, processing options, and format/latency of results varies. Table 1 gives

Each of the above-mentioned organisations have different technical specifications with respect to service features such as membership requirement, storage limitation of the GPS/GNSS RINEX data to be uploaded, process in static/kinematic modes, evaluation the data collected by single/dual or multi frequency receiver, GPS/GNSS antenna type selection, etc. The basic requirements that the user needs to take advantage of these different services are almost the same: access to the Internet and a valid email address. The user sends a Receiver Independent Exchange Format (RINEX) file to the service and within a short period of time, the estimated position of the receiver used to collect the RINEX data is sent back to the user. Solution quality from the various processing services depends on the availability, proximity and quality of base

Three online GNSS processing software were selected for this study. The selection was based on their mode of processing. One out of the selected three used the relative solution approach (i.e. AUSPOS) and the remaining two utilises the PPP technique (i.e. magicGNSS and GAPS). The study utilised data from the new Nigerian GNSS Network (NIGNET) [16, 17] for the evaluation of the selected online GNSS services. Daily GNSS data in Hatanaka-compressed ASCII format were downloaded from the NIGNET site at www.nignet.net. The files were uncompressed with the freely available CRX2RNX software. The GNSS data were downloaded at the location of five different stations in the NIGNET (see Figure 1) for the year 2014. These stations include: ABUZ (Zaria); BKFP (Birnin-Kebbi); CLBR (Calabar); FUTY (Yola); and UNEC (Enugu). The stations were selected based on the data available per day (data consistency) from

The GNSS data were collected at two epochs corresponding to GPS weeks 1774 and 1800, respectively. The data were collected for all 7 days in each week, it cuts across two different seasons of the year (months of January and July). The reason for this was to identify possible seasonal variations in the estimated coordinates from the different online facilities. The daily (24 h) RINEX files (observation data files) at each station were then decimated into 2, 6 and 12 h using the TEQC analysis software. This was done in order to check the effect of the length of observation session on the output of the different online GNSS processing services. The 24 h files and the decimated files were submitted to the three GNSS online processing services (magicGNSS, GAPs, and AUSPOS). After submission, both the 24 h and decimated files were

station data, and the availability of precise satellite orbits and clock corrections.

each station as the NIGNET is often characterised by large data gaps [18].

processed and all the results were received via e-mail.

In Eqs. (1), (2), and (4); Pi is the known station coordinates for the NIGNET stations and the

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

The coordinate of the NIGNET stations were obtained in geographic unit and were converted to equivalent Universal Traverse Mercator (UTM) coordinate system with projection on the WGS 84 ellipsoid. The coordinates of the selected five NIGNET station for this study in UTM (Northing, Easting and Height) system is presented in Table 2. Similarly, all 3D coordinates obtained from the magicGNSS, GAPS, and AUSPOS were converted to UTM system for easy comparison. Appendices A.1–A.5 contain the average 3D coordinates of the stations at the 2, 6,

To compare accuracy of magicGNSS, AUSPOS, and GAPS online services, the coordinates of the selected permanent GNSS site which were originally computed using BERNESE software are taken as reference. The coordinate differences of each online services subtracted from reference coordinates of all the stations and RMSE, HRMSE, and VRMSE have been computed by Eqs. (1)–(4). The combined results of the performance measures (RMSE, HRMSE, and VRMSE) is presented in Table 3 for observations at all the permanent GNSS stations in January 2014 (first epoch).

The RMSE values for the east and north components are typically less than 0.3 m for the magic GNSS and GAPS services; while those of the AUSPOS service were higher and greater than 0.3 m in all instances as seen in Table 3. Accordingly, the HRMSE values for the magicGNSS and GAPS were also less than those from AUSPOS; also, the VRMSE values for AUSPOS are higher than those of magicGNSS and GAPS which is an indication that AUSPOS results are less accurate when compared to magicGNSS and GAPS. Figure 2 is a plot of the different performance measures, it very evident form Figure 2 that AUSPOS performs less than the other two services. Also, it can be seen the 24 h file do not always give the best results. However, AUSPOS did gave some deterrent messages on the use of 2 h files for processing.

Again, the combined results of the performance measures (RMSE, HRMSE, and VRMSE) is presented in Table 4 for observations at all the permanent GNSS stations in July 2014 (second

S/no Stations Easting (m) Northing (m) Height (m) 1. ABUZ 352440.6939 1233094.064 705.0536 2. BKFP 633587.9715 1378678.241 249.9995 3. CLBR 428111.6667 547205.768 57.1295 4. FUTY 884308.222 1035426.663 247.3917 5. UNEC 334662.4162 710405.3358 254.3912

Table 2. The UTM coordinates of the selected GNSS stations from the NIGNET.

, and n is the

95

http://dx.doi.org/10.5772/intechopen.79924

estimated coordinates from the different online GNSS services are denote by Oi

total number of observations.

4. Results and discussions

12, and 24 h observation sessions.

epoch).

Figure 1. Location of permanent GNSS stations in the Nigerian GNSS network (NIGNET).

To compare the results from the online GNSS post processing facilities with known station coordinates which were originally obtained from long time station average using BERNESE software, the residuals (differences) in northing, easting and heights components were computed for all observations in the two epoch and were employed in subsequent analysis. Consequently, the root-mean-square error (RMSE) in both the vertical and horizontal directions were computed from the differences using Eqs. (1) and (2). Similarly, the Horizontal RMSE (HRMSE) and vertical RMSE (VRMSE) were calculated using Eqs. (3) and (4);

$$RMSE\_{Normh} = \sqrt{\sum\_{i=1}^{n} \frac{\left(P\_{i,Normh} - O\_{i,Normh}\right)^2}{n}} \tag{1}$$

$$RMSE\_{East} = \sqrt{\sum\_{i=1}^{n} \frac{\left(P\_{i,East} - O\_{i,East}\right)^2}{n}} \tag{2}$$

$$HRMSE = \sqrt{\left(RMSE\_{North} \right)^2 + \left(RMSE\_{East} \right)^2} \tag{3}$$

$$VRMSE = \sqrt{\sum\_{i=1}^{n} \frac{\left(P\_{i,Vertical} - O\_{i,Vertical}\right)^2}{n}} \tag{4}$$

In Eqs. (1), (2), and (4); Pi is the known station coordinates for the NIGNET stations and the estimated coordinates from the different online GNSS services are denote by Oi , and n is the total number of observations.

#### 4. Results and discussions

To compare the results from the online GNSS post processing facilities with known station coordinates which were originally obtained from long time station average using BERNESE software, the residuals (differences) in northing, easting and heights components were computed for all observations in the two epoch and were employed in subsequent analysis. Consequently, the root-mean-square error (RMSE) in both the vertical and horizontal directions were computed from the differences using Eqs. (1) and (2). Similarly, the Horizontal

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð Þ Pi,Vertical � Oi,Vertical

n

ð Þ Pi,East � Oi,East

n

<sup>2</sup> <sup>þ</sup> ð Þ RMSEEast

ð Þ Pi,North � Oi,North

n

2

2

vuut (1)

vuut (2)

2

2

vuut (4)

(3)

RMSE (HRMSE) and vertical RMSE (VRMSE) were calculated using Eqs. (3) and (4);

Xn i¼1

> Xn i¼1

ð Þ RMSENorth

Xn i¼1

RMSENorth ¼

Figure 1. Location of permanent GNSS stations in the Nigerian GNSS network (NIGNET).

94 Accuracy of GNSS Methods

RMSEEast ¼

q

HRMSE ¼

VRMSE ¼

The coordinate of the NIGNET stations were obtained in geographic unit and were converted to equivalent Universal Traverse Mercator (UTM) coordinate system with projection on the WGS 84 ellipsoid. The coordinates of the selected five NIGNET station for this study in UTM (Northing, Easting and Height) system is presented in Table 2. Similarly, all 3D coordinates obtained from the magicGNSS, GAPS, and AUSPOS were converted to UTM system for easy comparison. Appendices A.1–A.5 contain the average 3D coordinates of the stations at the 2, 6, 12, and 24 h observation sessions.

To compare accuracy of magicGNSS, AUSPOS, and GAPS online services, the coordinates of the selected permanent GNSS site which were originally computed using BERNESE software are taken as reference. The coordinate differences of each online services subtracted from reference coordinates of all the stations and RMSE, HRMSE, and VRMSE have been computed by Eqs. (1)–(4). The combined results of the performance measures (RMSE, HRMSE, and VRMSE) is presented in Table 3 for observations at all the permanent GNSS stations in January 2014 (first epoch).

The RMSE values for the east and north components are typically less than 0.3 m for the magic GNSS and GAPS services; while those of the AUSPOS service were higher and greater than 0.3 m in all instances as seen in Table 3. Accordingly, the HRMSE values for the magicGNSS and GAPS were also less than those from AUSPOS; also, the VRMSE values for AUSPOS are higher than those of magicGNSS and GAPS which is an indication that AUSPOS results are less accurate when compared to magicGNSS and GAPS. Figure 2 is a plot of the different performance measures, it very evident form Figure 2 that AUSPOS performs less than the other two services. Also, it can be seen the 24 h file do not always give the best results. However, AUSPOS did gave some deterrent messages on the use of 2 h files for processing.

Again, the combined results of the performance measures (RMSE, HRMSE, and VRMSE) is presented in Table 4 for observations at all the permanent GNSS stations in July 2014 (second epoch).


Table 2. The UTM coordinates of the selected GNSS stations from the NIGNET.


The results from Table 4 are in very good agreement with those in earlier discussed (Table 3 for the first epoch of observations). Figure 3 is a plot of the different performance measures for

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97

From Figure 3 it is evident that the 24 h observation files and the decimated files (2, 6 and 12 h), produce results with millimetre (mm) to a centimetre (cm) level of accuracy when processed with magicGNSS and GAPS. It is again evident from Figure 3 that magicGNSS produces the best results, followed by GAPS and then AUSPOS. This is the same for the two epochs.

The AUSPOS is the only one of the three facilities that utilises the relative approach, its results were not pleasing, the poor performances of AUSPOS is attributed long baselines in the processing because of non-availability of nearby IGS stations for the processing. Thus, baselines of shorter lengths will increase the quality of data, the reliability and dependability of the online AUSPOS facilities. As earlier stated, AUSPOS again gave a warning message in processing the 2 h files indicating that the precision of estimated coordinates are outside the

All the three services investigated in this study return results to users via email. Time delay on receiving the results depends on several factors including the traffic on the Internet and the number of users accessing the service at the same time. The displayed times in Table 5 are only a rough estimates in order to compare the speed of each of the services and were obtained by

The AUSPOS is the fastest to return results, followed by GAPS and then magicGNSS; again it was found to be more user friendly, followed by magicGNSS (e-mail version) and then GAPS.

Duration (h) RMSE (E) RMSE (N) HRMSE VRMSE

 0.12714 0.12379 0.03169 0.17745 0.10241 0.11328 0.02096 0.15271 0.07737 0.11046 0.02095 0.13486 0.10147 0.10527 0.02583 0.14622

 0.58026 0.11122 0.44654 0.59082 0.56693 0.11216 0.44207 0.57792 0.57561 0.11502 0.43894 0.58699 0.68495 0.30499 0.44182 0.74979

 0.03041 0.00040 0.03958 0.03041 0.06927 0.00434 0.04003 0.06941 0.11972 0.45249 0.03421 0.46806 0.26515 0.45061 0.03841 0.52284

Table 4. Performance of online GNSS services during the second epoch of observation.

confidence level but the situation was different with magicGNSS and GAPS.

submitting the same 24 h data set to each of the service.

the second epoch of observation.

Magic GNSS

AUSPOS

GAPS

Table 3. Performance of online GNSS services during the first epoch of observation.

Figure 2. A plot of the HRMSE and VRMSE for the different online GNSS services during the first epoch of observations.

The results from Table 4 are in very good agreement with those in earlier discussed (Table 3 for the first epoch of observations). Figure 3 is a plot of the different performance measures for the second epoch of observation.

Duration (h) RMSE (E) RMSE (N) HRMSE VRMSE

 0.10823 0.10840 0.04316 0.15318 0.09798 0.12607 0.04410 0.15967 0.10634 0.11150 0.04231 0.15408 0.10768 0.10840 0.04293 0.15280

 0.37673 0.69649 0.34905 0.62703 0.36023 0.71277 0.41569 0.63781 0.34954 0.71344 0.41882 0.63118 0.38925 0.70973 0.42112 0.80946

 0.22128 0.04342 0.03108 0.22550 0.19239 0.04253 0.03108 0.19703 0.20384 0.05975 0.03153 0.21242 0.22508 0.14803 0.02749 0.26940

Figure 2. A plot of the HRMSE and VRMSE for the different online GNSS services during the first epoch of observations.

Table 3. Performance of online GNSS services during the first epoch of observation.

magicGNSS

96 Accuracy of GNSS Methods

AUSPOS

GAPS

From Figure 3 it is evident that the 24 h observation files and the decimated files (2, 6 and 12 h), produce results with millimetre (mm) to a centimetre (cm) level of accuracy when processed with magicGNSS and GAPS. It is again evident from Figure 3 that magicGNSS produces the best results, followed by GAPS and then AUSPOS. This is the same for the two epochs.

The AUSPOS is the only one of the three facilities that utilises the relative approach, its results were not pleasing, the poor performances of AUSPOS is attributed long baselines in the processing because of non-availability of nearby IGS stations for the processing. Thus, baselines of shorter lengths will increase the quality of data, the reliability and dependability of the online AUSPOS facilities. As earlier stated, AUSPOS again gave a warning message in processing the 2 h files indicating that the precision of estimated coordinates are outside the confidence level but the situation was different with magicGNSS and GAPS.

All the three services investigated in this study return results to users via email. Time delay on receiving the results depends on several factors including the traffic on the Internet and the number of users accessing the service at the same time. The displayed times in Table 5 are only a rough estimates in order to compare the speed of each of the services and were obtained by submitting the same 24 h data set to each of the service.


The AUSPOS is the fastest to return results, followed by GAPS and then magicGNSS; again it was found to be more user friendly, followed by magicGNSS (e-mail version) and then GAPS.

Table 4. Performance of online GNSS services during the second epoch of observation.

(or better results in some cases) when compared to the 24 h data set. Among the three online facilities examined in this study, the AUSPOS seems to have the most flexible and user friendly interface, followed by magicGNSS and then GAPS. As mentioned earlier, magicGNSS produces the best result, followed by GAPS and then AUSPOS. When selecting a faster means of obtaining result from these software, AUSPOS is the fastest, followed by GAPS and then magicGNSS. The reason why AUSPOS did not perform as GAPS and magicGNSS is due to the effect of long baselines in the processing and this again affirm the advantage of the PPP techniques. Regardless of the problem that might be encountered in the return of results (processed coordinate values), magicGNSS is undoubtedly the best of the three. Undoubtedly, the online GNSS facilities have brought a paradigm shift in GNSS positioning applications, in view of the accuracy and efficiency (saving cost of buying and operating a second receiver) they offer to users. It is therefore necessary that if any of these facilities (including those not considered in this study) is to be used for processing, the need for reliability and accuracy must first be considered. Finally, creating awareness among surveyors and other professionals on the functionality and dependability of online GNSS post-processing services is needed so that they can fully explore the potential of these facilities in mapping and possibly cadastral

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

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99

The authors would wish to express their profound gratitude to the numerous reviewers for their productive observations that helped to perk up this chapter. We wish to thank the office of the Surveyor General of the federal republic of Nigeria (OSGOF) for the GNSS data used in the study.

The authors avow that there no conflicts of interest regarding the publication of this manuscript.

OAI conceived the idea of the paper, MM and LA downloaded, prepared and processed all dataset used in the report, manuscript was drafted by OAI. All authors read and approved the

The mean station coordinates for ABUZ, BKFP, CLBR, FUTY, and UNEC for the two epochs of

applications in Nigeria and other parts of the world.

Acknowledgements

Conflict of interest

Authors' contribution

Appendices and nomenclature

study are presented in Appendices A.1–A.5, respectively.

final draft.

Figure 3. A plot of the HRMSE and VRMSE for the different online GNSS services during the second epoch of observations.


Table 5. Latency results from magicGNSS, AUSPOS, and GAPS online GNSS post-processing services.

The GAPS facilities has some security features which sometimes exasperate the process of submitting files for processing. Also, the advanced mode of processing in GAPS gives room to decimate files automatically by just giving the range of observation without going into the tedious processes of doing it with TEQC software.

#### 5. Concluding remarks

In this work, a comparative analysis of some online GNSS post-processing services at locations of permanent GNSS stations in Nigeria has been made. Online GNSS processing services can help users either using precise point positioning (PPP) or differential method, and without requiring a prior knowledge of GNSS processing software. Results in this project indicate that users can expect reliable results from these online services. The similarity of the results between all of the services used is amazing. That they differ only by a few millimetre (mm) or centimetre (cm) demonstrates the robustness of the algorithms and processes they employ in processing GNSS observations. Results for decimated daily RINEX files also show that users can process data sets of less than 24 h observation period and expect almost the same results (or better results in some cases) when compared to the 24 h data set. Among the three online facilities examined in this study, the AUSPOS seems to have the most flexible and user friendly interface, followed by magicGNSS and then GAPS. As mentioned earlier, magicGNSS produces the best result, followed by GAPS and then AUSPOS. When selecting a faster means of obtaining result from these software, AUSPOS is the fastest, followed by GAPS and then magicGNSS. The reason why AUSPOS did not perform as GAPS and magicGNSS is due to the effect of long baselines in the processing and this again affirm the advantage of the PPP techniques. Regardless of the problem that might be encountered in the return of results (processed coordinate values), magicGNSS is undoubtedly the best of the three. Undoubtedly, the online GNSS facilities have brought a paradigm shift in GNSS positioning applications, in view of the accuracy and efficiency (saving cost of buying and operating a second receiver) they offer to users. It is therefore necessary that if any of these facilities (including those not considered in this study) is to be used for processing, the need for reliability and accuracy must first be considered. Finally, creating awareness among surveyors and other professionals on the functionality and dependability of online GNSS post-processing services is needed so that they can fully explore the potential of these facilities in mapping and possibly cadastral applications in Nigeria and other parts of the world.

#### Acknowledgements

The authors would wish to express their profound gratitude to the numerous reviewers for their productive observations that helped to perk up this chapter. We wish to thank the office of the Surveyor General of the federal republic of Nigeria (OSGOF) for the GNSS data used in the study.

#### Conflict of interest

The GAPS facilities has some security features which sometimes exasperate the process of submitting files for processing. Also, the advanced mode of processing in GAPS gives room to decimate files automatically by just giving the range of observation without going into the

Figure 3. A plot of the HRMSE and VRMSE for the different online GNSS services during the second epoch of observations.

Min Max Min Max Min Max 2 1440 1 2 2 3

Elapsed time (min) MagicGNSS AUSPOS GAPS

Table 5. Latency results from magicGNSS, AUSPOS, and GAPS online GNSS post-processing services.

In this work, a comparative analysis of some online GNSS post-processing services at locations of permanent GNSS stations in Nigeria has been made. Online GNSS processing services can help users either using precise point positioning (PPP) or differential method, and without requiring a prior knowledge of GNSS processing software. Results in this project indicate that users can expect reliable results from these online services. The similarity of the results between all of the services used is amazing. That they differ only by a few millimetre (mm) or centimetre (cm) demonstrates the robustness of the algorithms and processes they employ in processing GNSS observations. Results for decimated daily RINEX files also show that users can process data sets of less than 24 h observation period and expect almost the same results

tedious processes of doing it with TEQC software.

5. Concluding remarks

98 Accuracy of GNSS Methods

The authors avow that there no conflicts of interest regarding the publication of this manuscript.

#### Authors' contribution

OAI conceived the idea of the paper, MM and LA downloaded, prepared and processed all dataset used in the report, manuscript was drafted by OAI. All authors read and approved the final draft.

#### Appendices and nomenclature

The mean station coordinates for ABUZ, BKFP, CLBR, FUTY, and UNEC for the two epochs of study are presented in Appendices A.1–A.5, respectively.

#### A.1. Mean station coordinates for ABUZ in the two epochs of observation

A.2. Mean station coordinates for BKFP in the two epochs of observation

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

Epoch 1 MagicGNSS 2 633588.0497 1378678.305 250.049

AUSPOS 2 633588.0703 1378678.9 250.184

GAPS 2 633588.0933 1378678.284 250.001

EPOCH 2 MagicGNSS 2 633588.047 1378678.302 250.012

AUSPOS 2 633588.0402 1378678.778 250.19

GAPS 2 633588.0417 1378678.341 250.012

Easting (m) Northing (m) Height

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6 633588.0494 1378678.302 250.048 12 633588.0496 1378678.306 250.05 24 633588.0495 1378678.305 250.048

6 633588.07 1378678.902 250.18 12 633588.0701 1378678.903 250.183 24 633588.0702 1378678.901 250.184

6 633588.093 1378678.286 250.003 12 633588.0933 1378678.284 250.004 24 633588.0932 1378678.285 249.999

6 633588.0472 1378678.303 249.999

6 633588.0404 1378678.777 250.189 12 633588.0407 1378678.775 250.19 24 633588.0402 1378678.777 250.192

6 633588.0418 1378678.342 250.01 12 633588.042 1378678.34 250.009 24 633588.0417 1378678.34 250.008

12 633588.047 1378678.303 250 24 633588.0471 1378678.301 250.013

(m)

101

Duration (h) Coordinates


#### A.2. Mean station coordinates for BKFP in the two epochs of observation

A.1. Mean station coordinates for ABUZ in the two epochs of observation

Epoch 1 MagicGNSS 2 352440.7181 1233094.105 705.054

AUSPOS 2 352441.0593 1233094.676 705.234

GAPS 2 352440.8165 1233094.156 705.073

Epoch 2 MagicGNSS 2 352440.7617 1233094.105 705.053

AUSPOS 2 352440.7509 1233094.126 705.237

GAPS 2 352440.7302 1233094.15 705.064

Easting (m) Northing (m) Height

6 352440.718 1233094.108 705.051 12 352440.7182 1233094.103 705.053 24 352440.7185 1233094.104 705.054

6 352441.0581 1233094.679 705.232 12 352441.0592 1233094.679 705.236 24 352441.056 1233094.676 705.234

6 352440.8493 1233094.155 705.071 12 352440.8274 1233094.149 705.07 24 352440.8165 1233094.154 705.073

6 352440.7508 1233094.103 705.054 12 352440.7398 1233094.1 705.053 24 352440.718 1233094.102 705.053

6 352440.729 1233094.127 705.239 12 352440.7508 1233094.122 705.24 24 352440.7507 1233094.132 705.236

6 352440.7304 1233094.146 705.065 12 352440.7305 1233094.148 705.063 24 352440.7299 1233094.148 705.064

(m)

Duration (h) Station coordinate

100 Accuracy of GNSS Methods


### A.3. Mean station coordinates for CLBR in the two epochs of observation

A.4. Mean station coordinates for FUTY in the two epochs of observation

Comparative Study of Some Online GNSS Post-Processing Services at Selected Permanent GNSS Sites in Nigeria

EPOCH 1 MagicGNSS 2 884308.2235 1035426.664 247.393

AUSPOS 2 884308.4531 1035426.813 247.572

GAPS 2 884308.2816 1035426.356 247.4

EPOCH 2 MagicGNSS 2 884308.2342 1035426.7 247.4

AUSPOS 2 884308.2779 1035426.726 247.58

GAPS 2 884307.4646 1035426.76 247.4

Easting (m) Northing (m) Height

http://dx.doi.org/10.5772/intechopen.79924

6 884308.2133 1035426.701 247.401 12 884308.2334 1035426.668 247.39 24 884308.2224 1035426.663 247.393

6 884308.3431 1035426.81 247.57 12 884307.1331 1035426.798 247.571 24 884308.4532 1035426.802 247.572

6 884308.1815 1035426.466 247.404 12 884308.2246 1035426.555 247.401 24 884308.2812 1035426.733 247.399

6 884308.1904 1035426.677 247.395 12 884308.1464 1035426.675 247.4 24 884308.2225 1035426.662 247.392

6 884308.2713 1035426.726 247.578 12 884308.2669 1035426.725 247.572 24 884308.2757 1035426.727 247.579

6 884307.5736 1035426.75 247.401 12 884307.6836 1035426.749 247.401 24 884307.8574 1035426.754 247.402

(m)

103

Duration (h) Coordinates


#### A.4. Mean station coordinates for FUTY in the two epochs of observation

A.3. Mean station coordinates for CLBR in the two epochs of observation

EPOCH 1 MagicGNSS 2 428111.7174 547205.8302 57.183

AUSPOS 2 428111.8034 547205.8643 57.344

GAPS 2 428111.7848 547205.83 57.167

EPOCH 2 MagicGNSS 2 428111.7213 547205.8316 57.188

AUSPOS 2 428111.7158 547204.7951 57.357

GAPS 2 428111.3121 547204.4158 57.178

Easting (m) Northing (m) Height

6 428111.7173 547205.8324 57.184 12 428111.717 547205.8335 57.183 24 428111.7171 547205.8314 57.183

6 428111.7912 547205.8645 57.343 12 428111.769 547205.8644 57.344 24 428111.7468 547205.8649 57.343

6 428111.7845 547205.8296 57.17 12 428111.7846 547205.8293 57.171 24 428111.7848 547205.8317 57.167

6 428111.7202 547205.8319 57.185 12 428111.7191 547205.8312 57.181 24 428111.718 547205.8316 57.182

6 428111.7147 547204.7918 57.358 12 428111.7158 547204.7929 57.357 24 428111.9527 547204.3555 57.356

6 428111.2899 547204.4192 57.18 12 428111.2566 547204.417 57.172 24 428111.2613 547204.4157 57.178

(m)

Duration (h) Coordinates

102 Accuracy of GNSS Methods


### A.5. Mean station coordinates for UNEC in the two epochs of observation

Author details

References

357-368

211-73012-6(print)

tion Systems; Dubai, UAE. 2011

10.1179/003962611X13117748892074

Press; 1997. 624 p

craymer/geodesy/gps.html [Accessed: 2018-05-12]

Olalekan Adekunle Isioye\*, Mefe Moses and Lukman Abdulmumin

Department of Geomatics, Ahmadu Bello University, Zaria, Kaduna, Nigeria

New York: Springer-Verlag; 2012. ISBN: 978-3-540-88255-8(Print)

[1] Hoffmann-Wellenhof B, Litchtenegger H, Wasle E. GNSS—Global Navigation Satellite Systems: GPS, GLONASS, Galileo and More. Vienna: Springer-Verlag; 2008. ISBN: 987-3-

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[2] Shaw M. GPS Modernization: On the Road to the Future GPS IIR/IIR-M and GPS III.UN/ UAE/US Workshop on GNSS Applications, Session 1: Trends in Satellite-Based Naviga-

[3] Awange JL. Environmental Monitoring Using GNSS: Global Navigation Satellite Systems.

[4] Ocalan T. Accuracy assessment of GPS precise point positioning (PPP) technique using different web-based online Services in a forest environment. Sumarski List. 2016;7-8:

[5] Alkan RM, Ozulu M, Ilci V. Web-based GNSS data processing services as an alternative to conventional processing technique. In: FIG Working Week 2016; New Zealand. pp. 1-35

[6] Satirapod C, Wong K, Rizos C. A web-based automated GPS processing system. In: The Proceedings of the 2nd Trans-Tasman Surveyors Congress, Queenstown; 20–26 August 2000; New Zealand. Available from: https://www.researchgate.net/publication/250222229\_ A\_WEB-BASED\_AUTOMATED\_GPS\_PROCESSING\_SYSTEM. [Accessed: 2018-05-12]

[7] El-Mowafy A. Analysis of web-based GNSS post-processing services for static and kinematic positioning using short data spans. Survey Review. 2013;43(323):535-549. DOI:

[8] On-line Geodesy Resources: GPS. 2018. Available from: http://www3.sympatico.ca/

[9] Strang G, Borre K. Linear Algebra, Geodesy, and GPS. Wellesley: Wellesley-Cambridge

[10] Isioye OA, Enebeli I, Shebe MW, Mefe M. Near real time processing solution of differential GPS positioning using internet technology. Asian Journal of Engineering Science and Technology. 2011;1(2):58-66. A publication of the Faculty of Engineering, Sciences and

\*Address all correspondence to: lekkyside4u@yahoo.com


#### Author details

A.5. Mean station coordinates for UNEC in the two epochs of observation

EPOCH 1 MagicGNSS 2 334662.5036 710405.410 254.383

AUSPOS 2 334662.5126 710405.410 254.573

GAPS 2 334662.4889 710,405. 429 254.394

EPOCH 2 magicGNSS 2 334662.4904 710405.4100 254.383

AUSPOS 2 334662.483 710405.398 254.6

GAPS 2 334662.4897 710405.4041 254.4

Easting (m) Northing (m) Height

6 334662.4914 710405.413 254.380 12 334662.4899 710405.416 254.384 24 334662.5036 710405.418 254.383

6 334662.5134 710405.411 254.570 12 334662.5105 710405.417 254.569 24 334662.5145 710405.415 254.573

6 334662.4919 710405.433 254.389 12 334662.4962 710405.388 254.390 24 334662.4979 710405.391 254.390

6 334662.4907 710405.4102 254.380 12 334662.491 710405.4096 254.378 24 334662.4916 710405.4106 254.383

6 334662.4826 710405.3992 254.59 12 334662.4832 710405.3997 254.588 24 334662.4826 710405.3983 254.588

6 334662.4895 710405.4049 254.399 12 334662.4899 710405.406 254.397 24 334662.4871 710405.405 254.399

(m)

Duration (h) Coordinates

104 Accuracy of GNSS Methods

Olalekan Adekunle Isioye\*, Mefe Moses and Lukman Abdulmumin

\*Address all correspondence to: lekkyside4u@yahoo.com

Department of Geomatics, Ahmadu Bello University, Zaria, Kaduna, Nigeria

#### References


Technology, Iqra University, Karachi, Pakistan, September 2011. Available from: http:// ajest.iqra.edu.pk/journal.php. ISSN: 2007-1142

**Section 5**

**Accuracy of Positions Derived from the**

**and GNSS**

**Combination of Terrestrial Geodetic Techniques**

