4.5. Real time availability

The real time availability assessment is performed if the model strength assessment was passed successfully (VPL < VAL). At each epoch, once the observations are collected, the WSSE is computed and compared with the threshold. As in standard hypothesis testing, we have the following decision rule:

If WSSE > k, reject the fault-free hypothesis and declare Alert (20)

else standard operations continue.

#### 4.6. ARAIM

the error in the range domain propagates into the position domain. The original Weighted RAIM algorithm focuses on monitoring only the vertical component of the position solution, but the same reasoning can be made for the other components. In a simple two-dimensional

axis, their relation can be represented by a straight line (see Figure 3), with a steepness (slope),

<sup>V</sup>slope<sup>i</sup> <sup>¼</sup> <sup>∣</sup>S½ � <sup>3</sup>;<sup>i</sup> <sup>∣</sup>σ<sup>i</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

indicate the indexes of the matrix elements'. The Vertical Protection Level (VPL) is computed as:

<sup>q</sup> � �; kMD <sup>¼</sup> <sup>Ψ</sup>�<sup>1</sup> <sup>P</sup>HMI

dom, Ψð Þ� the tail probability of the cumulative distribution function of a zero mean unit Gaussian distribution, and p the a-priori probability of hazardous fault in one satellite. The above formulas for the VPL are based on the following expression of the integrity risk under

<sup>P</sup>HMI∣H<sup>i</sup> <sup>¼</sup> <sup>P</sup>MD<sup>i</sup> � <sup>P</sup> <sup>j</sup>bx<sup>3</sup> � <sup>x</sup>3<sup>j</sup> <sup>&</sup>gt; VALjH<sup>i</sup>

which assumes that an integrity event corresponds to the simultaneous occurrence of an MD and a positioning error larger than the Vertical AL (VAL), and is justified by the fact that test

CDFð Þ �; <sup>m</sup> � <sup>n</sup> the inverse of a central <sup>χ</sup><sup>2</sup> CDF function with <sup>m</sup> � <sup>n</sup> degrees of free-

ffiffiffiffiffiffiffi Qyi q

Vslope<sup>i</sup> � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

CDF PFA; m � n

WSSE p on the horizontal axis and the vertical position error on the vertical

<sup>p</sup> (16)

¼ σyi and where the subscripts in square brackets

k þ kMDσx^<sup>3</sup> i ¼ 1, 2, …, m (17)

m p � �

� � (19)

(18)

1 � PA½ � <sup>i</sup>;<sup>i</sup>

graph, plotting ffiffiffiffiffiffiffiffiffiffiffiffiffi

for satellite i given by:

with <sup>S</sup> <sup>¼</sup> <sup>A</sup>TQ�<sup>1</sup>

with inv-χ<sup>2</sup>

<sup>y</sup> A � ��<sup>1</sup>

34 Multifunctional Operation and Application of GPS

where k and kMD are obtained as:

an alternative hypothesis:

k ¼

Figure 3. Representation of the weighted RAIM's Vslope concept.

ATQ�<sup>1</sup>

<sup>y</sup> , σ<sup>i</sup> ¼

VPL � max i

inv-χ<sup>2</sup>

The Weighted RAIM presented in the previous section was developed for the single GPS constellation and has been found generally suboptimal, even though presenting a very practical and efficient approach. An enhanced approached, known as ARAIM, provides the following improvements [14]:


The basic concepts of ARAIM are here outlined. For more details, see [14, 18, 19]. Figure 4 shows a block diagram representation of the ARAIM algorithm. From a statistical point of view, ARAIM is based on the following concepts:


Figure 4. ARAIM baseline architecture. The algorithm checks the coherency of the observations by means of the solution separation tests, evaluates the possibility of excluding corrupted observations with exclusion specific tests, and computes the PLs. Integrity is guaranteed if PLs < ALs.

If one characterizes each alternative hypothesis by a different subscript i, the i th Solution Separation vector can be written as:

$$\underline{T}\_{\rm SS} = \underline{\widehat{\nabla}\widehat{\mathbf{x}}\_{i}} = \widehat{\underline{\mathbf{x}}}\_{0} - \widehat{\underline{\mathbf{x}}}\_{i} \tag{21}$$

where in the last equality the relation (19) is applied. As a result, the VPL must satisfy the

where ki,<sup>3</sup> is the test threshold for the i th SS test, 3 rd component (vertical), and ζ is the fraction of the full PHMI allocated to the vertical direction (0 < ζ < 1). The HPL instead is computed

x2

where σ∇^ <sup>x</sup>^i,j is the standard deviation of the corresponding SS test statistic (see [18]). If any

1. Detection tests: the SS tests are computed and compared to their thresholds; if none of the tests exceeds the threshold, the fault-free hypothesis is confirmed and standard operations

2. Exclusion confirmation tests: extra tests are run to determine if it is safe to exclude some observations and continue to provide navigation service. These tests are meant to mini-

After detection and eventual exclusion of observations, the PLs are re-computed (as postobservations PLs) and compared with the thresholds. If any PLpost > AL, an Alert is raised.

As mentioned in Section 1.2, when moving from aviation to land applications, a number of issues have to be taken into account in the context of integrity monitoring. The main two issues are:

• Positioning has to be performed in urban environment: additional vulnerabilities are to be

• Higher precision/smaller PLs are required: this may lead to the use of precise positioning techniques (PPP, RTK) with their additional vulnerabilities, as well as additional naviga-

The main assumptions on which the FDE procedures and RAIM algorithms described so far rely on are (Section 4.2): 1) linear estimation problem, 2) Gaussianity of the observables and 3)

4Na

<sup>Ψ</sup> VPL � ki, <sup>3</sup> σbxi ,1 !

¼ ζPHMI (24)

http://dx.doi.org/10.5772/intechopen.75777

37

, the PLs for the two horizontal components,

Integrity Monitoring: From Airborne to Land Applications

� �σ∇^ <sup>x</sup>^i,j (25)

following equation [18]:

q

4.8. Real time availability

5. The ITS challenge

with HPL ¼

<sup>2</sup><sup>Ψ</sup> VPL σbx0,3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PL<sup>2</sup>

<sup>x</sup><sup>1</sup> <sup>þ</sup> PL<sup>2</sup> x2

In ARAIM the testing is subdivided in two steps:

!

, where PL<sup>2</sup>

PL > AL, integrity is not available for the geometry considered.

continue, otherwise the algorithm proceeds to the next step.

mize the risk of wrong identification. More details are given in [18].

taken into account, i.e., multipath, NLOS, interference and spoofing.

tion sensors/technologies (INS,V2I and V2I communication, camera, etc.).

þ<sup>X</sup> Na

i¼1 pi

<sup>x</sup><sup>1</sup> and PL2

are computed with formulas equivalent to (24). The thresholds ki,j are computed with

ki,j ¼ �Ψ�<sup>1</sup> <sup>P</sup>FA

where <sup>b</sup>x<sup>0</sup> and <sup>b</sup>xi are the position solutions obtained employing the null and the alternative model respectively, i e.:

$$\begin{aligned} \widehat{\underline{\mathbf{x}}}\_{0} &= \left(A^{T} \mathbf{Q}\_{y}^{-1} A\right)^{-1} A^{T} \mathbf{Q}\_{y}^{-1} \underline{\mathbf{y}} = \underline{\mathbf{S}} \underline{\mathbf{y}} \\ \widehat{\underline{\mathbf{x}}}\_{i} &= \left(A^{T} \mathbf{Q}\_{y\_{i}}^{-1} A\right)^{-1} A^{T} \mathbf{Q}\_{y\_{i}}^{-1} \underline{\mathbf{y}} = \mathbf{S}\_{i} \underline{\mathbf{y}} \end{aligned} \tag{22}$$

where Q�<sup>1</sup> yi is obtained from <sup>Q</sup>�<sup>1</sup> <sup>y</sup> replacing the diagonal elements corresponding to the faulty satellites in hypothesis H<sup>i</sup> with 0 (this means giving zero weight to such observations). In practice, these tests have similar performance to the UMPI tests (see [20, 21]).

#### 4.7. Model strength assessment

The PLs are computed on the basis of the model strength (satellite geometry and stochastic model), and compared to the AL to determine the integrity availability. The computation of the PLs is based on an iterative procedure: the PLs are determined in such a way that the sum of the PHMI<sup>i</sup> under each alternative hypothesis is equal to the full PHMI requirement:

$$\overline{P}\_{\text{HMI}} = \sum\_{i}^{N\_x} P\_{\text{HMI}\_i} = \sum\_{i}^{N\_x} \left[ P\_{\text{MD}\_i} \cdot P(\widehat{\underline{\mathbf{x}}} - \mathbf{x} \notin \Omega\_{\text{AL}} | \mathcal{H}\_i) \right] \tag{23}$$

where in the last equality the relation (19) is applied. As a result, the VPL must satisfy the following equation [18]:

$$2\Psi\left(\frac{\text{VPL}}{\sigma\_{\widehat{x}\_{0,3}}}\right) + \sum\_{i=1}^{N\_s} p\_i \Psi\left(\frac{\text{VPL} - k\_{i,3}}{\sigma\_{\widehat{x}\_i} \cdot 1}\right) = \zeta \overline{P}\_{\text{HMI}}\tag{24}$$

where ki,<sup>3</sup> is the test threshold for the i th SS test, 3 rd component (vertical), and ζ is the fraction of the full PHMI allocated to the vertical direction (0 < ζ < 1). The HPL instead is computed with HPL ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PL<sup>2</sup> <sup>x</sup><sup>1</sup> <sup>þ</sup> PL<sup>2</sup> x2 q , where PL<sup>2</sup> <sup>x</sup><sup>1</sup> and PL2 x2 , the PLs for the two horizontal components, are computed with formulas equivalent to (24). The thresholds ki,j are computed with

$$k\_{i,j} = -\Psi^{-1}\left(\frac{P\_{\rm FA}}{4N\_d}\right)\sigma\_{\bar{\nabla}\hat{x}\_{i,j}}\tag{25}$$

where σ∇^ <sup>x</sup>^i,j is the standard deviation of the corresponding SS test statistic (see [18]). If any PL > AL, integrity is not available for the geometry considered.

#### 4.8. Real time availability

If one characterizes each alternative hypothesis by a different subscript i, the i th Solution

Figure 4. ARAIM baseline architecture. The algorithm checks the coherency of the observations by means of the solution separation tests, evaluates the possibility of excluding corrupted observations with exclusion specific tests, and computes

where <sup>b</sup>x<sup>0</sup> and <sup>b</sup>xi are the position solutions obtained employing the null and the alternative

satellites in hypothesis H<sup>i</sup> with 0 (this means giving zero weight to such observations). In

The PLs are computed on the basis of the model strength (satellite geometry and stochastic model), and compared to the AL to determine the integrity availability. The computation of the PLs is based on an iterative procedure: the PLs are determined in such a way that the sum of

ATQ�<sup>1</sup>

ATQ�<sup>1</sup>

<sup>y</sup> y ¼ Sy

yi y ¼ Siy

<sup>P</sup>MD<sup>i</sup> � <sup>P</sup>ð Þ <sup>b</sup><sup>x</sup> � <sup>x</sup> <sup>∉</sup> <sup>Ω</sup>ALjH<sup>i</sup>

� � (23)

<sup>y</sup> replacing the diagonal elements corresponding to the faulty

<sup>y</sup> A � ��<sup>1</sup>

yi A � ��<sup>1</sup>

<sup>b</sup>x<sup>0</sup> <sup>¼</sup> ATQ�<sup>1</sup>

<sup>b</sup>xi <sup>¼</sup> <sup>A</sup>TQ�<sup>1</sup>

practice, these tests have similar performance to the UMPI tests (see [20, 21]).

the PHMI<sup>i</sup> under each alternative hypothesis is equal to the full PHMI requirement:

<sup>P</sup>HMI<sup>i</sup> <sup>¼</sup> <sup>X</sup> Na

i

<sup>P</sup>HMI <sup>¼</sup> <sup>X</sup> Na

i

<sup>T</sup>SS<sup>i</sup> <sup>¼</sup> <sup>∇</sup>bbxi <sup>¼</sup> <sup>b</sup>x<sup>0</sup> � <sup>b</sup>xi (21)

(22)

Separation vector can be written as:

the PLs. Integrity is guaranteed if PLs < ALs.

36 Multifunctional Operation and Application of GPS

yi is obtained from <sup>Q</sup>�<sup>1</sup>

4.7. Model strength assessment

model respectively, i e.:

where Q�<sup>1</sup>

In ARAIM the testing is subdivided in two steps:


After detection and eventual exclusion of observations, the PLs are re-computed (as postobservations PLs) and compared with the thresholds. If any PLpost > AL, an Alert is raised.

#### 5. The ITS challenge

As mentioned in Section 1.2, when moving from aviation to land applications, a number of issues have to be taken into account in the context of integrity monitoring. The main two issues are:


The main assumptions on which the FDE procedures and RAIM algorithms described so far rely on are (Section 4.2): 1) linear estimation problem, 2) Gaussianity of the observables and 3) mean-shift model for the anomalies. In land applications, these assumptions are likely to hold, though multipath and NLOS may challenge the second one, while the large number of observations available and vulnerabilities increases the computational complexity of FDE procedures. These aspects are addressed in more detail in the following.

one of the critical elements in determining the Time to Ambiguity Resolution (TAR), which can become of concern in regards of timeliness requirements. Furthermore, cycle-slips, which constitute the main RTK-specific threat, as they can cause wrong ambiguity fixing and result in large errors in the positioning, require specific additional monitoring. There is a vast literature on cycle-slip detection, e.g., by [26, 27]. Most cycle-slip detection methods are based on hypothesis

Integrity Monitoring: From Airborne to Land Applications

http://dx.doi.org/10.5772/intechopen.75777

39

Use of multiple sensors for navigation means that extra observations shall be integrated with the GNSS observations. If the extra observations are linear in the unknown parameters, they can be simply stacked together in the same linear estimation problem. Integration with INS is a complex problem on which a large literature exist [28]. Finally, while the focus of this chapter was only on snapshot RAIM (single epoch), RAIM techniques for multi-epoch recursive data

Section 2.4 shows that an integrity assessment can be made before the observations are taken, when only satellite geometry and environment are known or partially known. New IM concepts intend to exploit the fact that satellite geometry and satellite visibility can be reasonably predicted at any time and location (for instance with the use of city models), and that the same observability conditions repeat periodically over time. Beside the environment nearby the receiver in its nominal conditions, these new concepts plan to exploit also the potentialities offered by a Vehicular Ad-hoc Network (VANET) infrastructure [30]. The potential availability of multiple observations of GNSS signals, taken by different vehicles participating to a VANET, can be shared and combined in order to implement a collaborative spatial/temporal character-

In this section, the results of a first attempt to perform IM in urban environment employing the RTK positioning method with a short baseline, and applying a prototype ARAIM algorithm, are shown. Such results are only indicative, since most of the assumptions behind the use of

A kinematic test is conducted for practical demonstration of IM for ITS. A small vehicle is fitted with a Trimble multi-GNSS geodetic receiver and a survey-grade antenna. The test is carried out in a dense urban area in Tokyo, Japan. The RTK system uses GPS, GLONASS and BeiDou dualfrequency observations with a sampling rate of 10 Hz. A prototype RAIM algorithm derived from ARAIM is implemented. Due to the lack of common standards, the PLs are computed in the test using different values of PHMI ranging from 10<sup>3</sup> to 10<sup>6</sup> in order to track empirically the

impact of PHMI on the obtained results. A false alert probability (PFA) of 0.01 is applied.

testing, but exploit the multi-epoch data processing to increase their detection power.

5.2.2. Multi-sensor integration and recursive data processing

processing are under development [29].

6. An example

5.2.3. Cooperative integrity monitoring (CIM) concept

ARAIM in an RTK set-up are yet to be justified.

ization and prediction of the local degradation of the GNSS signals.

#### 5.1. Urban environment: multipath, NLOS and interference

Multipath is the most significant source of measurement errors in ITS applications, as it is dependent on the environment surrounding the antenna and is especially intense in dense urban areas. Buildings and other obstacles degrade the signal reception in three ways: 1) signals are completely blocked and unavailable for positioning, 2) signals are blocked in their direct path, but are still received via a reflected path, with the NLOS reception, 3) both direct Line-Of-Sight (LOS) and reflected signals are received, i.e., the case of multipath. NLOS code signals can exhibit positive ranging errors of tens of meters magnitude in dense urban areas.

Numerous innovative techniques have been developed in the recent years to address the multipath and NLOS threats in urban environment. Interest was raised by 3D-map-aided (3DMA) GNSS, a range of different techniques that use 3D mapping data to improve GNSS positioning accuracy in dense urban areas. 3D models of the buildings can be used to predict which signals are blocked and which are directly visible at any location [22, 23]. A technique that determines position by comparing the measured signal availability and strength with predictions made using a 3D city model over a range of candidate positions is known as the shadow matching technique [24]. Such techniques may possibly be integrated with RAIM algorithms for ITS in the near future.

#### 5.2. Precise positioning techniques and multi-sensor integration

The use of precise positioning techniques rather than SPP and the need of integration with other sensors bring a number of complications to the IM for land applications. Some of the main challenges are summarized in the following.

#### 5.2.1. PPP and RTK: Carrier phase observations vulnerabilities

Precise positioning techniques employ carrier phase observations next to code observations. Even though the estimation problem is characterized by a much larger number of observations and unknowns to solve for, it is still a linear estimation problem. The same hypothesis testing theory applies, and therefore, the same RAIM concepts developed for aviation can be implemented, with appropriate adjustments. However, one drawback of the ARAIM is the associated heavy computational burden, due to the need of running a test for each possible combination of simultaneously biased observations. When multi-systems, multi-frequency and carrier phase based positioning is in use, the total number of combinations of possibly biased observations increases dramatically — so does the computational load for the algorithm. It is thus possible that the current ARAIM approach will not be optimal.

Another issue is constituted by the additional vulnerabilities that affect the precise positioning techniques, mainly carrier phase multipath and cycle-slips. Multipath affects carrier-phase observations with the same mechanism as code observations [25]. Carrier-phase multipath is one of the critical elements in determining the Time to Ambiguity Resolution (TAR), which can become of concern in regards of timeliness requirements. Furthermore, cycle-slips, which constitute the main RTK-specific threat, as they can cause wrong ambiguity fixing and result in large errors in the positioning, require specific additional monitoring. There is a vast literature on cycle-slip detection, e.g., by [26, 27]. Most cycle-slip detection methods are based on hypothesis testing, but exploit the multi-epoch data processing to increase their detection power.

#### 5.2.2. Multi-sensor integration and recursive data processing

Use of multiple sensors for navigation means that extra observations shall be integrated with the GNSS observations. If the extra observations are linear in the unknown parameters, they can be simply stacked together in the same linear estimation problem. Integration with INS is a complex problem on which a large literature exist [28]. Finally, while the focus of this chapter was only on snapshot RAIM (single epoch), RAIM techniques for multi-epoch recursive data processing are under development [29].

#### 5.2.3. Cooperative integrity monitoring (CIM) concept

Section 2.4 shows that an integrity assessment can be made before the observations are taken, when only satellite geometry and environment are known or partially known. New IM concepts intend to exploit the fact that satellite geometry and satellite visibility can be reasonably predicted at any time and location (for instance with the use of city models), and that the same observability conditions repeat periodically over time. Beside the environment nearby the receiver in its nominal conditions, these new concepts plan to exploit also the potentialities offered by a Vehicular Ad-hoc Network (VANET) infrastructure [30]. The potential availability of multiple observations of GNSS signals, taken by different vehicles participating to a VANET, can be shared and combined in order to implement a collaborative spatial/temporal characterization and prediction of the local degradation of the GNSS signals.
