**1. Introduction**

The ionosphere is important to our existence as it affects our radio communication systems, especially our satellite communication systems. Particularly, the ionosphere poses the greatest natural challenge for our global navigation satellite systems (GNSS) when it comes to precise position measurement by ground-based receivers. There are a couple of satellite navigation systems, e.g. the United States' GPS (Global Positioning System), Russia's GLONASS (Global Navigation Satellite System), European Union's GALILEO, China's

© 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.

BEIDOU (or COMPASS), etc. The GPS is the most common and the most popular of the GNSS systems, and so in this chapter, we will carefully use the two words interchangeably. The evolution of our navigation requirements into satellite-based systems is therefore adding a rapid stair to interest in ionospheric research. The greatest efforts in ionospheric research have been directed towards ionospheric modeling, and related studies that tend to understand how the ionosphere changes in time and space. Several ionospheric models have been developed (e.g. Ref. [1–7]).

The computation in Eq. (1) is based on the assumption that radio signals (which are electromagnetic) travel at the constant speed of about c = 2.998 × 108 ms−1 in vacuum. And this is where the problem of the ionosphere comes in. The space between the satellites and receivers is not entirely vacuum; there is an intervening region containing ionized matter known as the ionosphere. Because of ionized matter contained in the ionosphere, electromagnetic waves (e.g. the transmitted radio signals) do not travel through the ionosphere at the constant speed of about c = 2.998 × 108 ms−1. The signals are delayed, and this delay is interpreted in Eq. (1) as part of the travel time. This introduces an error into the computed range (the computed range is greater than the actual or true range) which therefore subsequently manifests as an error in

GPS Modeling of the Ionosphere Using Computer Neural Networks

http://dx.doi.org/10.5772/intechopen.75087

49

An obviously intelligent thing to do is to remove this effect of the delay introduced by the ionosphere, but this is only possible if we know how much the delay is. To make the situation worse, the ionosphere is highly dynamic; it changes appreciably over space and time. We therefore need to know the extent of ionospheric ionization at any given time along the radio route so as to be able to correct for the effect of the ionosphere on the radio signal. This is where ionospheric models are useful. Ionospheric models can be used to now-cast (and even fore-cast) the extent of ionospheric ionization over space and time. And by so doing, ionospheric models are useful and usually applied in GPS error correction for single frequency

Single frequency receivers are GNSS receivers that can receive radio signals from the satellites in only one frequency. These are the most common types of GNSS receivers we see in everyday usage. They are cost-effective but incapable of estimating the ionospheric delay. On the other hand, there are dual or more frequency receivers which can receive GNSS radio signals at two or more frequencies. In the explanation that follows (on the Data and Methods section), dual or more frequency GNSS receivers are capable of estimating the ionospheric delays, and therefore capable of internally removing the effects of such delays. These types of receivers are mainly used for research and other specialized usages. It is from these types of receivers that data used in this chapter was obtained. There is general intuition that dual-frequency receivers are better than single frequency ones, but in highlighting the tradeoffs between the two, Ref. [9] explained that, asides cost effectiveness of the single frequency receivers, a single frequency receiver may actually outperform the more advanced dual-frequency receiver in terms of accuracy during the first 10 minutes or so, and also in places associated with frequent loss of lock on GNSS signals. Rather than using dual-frequency receivers, some applications therefore prefer using ionospheric models on single frequency receivers to correct for the effects of the ionosphere. The accuracy obtained from this practice however depends on the accuracy of the model used; more accurate models will give more accurate GNSS positions. The development of a regional GPS model of the ionosphere (with improved accuracy) is presented in this chapter. The modeling technique used is the method of computer neural

Computer neural networks (also commonly referred to as neural networks or just NNs for short) have capability for machine learning as well as pattern recognition, and they have been demonstrated to be powerful tools for predictive modeling. NNs operate in a manner

the computed receiver position.

receivers.

networks.

To understand exactly how the ionosphere influences our satellite-based navigation systems, it is important to understand how satellite-based navigation systems work. A more detailed introduction to the GNSS is presented by Ref. [8], but the core ideas are briefly and elegantly presented here. A satellite-based navigation system basically consists of some satellites in space. The satellites know their positions in space through the help of ground-based control stations and some internal programming. Through on-board transmitters on the satellites, each satellite continuously transmits radio signals. Each radio signal contains information about the 3-D position in space of the satellite from which it is transmitted, and the time in which the signal is transmitted. GPS receivers on ground (like the ones you and I own in cell phones and other devices) can receive these signals and automatically be able to compute the receivers' 3-D positions.

Exactly how does this happen? How does a GPS receiver know its position by merely receiving position and time stamped radio signals from the satellites? The GPS receivers use in-built computer programs to compute their own positions from the positions of the satellite they receive signals from. The computer programs are based on quite simple geometric calculations. The geometric calculations are based on the premise that if we know the exact 3-D positions of any three objects and the exact range to each of them, then we would be able to determine our own 3-D position. It is emphasized here that the positions of three objects are required because we are interested in 3-D positions. If we are interested in knowing our position in 2-D space, then we will require the positions of only two objects. In the case of the GPS, the interest is to know the 3-D position of the receiver as well as the time the signal is received (this makes 4-D), so we need four objects. A GPS receiver will therefore be able to compute its exact position and time if it receives signals from at least four satellites. From the satellite radio signals they receive, GPS receivers retrieve information on the 3-D positions and times of the satellites as well as the exact range to each of them.

As explained earlier, we know that each of the signals already contain information on the 3-D positions and times of the satellites, but how do the receivers know the ranges to the satellites? GPS receivers estimate ranges to the satellites by using the formula

$$\text{Range} = \text{speed of radio signal} \times \text{travel time} \tag{1}$$

The travel time is how long the radio signals have traveled between their transmission and their reception (That is the time difference between when the signals were transmitted from the satellite and when they were received). The signals already contain information on when they were transmitted from the satellite, and the receiver time is one of the four parameters the receiver will compute.

The computation in Eq. (1) is based on the assumption that radio signals (which are electromagnetic) travel at the constant speed of about c = 2.998 × 108 ms−1 in vacuum. And this is where the problem of the ionosphere comes in. The space between the satellites and receivers is not entirely vacuum; there is an intervening region containing ionized matter known as the ionosphere. Because of ionized matter contained in the ionosphere, electromagnetic waves (e.g. the transmitted radio signals) do not travel through the ionosphere at the constant speed of about c = 2.998 × 108 ms−1. The signals are delayed, and this delay is interpreted in Eq. (1) as part of the travel time. This introduces an error into the computed range (the computed range is greater than the actual or true range) which therefore subsequently manifests as an error in the computed receiver position.

BEIDOU (or COMPASS), etc. The GPS is the most common and the most popular of the GNSS systems, and so in this chapter, we will carefully use the two words interchangeably. The evolution of our navigation requirements into satellite-based systems is therefore adding a rapid stair to interest in ionospheric research. The greatest efforts in ionospheric research have been directed towards ionospheric modeling, and related studies that tend to understand how the ionosphere changes in time and space. Several ionospheric models

To understand exactly how the ionosphere influences our satellite-based navigation systems, it is important to understand how satellite-based navigation systems work. A more detailed introduction to the GNSS is presented by Ref. [8], but the core ideas are briefly and elegantly presented here. A satellite-based navigation system basically consists of some satellites in space. The satellites know their positions in space through the help of ground-based control stations and some internal programming. Through on-board transmitters on the satellites, each satellite continuously transmits radio signals. Each radio signal contains information about the 3-D position in space of the satellite from which it is transmitted, and the time in which the signal is transmitted. GPS receivers on ground (like the ones you and I own in cell phones and other devices) can receive these signals and automatically be able to compute the receivers' 3-D positions.

Exactly how does this happen? How does a GPS receiver know its position by merely receiving position and time stamped radio signals from the satellites? The GPS receivers use in-built computer programs to compute their own positions from the positions of the satellite they receive signals from. The computer programs are based on quite simple geometric calculations. The geometric calculations are based on the premise that if we know the exact 3-D positions of any three objects and the exact range to each of them, then we would be able to determine our own 3-D position. It is emphasized here that the positions of three objects are required because we are interested in 3-D positions. If we are interested in knowing our position in 2-D space, then we will require the positions of only two objects. In the case of the GPS, the interest is to know the 3-D position of the receiver as well as the time the signal is received (this makes 4-D), so we need four objects. A GPS receiver will therefore be able to compute its exact position and time if it receives signals from at least four satellites. From the satellite radio signals they receive, GPS receivers retrieve information on the 3-D positions and times

As explained earlier, we know that each of the signals already contain information on the 3-D positions and times of the satellites, but how do the receivers know the ranges to the satel-

Range = speed of radio signal × travel time (1)

The travel time is how long the radio signals have traveled between their transmission and their reception (That is the time difference between when the signals were transmitted from the satellite and when they were received). The signals already contain information on when they were transmitted from the satellite, and the receiver time is one of the four parameters

have been developed (e.g. Ref. [1–7]).

48 Multifunctional Operation and Application of GPS

of the satellites as well as the exact range to each of them.

the receiver will compute.

lites? GPS receivers estimate ranges to the satellites by using the formula

An obviously intelligent thing to do is to remove this effect of the delay introduced by the ionosphere, but this is only possible if we know how much the delay is. To make the situation worse, the ionosphere is highly dynamic; it changes appreciably over space and time. We therefore need to know the extent of ionospheric ionization at any given time along the radio route so as to be able to correct for the effect of the ionosphere on the radio signal. This is where ionospheric models are useful. Ionospheric models can be used to now-cast (and even fore-cast) the extent of ionospheric ionization over space and time. And by so doing, ionospheric models are useful and usually applied in GPS error correction for single frequency receivers.

Single frequency receivers are GNSS receivers that can receive radio signals from the satellites in only one frequency. These are the most common types of GNSS receivers we see in everyday usage. They are cost-effective but incapable of estimating the ionospheric delay. On the other hand, there are dual or more frequency receivers which can receive GNSS radio signals at two or more frequencies. In the explanation that follows (on the Data and Methods section), dual or more frequency GNSS receivers are capable of estimating the ionospheric delays, and therefore capable of internally removing the effects of such delays. These types of receivers are mainly used for research and other specialized usages. It is from these types of receivers that data used in this chapter was obtained. There is general intuition that dual-frequency receivers are better than single frequency ones, but in highlighting the tradeoffs between the two, Ref. [9] explained that, asides cost effectiveness of the single frequency receivers, a single frequency receiver may actually outperform the more advanced dual-frequency receiver in terms of accuracy during the first 10 minutes or so, and also in places associated with frequent loss of lock on GNSS signals. Rather than using dual-frequency receivers, some applications therefore prefer using ionospheric models on single frequency receivers to correct for the effects of the ionosphere. The accuracy obtained from this practice however depends on the accuracy of the model used; more accurate models will give more accurate GNSS positions. The development of a regional GPS model of the ionosphere (with improved accuracy) is presented in this chapter. The modeling technique used is the method of computer neural networks.

Computer neural networks (also commonly referred to as neural networks or just NNs for short) have capability for machine learning as well as pattern recognition, and they have been demonstrated to be powerful tools for predictive modeling. NNs operate in a manner that is similar to the human brain; the networks are composed of simple elements operating in parallel and inspired by the biological nervous system. NNs can learn trends and patterns in particular data they are given and consequently be able to correctly predict unseen and future trends for the data. A neural network can be trained to perform a particular function by adjusting the value of connections (also called weights) between elements [7]. The true power and advantages of neural networks lies in the ability to represent both linear and nonlinear relationships directly from the data being modeled. Traditional linear models are simply inadequate when it comes for true modeling data that contains non-linear characteristics [8]. Recent explosion of ionospheric data from the GNSS is spurring interest in using computer neural networks for ionospheric modeling. A number of works have shown that neural networks (NNs) are good candidates for ionospheric modeling [6, 7, 10–13]. In this chapter, neural networks have been used to develop a regional model of the ionosphere over Nigeria. Predictions from the model have also been demonstrated to be more improved in terms of accuracy when compared to predictions from global ionospheric models like the IRI-Plas (International Reference Ionosphere—extended to the Plasmasphere) and the NeQuick.
