Advanced Receiver Autonomous Integrity Monitoring and Local Effect Models for Rail, Maritime, and Unmanned Aerial Vehicles Sectors ^†

Abstract

Advanced Receiver Autonomous Integrity Monitoring (ARAIM) represents an advancement over RAIM, designed to utilize dual-frequency and multi-constellation technologies. Originally developed for aviation, the European Commission (EC) is now exploring its broader application. This paper examines the adaptation of ARAIM for rail, maritime, and Unmanned Aerial Vehicles (UAVs) sectors. It briefly discusses aspects of the integrity concept, including architecture and user algorithms while the main focus is on characterizing local error models for local effects using real data campaigns.

1. Introduction

GNSS systems provide users with the capability of global navigation at a relatively low cost and an accuracy of a few meters. This level of accuracy suffices for most navigation applications, including en-route civil aviation. However, certain applications require enhanced performance in terms of accuracy or integrity, such as autonomous vehicles and the approach phase in aviation. To ensure that the European GNSS provides adequate Positioning, Navigation, and Timing (PNT) services that reflect the changing environment, the EC is tasked with managing the analysis of mission evolution directions. The goal is to implement and maintain future GNSS services and maximize the benefits for European civil society. In this context, the ARAIMFUSE project focuses on evaluating the ARAIM concept and its potential evolutions for applications beyond the aviation sector.

The ARAIM concept and the Integrity Support Message (ISM) disseminated in the GNSS SIS could be utilized by GNSS users from various markets. The ARAIM solution developed for Aviation [1] includes an offline ground monitoring architecture, which provides updates on the nominal performance and fault rates of multiple constellations. This integrity data are contained in the ISM [2,3] that is generated by an offline ground monitoring network and is provided to the airborne fleet through the GNSS signals.

The current ARAIM concept has been designed initially to serve the Aviation sector where operations are typically operated in open sky conditions. An extensive data campaign was conducted to characterize the open sky environment and derive a multipath model [4]. Nevertheless, other applications, and especially safety-critical applications, can take advantage of this service, or a modified version of it since they have similar and even more demanding requirements than aviation users, as can be seen in [5]. For Rail, Maritime, and UAVs sectors, local effects models are to be defined and fully validated.

This paper focuses on the modeling of local errors. Initially, it presents aspects related to the integrity concept, including the definition of the architecture and the user algorithm, for each market segment. More details are provided in [5]. Then, it focuses on the characterization of local effect models, presenting the results obtained from the processing of real GNSS data.

2. Architecture

2.1. Rail

The proposed architecture for Rail includes the integration of a GPS+Galileo receiver, compatible with ARAIM and SBAS, with an Odometer. Navigation data and observations from GNSS satellites are processed by the onboard user equipment, along with SBAS messages disseminated by EGNOS. Allocation of the integrity budget to the along-track dimension is also proposed, which exploits the characteristic of most applications within the Rail sector, where movement occurs in a one-dimensional space. A multipath model is derived to cope with local effects, and a sequential ARAIM approach is proposed to replace the snapshot approach currently employed, so it can better meet the required rail service levels under harsh conditions. The use of digital maps is also proposed, as it would aid the receiver in characterizing the environment in which it operates, particularly in identifying the multipath model and the presence of NLOS conditions. Regarding the user algorithm, a filtered approach is proposed based on the Kalman Filter, which performs the hybridization of GNSS and odometer measurements. A bank of Kalman Filters is utilized for monitoring fault cases with a solution separation approach.

2.2. Maritime

For maritime applications, the architecture includes the use of multi-antenna GPS+Galileo augmented with SBAS and ARAIM. Additionally, the solution implements local effects models tailored for typical maritime environments. In this case, the integrity budget is allocated to the horizontal component, as most applications predominantly reflect integrity user needs in this dimension. Regarding the user algorithm, GNSS measurements and navigation data serve as inputs to the dual-antenna algorithms. The outputs from these algorithms are fed into the Weighted Least Squares (WLSQ) algorithm and combined with SBAS corrections. Filter estimates are utilized to characterize the environment and apply the satellite multipath sigma. These, along with GNSS pseudorange smoothing, are input to the snapshot ARAIM algorithm.

2.3. UAVs

The proposed evolution of the ARAIM algorithm for UAVs implementation consists of augmenting and extending the GNSS signal through Precise Point Positioning (PPP) via the High Accuracy Service (HAS), combined with hybridization with an Inertial Measurement Unit (IMU). This combination is expected to yield high-accuracy Position, Velocity, and Time (PVT) solutions, along with tight integrity budgets, suitable for the demanding urban user environment. Furthermore, it is proposed to utilize more than two constellations. However, this approach requires a means of augmentation beyond the HAS, which addresses only the Galileo and GPS constellations. As an alternative, correction data from the International GNSS Service (IGS) reference network can be used. Regarding the user algorithm, a loose coupling approach is proposed, combining IMU measurements and PPP in a bank of Extended Kalman Filters, with each filter computing a solution for a different fault mode. Although tight coupling Kalman filtering is expected to yield better results, the effectiveness heavily depends on the manufacturer’s implementation. Therefore, to simplify the system a loosely coupled filter is implemented instead.

3. Methodology

As detailed in the ARAIM Algorithm Description Document [6] “the first step of the proposed baseline ARAIM algorithm consists of computing the pseudorange error diagonal covariance matrices ${\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{t}}$ (the nominal error model used for integrity) and ${\mathrm{C}}_{\mathrm{a}\mathrm{c}\mathrm{c}}$ (the nominal error model used for accuracy and continuity)” as described in Equation (1), where multipath is characterized by a zero-mean gaussian $\mathrm{N}(0,{\mathsf{\sigma }}_{\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}{\mathrm{h},}_{\mathrm{i}}})$.

$$\begin{gathered} {\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{t}}\left(\mathrm{i},\mathrm{i}\right)={\mathsf{\sigma }}_{\mathrm{U}\mathrm{R}{\mathrm{A}}_{\mathrm{i}}}^2+{\mathsf{\sigma }}_{\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}{\mathrm{o}}_{\mathrm{i}}}^2+{\mathsf{\sigma }}_{\mathrm{U}\mathrm{I}\mathrm{R}{\mathrm{E}}_{\mathrm{i}}}^2+{\mathsf{\sigma }}_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{r},\mathrm{i}}^2+{\mathsf{\sigma }}_{\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{i}}^2 \\ {\mathrm{C}}_{\mathrm{a}\mathrm{c}\mathrm{c}}\left(\mathrm{i},\mathrm{i}\right)={\mathsf{\sigma }}_{\mathrm{U}\mathrm{R}{\mathrm{E}}_{\mathrm{i}}}^2+{\mathsf{\sigma }}_{\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}{\mathrm{o}}_{\mathrm{i}}}^2+{\mathsf{\sigma }}_{\mathrm{U}\mathrm{I}\mathrm{R}{\mathrm{E}}_{\mathrm{i}}}^2+{\mathsf{\sigma }}_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{r},\mathrm{i}}^2+{\mathsf{\sigma }}_{\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{i}}^2 \end{gathered}$$

(1)

Usually, multipath models follow an exponential function, which should overbound the error after carrier smoothing. More generally, the function can be described by the Jahn’s and Brenner [7] multipath model described in Equation (2), where measurement variance is a function of satellite elevation ε and coefficients a, b, and c.

$${\mathsf{\sigma }}_{\mathrm{m}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}{\mathrm{h}}_{\mathrm{i}}}[\mathrm{m}]=\mathrm{m}\mathrm{a}\mathrm{x}\{\mathrm{a}+\mathrm{b}\times \mathrm{e}\mathrm{x}\mathrm{p}(\mathrm{c}\times \mathsf{\epsilon }[\mathrm{d}\mathrm{e}\mathrm{g}]),\mathrm{t}\mathrm{h}\}$$

(2)

Since errors introduced by signal multipath depend on the local user environment, the model designed for aviation, typically operating in open-sky environment, is unsuitable for rail, maritime and UAVs.

3.1. Rail and Maritime

For a clearer understanding of the logic behind the model derivations, an insight into the user logic for computing the multipath sigma is provided: first, the user determines the type of error level at the current epoch by using general indicators as inputs. With this error level, FDE limits based on pseudorange values are applied to the measurements, rejecting those with residuals outside the thresholds. Then, using the model corresponding to the determined error level, each measurement is assigned its appropriate sigma value before being processed by the ARAIM algorithm. Thus, the methodology is divided into three main parts:

• Development of the error level monitoring function;
• Development of an FDE;
• Derivation of the multipath models for each error level.

For the error level monitoring a Support Vector Machine (SVM) algorithm is employed [8]. The SVM is a powerful deterministic machine learning algorithm used for classification and regression tasks [9,10]. Its primary objective is to find the optimal hyperplane that best separates the data points of different classes in a high-dimensional feature space [11,12]. In the context of this project, SVM was employed for the classification of error levels based on pseudorange residuals statistics.

The input for the SVM is the pseudorange residual parameter, and the output is the error level. Initially, 3 error levels were foreseen, corresponding to the common environmental classifications of open-sky, semi-urban, and deep urban. However, due to the limited availability of real GNSS data, only two error levels are ultimately specified in the project. This would have to be extended in the future to at least 3 error levels once massive data campaigns are conducted. The error level assigned depends on the value of the pseudorange error parameter.

Table 1. Error level class. Error level monitoring function output and pseudorange error parameter values.

Error Level	Output	Pseudorange Error Parameter
Error 0	0	[0.0, 1.5] m
Error 1	1	>1.5 m

depicts the correspondence among the error levels, the output of the error level monitoring function, and the pseudorange error parameter range. Pseudorange residual and pseudorange error parameters are computed in a similar way. For each epoch, an RMS of all the pseudorange residuals/errors is calculated. This RMS value is stored in a buffer with a size equal to ${\mathrm{N}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$. Then, $\mathrm{N}$ past values are taken from the buffer, and a weighted sum is performed. The weights follow a Truncated Exponentially Weighted Moving Average (TEWMA), giving more weight to the most recent values to enhance the ability to react to rapid changes in the environment.$\mathrm{N}$ is calculated each epoch as detailed in Equation (3), where $\mathrm{U}\mathrm{s}\mathrm{e}{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{d}}$ corresponds to the maximum velocity of the vehicle in which the receiver is embedded.

$$\begin{gathered} \mathrm{N}=\min \left(\max \left({\displaystyle \frac{{\mathrm{U}\mathrm{s}\mathrm{e}\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{d}}}{{\mathrm{U}\mathrm{s}\mathrm{e}\mathrm{r}}_{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{d}}}}\times {\mathrm{N}}_{\mathrm{m}\mathrm{i}\mathrm{n}}; {\mathrm{N}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right); {\mathrm{N}}_{\mathrm{m}\mathrm{á}\mathrm{x}}\right) \\ \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}:{\mathrm{N}}_{\mathrm{m}\mathrm{a}\mathrm{x}}={\displaystyle \frac{40}{\mathrm{g}\mathrm{n}\mathrm{s}{\mathrm{s}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}}}}, {\mathrm{N}}_{\mathrm{m}\mathrm{i}\mathrm{n}}={\displaystyle \frac{10}{\mathrm{g}\mathrm{n}\mathrm{s}{\mathrm{s}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}}}} \end{gathered}$$

(3)

For each application, the pseudorange errors and pseudorange residuals are computed using GMV’s GARLIC tool. The GARLIC navigation module is responsible for processing raw GNSS observational data, utilizing navigation information to provide a PVT navigation solution through various algorithms. For maritime applications, the WLSQ algorithm is employed, while for rail, the GNSS/Odometer tightly coupled Kalman filter is used. The tropospheric term is derived using the Neil model, and the ionospheric-free term is considered negligible since all observations used are dual-frequency measurements. Satellite position and clock bias are obtained from the navigation message. The main difference between pseudorange residuals and errors is that for the latter, the true position (from the reference track) is used to compute the geometrical range, and the user clock bias is estimated per frequency as the median of the three best carrier-to-noise ratio (C/N0) observations over a fixed threshold.

Once the pseudorange residuals and errors are obtained, the parameters can be calculated and the SVM can be trained. The data were separated for each application as follows: 70% for training and 30% for validation. The SVM employed is from the scikit-learn Python library, which separates the training learning into an 80/20 proportion for deriving the metrics. These training metrics are then compared with the metrics obtained by the model when predicting the error level in the 30% dataset apart to see if any major discrepancies appear. Once the error level monitoring algorithm has proven to have optimal performance, the next step is to define an FDE before using the measurements to derive the multipath model. The defined FDE limits are those that the user must apply before computing the sigmas. The FDE limits are set considering the relationship between pseudorange residuals and pseudorange errors, which tend to be linear for high absolute values. In this manner, the residuals of each application are computed, and the 1% and 99% percentiles are set as the boundary limits. All measurements whose residuals exceed these limits are rejected.

After the FDE has been performed the objective is to obtain a sigma that overbounds the errors at the required integrity risks (IR). For that, the remaining samples are segregated according to C/N0 bins. Then, percentiles ranging from ${10}^{-3}$ to ${10}^{-7}$ are calculated for the distribution of samples within each bin. Following the acquisition of these percentiles, and in accordance with the tail-overbounding technique as performed in [13], the zero-mean normal distributions intersecting each bin value are computed. The most stringent of these distributions is chosen and its sigma value is selected as the sigma value for the respective C/N0 bin. Once each C/N0 bin has a sigma value assigned, an exponential curve is used to fit the values in such a way that all values are below the curve. The expression of the curve is detailed in Equation (4), where $\mathrm{x}$ represents the C/N0 value of the measurement, and 30 is an offset used to establish the initial point of the curve at 30 dB-Hz.

$${\mathsf{\sigma }\left(\mathrm{x}\right)}_{\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}}\left[\mathrm{m}\right]=\mathrm{a}\times {\mathrm{e}}^{\mathrm{b}\times (\mathbf{x}-30)}$$

(4)

3.2. UAVs

The positioning solution obtained through the PPP+ARAIM algorithm is compared to the reference track to analyze its performance. The residuals of the reference solutions can be analyzed as a metric of accuracy. Consulting different studies for the open sky multipath experience it is found that the multipath error is described in a similar manner as a function of the elevation of the satellite using the Mats Brenner Multipath Model [7]. Instead of elevation, the equation is adapted for carrier to noise (C/N0) to yield an exponential relationship. The model fitting must be performed on the experimental measurement data which is filtered to remove as much as possible of any other known error sources. Using the RINEX data the pseudorange measurements of the UAV are deducted which include errors and biases. The known errors such as clock, ephemeris and atmospheric errors are then analyzed and compensated for. The remaining errors are the multipath delay and other errors due to non-accounted elements (residual local error). With the use of a reference positioning system, the true geometric distance is found. Using this information the errors can be estimated for the different signals.

4. Data

4.1. Rail and Maritime

Local effects models are studied from the analysis of real GNSS data. For maritime applications, most of the data are sourced from open-ocean environments in the Black Sea. Additionally, data from port areas and inland waters (Danube Delta) are available. In the case of rail, data coming from three different projects CAPRESSE, CLUG and ERASMO were used. The reference track for maritime data were obtained using a PPP post-processing service [14], which provides a position accuracy with a 95% standard deviation on the order of centimeters. For rail, different sources were used for the reference track. In all cases, the standard deviation of the reference is on the order of decimeters or below.

4.2. Data Campaign

For UAVs, multi-frequency and multi-constellation GNSS data are needed in combination with the associated HAS information and IMU data. This study used a dedicated flight trial to gather data to be able to analyze and model the local user errors. To analyze the effects of the environment, different user locations were used with different satellite blockages. The biggest differentiator for the GNSS receiver was the user dynamics of the UAV. Higher user dynamics can degrade the positioning performances, due to loss of track of satellites. A DJI MATRICE 600 PRO (DJI, Frankfurt Am Main, Germany) with a multi-frequency multi-constellation GNSS receiver (AsteRx SB3 Pro (Septentrio, Leuven, Belgium)) has been used to collect GNSS data. The receiver logged the raw data internally and sent a pulse-per-second to onboard processer (Raspberry Pi 4 (Raspberry Pi Foundation, Cambridge, UK)). Furthermore, an IMU and camera were connected to the onboard processor. By making use of the IMU, the user dynamics of the UAV can be logged. The camera was used to be able, during post-processing, to analyze the environment in case of multipath, satellite obstruction, or NLOS. To analyze the performance of the positioning solution obtained, a reference track of the UAV is needed. Two different sets of data with different reference tracks were used:

• The reference track is created by post-processing a kinematic solution (PPK) and fusing it together with IMU data. The precise orbit and clock files are obtained from NASA’s Archive of Space Geodesy Data through the IGS Multi-GNSS Experiment (MGEX). The PPK is obtained by combining a forward and backward processed solution. The sensor fusion is performed based on a UAV model, which is tuned for high dynamic operations based on a tightly coupled extended Kalman filter. The initial attitude is corrected by means of the dual-antenna GNSS heading obtained directly from the receiver.
• The second set used a reference track created using a private total station with a known position to trace the UAV position throughout each flight. The total station consists of a Leica MS60 multistation which uses a Leica prism reflector mounted on the UAV to determine its position.

5. Results

For the case of Maritime and Rail, two types of models were obtained: those detailed in the methodology, with data classified by the SVM (30% of total data) and the best-case models, which correspond to models obtained from all available data (100% of the data) classified manually. The model coefficients and the graphs of the fitting curve correspond to the best-case models, as these models are considered the closer to the ones that will be obtained on an extensive data campaign. As the data used is classified manually, it can be considered as having an SVM with a 100% in all metrics.

5.1. Rail

The total number of epochs used for the training is 85.144 for Error 0 and 45.300 for Error 1. After training the SVM with the dataset, predictions were made on the remaining 30%. Metrics are depicted in

Table 2. SVM metrics for Rail.

	Precision	Recall	F1-Score
Error 0	0.91	0.98	0.94
Error 1	0.93	0.72	0.81
Accuracy	-	-	0.91
Macro Avg.	0.92	0.85	0.88
Weighted Avg.	0.91	0.91	0.91

. A predisposition of the model to classify epochs as Error 0 rather than Error 1 was observed, attributed to the dataset containing nearly twice as many epochs for Error 0 as for Error 1. The precision for Error 1 is higher, indicating that when the SVM classifies an epoch as belonging to Error 1, it does so correctly 93% of the time. However, the recall for Error 1 is lower, capturing only 72% of the total Error 1 epochs, compared to 98% for Error 0 epochs.

The overbounding curve for the multipath models obtained in Rail is depicted in Figure 1. In

Table 3. Multipath Model Coefficients. Rail.

	Multipath Model Coefficients
Error 0	$\mathrm{a}=2.347; \mathrm{b}=-0.004119$;
Error 1	$\mathrm{a}=16.562; \mathrm{b}=-0.06979;$

, the coefficients detailed in Equation (4) for each model are presented. The models are derived from all available rail data that were manually classified, not by the SVM. This method increases the number of available samples per C/N0 bin, leading to a more representative final model. The total number of samples (observations) is 1.358.715 for Error 0 and 783.533 for Error 1.

5.2. Maritime

The metrics obtained in the SVM for Maritime application are depicted in

Table 4. SVM Metrics. Maritime.

	Precision	Recall	F1-Score (95%)
Error 0	0.94	1.00	0.97
Error 1	0.80	0.24	0.37
Accuracy	-	-	0.94
Macro Avg.	0.87	0.62	0.67
Weighted Avg.	0.93	0.94	0.93

. The SVM was trained with 1.294.136 epochs for Error 0 and 86.659 epochs for Error 1.

The proportion of samples is unbalanced, with Error 0 having more than ten times the number of epochs compared to Error 1. This imbalance is expected to affect the SVM, which will likely encounter difficulties in detecting Error 1 epochs, as their proportion in the training set is an order of magnitude smaller than that of Error 0 samples. The ’balanced’ parameter, which adjusts weights inversely proportional to class frequencies in the input data, was employed to mitigate this issue; however, no improvement was observed.

After the model was trained, it was utilized to classify the remaining 30% of the data. The overall accuracy of the model is 0.94, indicating that the model correctly predicts 94% of the cases across all classes. When comparing these metrics with those from the rail dataset, which is more limited but has a more balanced proportion between the two error classes, it becomes evident that the unbalanced proportion is the primary reason the SVM tends to classify more samples as Error 0 and fails to adequately identify Error 1 classes, as indicated by a recall of 0.24. In contrast, all the Error 0 samples were identified, resulting in a recall of 1. This issue can be addressed by ensuring a similar proportion of samples for training. Additionally, further exploration of weighting techniques may prove beneficial. For this project, the methodology is the critical component.

The overbounding curve for the multipath models obtained in Maritime is depicted in Figure 2. Each dot represents the sigma value obtained for each C/N0 bin. In

Table 5. Multipath Model Coefficients for Maritime.

	Multipath Model Coefficients
Error 0	$\mathrm{a}=2.663; \mathrm{b}=-0.05117$;
Error 1	$\mathrm{a}=3.600; \mathrm{b}=-0.04216;$

the coefficients for each model, which are detailed in Equation (4), are presented.

5.3. UAVs

An analysis is performed for two different environments: First the open sky for a reference of UAV performance and then the flights close to buildings for urban performance. Two different approaches have been taken. As the correlation between residual and CN0 is not particularly strong for UAVs case, a first attempt was made to determine the absolute value of the residual after removing local effects by means of single and double differencing. The relation between the empirical CDF and the environment is given in

Table 6. Overview of 95th percentile CDF values of residual error.

Environment	Min. Multipath (95%)	Max. Multipath (95%)
Open Sky	1.5 m	14 m
Semi-Urban	4.8 m	23.5 m
Urban	12.6 m	51.2 m

. In this relationship, the lower and upper bounds are given, which are now independent of satellite elevation or CN0.

The second approach was to determine the 95th percentile of the residual per CN0 bin. This relationship was then fitted with a third order polynomial which behaves as expected for this relationship. For each environment, the function is given as follows:

$$\mathrm{A}\mathrm{b}\mathrm{s}.\mathrm{R}\mathrm{e}\mathrm{s}.\left[\mathrm{m}\right]=55.98\mathrm{e}\mathrm{x}\mathrm{p}(-0.0437\times \mathrm{C}\mathrm{N}0[\mathrm{d}\mathrm{B}-\mathrm{H}\mathrm{z}\left]\right) \mathrm{O}\mathrm{p}\mathrm{e}\mathrm{n}‐\mathrm{S}\mathrm{k}\mathrm{y}.$$

(5)

$$\mathrm{A}\mathrm{b}\mathrm{s}.\mathrm{R}\mathrm{e}\mathrm{s}.\left[\mathrm{m}\right]=256\mathrm{e}\mathrm{x}\mathrm{p}(-0.086\times \mathrm{C}\mathrm{N}0[\mathrm{d}\mathrm{B}-\mathrm{H}\mathrm{z}\left]\right) \mathrm{S}\mathrm{e}\mathrm{m}\mathrm{i}‐\mathrm{U}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}.$$

(6)

$$\mathrm{A}\mathrm{b}\mathrm{s}.\mathrm{R}\mathrm{e}\mathrm{s}.\left[\mathrm{m}\right]=176.7\mathrm{e}\mathrm{x}\mathrm{p}(-0.0573\times \mathrm{C}\mathrm{N}0[\mathrm{d}\mathrm{B}-\mathrm{H}\mathrm{z}\left]\right) \mathrm{D}\mathrm{e}\mathrm{e}\mathrm{p}‐\mathrm{U}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}.$$

(7)

6. Discussions

For Rail and Maritime applications, an SVM is used as the error level monitoring function, using a statistic of pseudorange errors as input. Although the results are not presented in this paper, a study was conducted in which the inclusion of other parameters, such as user speed and various statistics over raw measurements (C/N0, elevation, and Doppler residuals), were evaluated as inputs to the SVM. The major conclusion of this study was that no correlation between these parameters and the error level was observed, and the SVM does not improve after their inclusion. The use of other parameters (different types of statistics over the raw measurements or entirely new ones) should be studied, as their inclusion could improve the SVM [10].

Another test was conducted to study the SVM’s sensitivity to changes. The major conclusion was that the amount of data, as well as having similar proportions of each error level, are the primary contributors to SVM performance. Regarding the models, it is important to note the following:

• For Error Level 1 model in rail, each sigma value is greater than that in maritime due to the deep-urban epochs used in rail that are not present in maritime;
• Best-case models are presented as the data used is insufficient for making safety-of-life models and are the ones closest to those that will be obtained through an extensive data campaign;
• With an extensive data campaign, at least three models must be derived and Error Level 1 samples will be divided into Error Level 1 and Error Level 2.

7. Conclusions

The main objective of this study is to prove that ARAIM is a feasible technology for delivering integrity in applications beyond aviation. A key aspect is having a local error model that accounts for the local effects, such as multipath error, and can overbound it in the proportion required for the different integrity risks. In this study, two methodologies were employed. For Rail and Maritime, the proposed methodology involves the use of a machine learning algorithm to detect the type of environment and then derive the multipath model based on the C/N0 values instead of elevation.

The results show that the SVM is a valid method for deriving the error level at each epoch. More data are needed to obtain a comprehensive trained model and, specifically, a better balance between the classes is necessary to avoid class preference. Regarding the models obtained, the proposed methodology appears to be a valid approach for obtaining different models depending on the type of environment. As mentioned, with more data, classification between three different error levels can be achieved, and one model per constellation can also be obtained. In this case, best-case models were used, as the available data were limited.

In future work, a massive data campaign should be conducted to characterize the local effects for safety-of-life applications, as it is nearly infeasible to model all possible eventualities and their combinations. The length of the data campaign should allow the characterization in line with the Integrity Risk. This campaign would also allow to improve the SVM performances. Models derived in this study are then used in the Proof-of-Concept (PoC) to validate the proposed evolutions of ARAIM for non-aviation sectors. Results will be presented in a future publication.