Receiver Autonomous Integrity Monitoring Algorithm Research Articles

A computationally efficient Kalman filter-based RAIM algorithm for aircraft navigation with GPS and NavIC

Integrity monitoring with a Kalman filter (KF) has recently attracted significant attention. In this paper, a computationally efficient architecture of a KF-based receiver autonomous integrity monitoring (RAIM) algorithm is discussed for aviation applications to ensure reliable operations of Global Navigation Satellite Systems (GNSS). It is built on the Schmidt KF navigation processor to model time-correlated measurement errors. Reasons for important design choices of the algorithm are clarified. Different strategies are adopted to efficiently include the contributions of past KF measurements in fault detection as well as protection level (PL) calculations. Module-wise most significant numerical complexity is also analyzed in detail. The algorithm performance is studied with simulated Global Positioning System (GPS) and Navigation with Indian Constellation (NavIC) signals for a number of scenarios. They comprise different configurations related to the number of satellites, geometry, total duration, and aircraft dynamics. Fault detection performance of presented KF RAIM is shown to be superior to another innovation-based test with a moving time window. It is demonstrated that KF RAIM running on a single-core virtual machine can complete processing within a small fraction of each time interval. The performance is also analyzed by restricting CPU usage. The processing time of GPS-NavIC KF RAIM at every interval is shown to be consistently less than that of standalone GPS in all scenarios. Therefore, dual constellations not only result in lower PLs, but also require shorter execution times. An explanation for faster execution times with dual GNSS is provided using the numerical complexity of different modules.

Development and evaluation of a generalized model of RAIM availability for single-, dual- and multi-satellite faults

Receiver autonomous integrity monitoring (RAIM) fault monitoring and identification requires first to judge the geometric distribution of currently visible satellites based on performance indicators and to determine whether it is suitable for integrity monitoring, that is, to judge the availability of the RAIM algorithm. With the rapid development of the global navigation satellite system (GNSS), the possibility of dual-satellite faults and multiple-satellite faults in GNSS navigation and positioning has greatly increased. The existing literature mainly focuses on RAIM availability evaluation for single-satellite fault or dual-satellite faults, ignoring the occurrence possibility of multiple-satellite faults, and thus there is no unified RAIM availability evaluation model. To this end, we use the characters of the quadratic matrix to derive a generalized model of RAIM availability evaluation, and the model is suitable for situations of single-, dual- and multi-satellite faults. Based on the observation data of Beidou Navigation Satellite System (BDS) from 332 International GNSS Service (IGS) stations distributed globally on 24 March 2021 and the global ephemeris file, the global RAIM availability of BDS is evaluated. The results show that the generalized model of RAIM availability evaluation has a rigorous derivation process, strong applicability and easy implementation. When the cutoff elevation angle is greater than 5°, the average number of BDS visible satellites at 332 IGS stations worldwide is 12.289 and the average geometry dilution of precision value is 8.090. This can fully meet RAIM availability evaluation and integrity monitoring requirements at most IGS stations and regions. The RAIM availability of triple-satellite faults is lower than that of dual-satellite faults, and the RAIM availability of dual-satellite faults is lower than that of single-satellite fault. For the three different faults, the RAIM availability cannot fully satisfy the four stages in aviation all over the world. Among them, the RAIM availability is highest in the en-route (oceanic/continental low density) stage for all three types of faults, which is 93.146%, 74.848%, and 67.576%, respectively, while the non-precision approach stage has the lowest RAIM availability, which is 78.193%, 13.636%, 3.333% for the three types of faults, respectively.

Kalman Filter-Based Integrity Monitoring for GNSS and 5G Signals of Opportunity Integrated Navigation

A Kalman filter-based receiver autonomous integrity monitoring algorithm (RAIM) is proposed to exploit sequential measurements from global navigation satellite systems (GNSS) and cellular 5G signals of opportunity (SOPs), to ensure safe vehicular navigation in urban environments. To deal with frequent threats caused by multipath and non-line-of-sight conditions, an innovation-based outlier rejection method is introduced. Next, a fault detection technique based on solution separation test is developed, and the quantification of protection levels is derived. Experimental results of a ground vehicle traveling in an urban environment, while making pseudorange measurements to GPS satellites and cellular 5G towers, are presented to demonstrate the efficacy of the proposed method. Incorporating 5G signals from only 2 towers is shown to reduce the horizontal protection level (HPL) by 0.22 m compared to using only GPS. Moreover, the proposed method is shown to reduce the HPL and vertical protection level (VPL) by 84.42% and 69.63%, respectively, over the snapshot advanced RAIM (ARAIM).

Performance Analyses of a RAIM Algorithm for Kalman Filter with GPS and NavIC Constellations.

This paper evaluates the performance of an integrity monitoring algorithm of global navigation satellite systems (GNSS) for the Kalman filter (KF), termed KF receiver autonomous integrity monitoring (RAIM). The algorithm checks measurement inconsistencies in the range domain and requires Schmidt KF (SKF) as the navigation processor. First, realistic carrier-smoothed pseudorange measurement error models of GNSS are integrated into KF RAIM, overcoming an important limitation of prior work. More precisely, the error covariance matrix for fault detection is modified to capture the temporal variations of individual errors with different time constants. Uncertainties of the model parameters are also taken into account. Performance of the modified KF RAIM is then analyzed with the simulated signals of the global positioning system and navigation with Indian constellation for different phases of aircraft flight. Weighted least squares (WLS) RAIM used for comparison purposes is shown to have lower protection levels. This work, however, is important because KF-based integrity monitors are required to ensure the reliability of advanced navigation methods, such as multi-sensor integration and vector receivers. A key finding of the performance analyses is as follows. Innovation-based tests with an extended KF navigation processor confuse slow ramp faults with residual measurement errors that the filter estimates, leading to missed detection. RAIM with SKF, on the other hand, can successfully detect such faults. Thus, it offers a promising solution to developing KF integrity monitoring algorithms in the range domain. The modified KF RAIM completes processing in time on a low-end computer. Some salient features are also studied to gain insights into its working principles.

A CIPSO-FCM-Based RAIM Algorithm for the GPS/BDS Integrated Navigation System

The receiver integrity monitoring of a satellite navigation system directly affects positioning accuracy and train safety. The GPS/BDS (Global Positioning System/BeiDou Navigation System) integrated navigation system can meet the requirements of RAIM (Receiver Autonomous Integrity Monitoring) for the minimum number of visible satellites. However, the probability of multiple satellite simultaneous failures increases in the GPS/BDS integrated navigation system so that when the failures occur, the RAIM algorithm cannot meet the requirements of safety for the receiver when positioning trains. In response to the problem, this paper applies the CIPSO-FCM (Chaotic Immune-vaccine Particle Swarm Optimization_ Fuzzy C-means) algorithm to RAIM to establish a new algorithm. It can predict the HPL (Horizontal Protection Level) value of the GPS/BDS integrated navigation system to verify RAIM availability. It also uses the parity space vector to obtain cluster samples through a pseudo-range observation matrix. The CIPSO algorithm obtains the initial cluster centers by iteration to prevent the FCM algorithm from falling into the local optimum, leading to inconsistent classification. A test based on actual field data shows that the CIPSO-FCM-based RAIM algorithm achieves a probability of 99.98% for detecting and identifying multiple satellite failures with a gross error of 28m, which can meet the safety requirements for the receiver when positioning trains.

Kalman Filter-Based RAIM for Reliable Aircraft Positioning with GPS and NavIC Constellations.

This paper presents a novel Kalman filter (KF)-based receiver autonomous integrity monitoring (RAIM) algorithm for reliable aircraft positioning with global navigation satellite systems (GNSS). The presented method overcomes major limitations of the authors’ previous work, and uses two GNSS, namely, Navigation with Indian Constellation (NavIC) of India and the Global Positioning System (GPS). The algorithm is developed in the range domain and compared with two existing approaches—one each for the weighted least squares navigation filter and KF. Extensive simulations were carried out for an unmanned aircraft flight path over the Indian sub-continent for validation of the new approach. Although both existing methods outperform the new one, the work is significant for the following reasons. KF is an integral part of advanced navigation systems that can address frequent loss of GNSS signals (e.g., vector tracking and multi-sensor integration). Developing KF RAIM algorithms is essential to ensuring their reliability. KF solution separation (or position domain) RAIM offers good performance at the cost of high computational load. Presented range domain KF RAIM, on the other hand, offers satisfactory performance to a certain extent, eliminating a major issue of growing position error bounds over time. It requires moderate computational resources, and hence, shows promise for real-time implementations in avionics. Simulation results also indicate that addition of NavIC alongside GPS can substantially improve RAIM performance, particularly in poor geometries.

An Improved Weight Optimization AAIM Method Aided by Barometric Altimeter

Aiming at the problem of insufficient availability in the satellite receiver autonomous integrity monitoring (RAIM) method, an improved aircraft autonomous integrity monitoring (AAIM) method aided by barometric altimeter based on weight optimization is proposed under the actual configuration of the airborne navigation system. The information of satellite navigation system and barometric altimeter is used to establish the observation equation of the integrated system. The algorithm for integrity monitoring and protection-level calculation is derived based on multiple solution separation, and a weight optimization is adopted to achieve a trade-off between position accuracy and integrity, which can improve the availability of AAIM method. The simulation experiment shows that when the number of visible stars is 5, the traditional method cannot effectively detect the satellite fault, and the positioning error is 43.65 m. The improved algorithm can effectively isolate the fault and reduce the positioning error to 0.37 m. Compared with the traditional RAIM algorithm and the Baro-aided AAIM algorithm, the proposed algorithm has a lower vertical protection threshold. Therefore, the algorithm in this paper improves the performance of satellite navigation system integrity monitoring and ensure the accuracy and reliability of the satellite navigation system.

An enhanced least squares residual RAIM algorithm based on optimal decentralized factor

The Least Squares Residual (LSR) algorithm is commonly used in the Receiver Autonomous Integrity Monitoring (RAIM). However, LSR algorithm presents high Missed Detection Risk (MDR) caused by a large-slope faulty satellite and high False Alert Risk (FAR) caused by a small-slope faulty satellite. In this paper, the LSR algorithm is improved to reduce the MDR for a large-slope faulty satellite and the FAR for a small-slope faulty satellite. Based on the analysis of the vertical critical slope, the optimal decentralized factor is defined and the optimal test statistic is conceived, which can minimize the FAR with the premise that the MDR does not exceed its allowable value of all three directions. To construct a new test statistic approximating to the optimal test statistic, the Optimal Decentralized Factor weighted LSR (ODF-LSR) algorithm is proposed. The new test statistic maintains the sum of pseudo-range residual squares, but the specific pseudo-range residual is weighted with a parameter related to the optimal decentralized factor. The new test statistic has the same decentralized parameter with the optimal test statistic when single faulty satellite exists, and the difference between the expectation of the new test statistic and the optimal test statistic is the minimum when no faulty satellite exists. The performance of the ODF-LSR algorithm is demonstrated by simulation experiments.

Robust-Extended Kalman Filter and Long Short-Term Memory Combination to Enhance the Quality of Single Point Positioning

In the recent years, multi-constellation and multi-frequency have improved the positioning precision in GNSS applications and significantly expanded the range of applications to new areas and services. However, the use of multiple signals presents advantages as well as disadvantages, since they may contain poor quality signals that negatively impact the position precision. The objective of this study is to improve the Single Point Positioning (SPP) accuracy using multi-GNSS data fusion. We propose the use of robust-Extended Kalman Filter (referred to as robust-EKF hereafter) to eliminate outliers. The robust-EKF used in the present work combines the Extended Kalman Filter with the Iterative ReWeighted Least Squares (IRWLS) and the Receiver Autonomous Integrity Monitoring (RAIM). The weight matrix in IRWLS is defined by the MM Estimation method which is a robust statistics approach for more efficient statistical data analysis with high breaking point. The RAIM algorithm is used to check the accuracy of the protection zone of the user. We apply the robust-EKF method along with the robust combination of GPS, Galileo and GLONASS data from ABMF base station, which significantly improves the position accuracy by about 84% compared to the non-robust data combination. ABMF station is a GNSS reception station managed by Météo-France in Guadeloupe. Thereafter, ABMF will refer to the acronym used to designate this station. Although robust-EKF demonstrates improvement in the position accuracy, its outputs might contain errors that are difficult to estimate. Therefore, an algorithm that can predetermine the error produced by robust-EKF is needed. For this purpose, the long short-term memory (LSTM) method is proposed as an adapted Deep Learning-Based approach. In this paper, LSTM is considered as a de-noising filter and the new method is proposed as a hybrid combination of robust-EKF and LSTM which is denoted rEKF-LSTM. The position precision greatly improves by about 95% compared to the non-robust combination of data from ABMF base station. In order to assess the rEKF-LSTM method, data from other base stations are tested. The position precision is enhanced by about 87%, 77% and 93% using the rEKF-LSTM compared to the non-robust combination of data from three other base stations AJAC, GRAC and LMMF in France, respectively.

Optimized Fault Detection Algorithm Aided by BDS Baseband Signal for Train Positioning

The satellite navigation integrity monitoring technology is closely related to the reliability of train positioning. It is of great significance to study satellite navigation Receiver autonomous integrity monitoring (RAIM) algorithm suitable for train positioning. Some existing conventional RAIM algorithms do not consider the influence of satellite navigation signal on algorithms performance. Aiming at the influence of satellite navigation signal on the propagation processes, such as shadow and multipath effects, the fault detection algorithm based on BeiDou navigation satellite system (BDS) baseband signal is proposed. The innovation parameters contained in the satellite navigation baseband signal are combined into the covariance matrix to set up a new test statistics of RAIM. A new fault detection algorithm based on optimized BDS baseband signal is discussed. And combined with weighted least square method, the noise power balance factor is established to realize satellite fault detection. Experimental results show that the proposed algorithm can improve the monitoring performance of train satellite positioning integrity, and lay the foundation for meeting the railway industry's security requirements for positioning services.

Improved receiver autonomous integrity monitoring algorithm

The integrity monitoring algorithm guarantees that the receiver can get the correct positioning and speed, which has very important theoretical significance and practical application value. It is one of the most important development contents of the satellite navigation system. Based on the introduction of the traditional least square residual method, this paper compares the binomial fitting time-assisted receiver autonomous integrity monitoring (RAIM) algorithm and a grey model time-assisted RAIM algorithm and finds that the latter can well solve the clock error accumulation problem in the binomial fitting time-assisted RAIM algorithm. In the faulty satellite detection experiments with the same pseudo-range error, the minimum detectable pseudo-range error of the grey model time-assisted RAIM algorithm is 15 m, while the binomial fitting time-assisted RAIM algorithm is 28 m. Incidentally, the detection probability of a faulty satellite with 20 m pseudo-range error of the binomial fitting time-assisted RAIM algorithm is 10%, whereas the grey model time-assisted RAIM algorithm is 81%.

On hypothesis testing in RAIM algorithms: generalized likelihood ratio test, solution separation test and a possible alternative

Integrity for GNSS-based navigation can be monitored at user level by means of RAIM (receiver autonomous integrity monitoring) algorithms. Most of these algorithms are based on statistical tests that are able to detect and identify outliers or other anomalies in the measurements, and then either exclude suspected measurements from the position solution or forward a warning to the user. In this paper the two statistical tests most commonly used in RAIM algorithms, the generalized likelihood ratio (GLR) test and the solution separation (SS) test, are compared. The main differences between the two tests are pointed out, in general statistical terms and in view of their use in integrity monitoring. As both tests are found not optimal for integrity monitoring, a new test is proposed that targets only the faults that represent a threat to the integrity. Simulation results are shown to substantiate the theoretical findings, and confirm the effectiveness of the new testing procedure.

Improved Method for Single and Multiple GNSS Faults Exclusion based on Consensus Voting

Receiver Autonomous Integrity Monitoring (RAIM) provides an integrity service for Global Navigation Satellite Systems (GNSS). The conventional RAIM algorithm is based on the assumption of a single fault and typically uses the forward-backward method, which is based on thew-test or correlation analysis methods, to exclude the faults. It is suitable for single fault detection and exclusion, while it can lead to inefficiency, can be misleading and can even fail in the exclusion of multiple faults. To solve this problem, an improved method based on consensus voting of thew-test and correlation analysis methods is presented. To verify the performance of the improved method, tests using Global Positioning System (GPS)/BeiDou System (BDS) data have been carried out in comparison with the conventional methods in terms of false and correct faults exclusion rate and computational complexity in the case of a different number of faults. Results show that the improved method has almost the same correct exclusion rate compared to the conventional RAIM in the case of a single fault. It is worth noting that the improved method has a higher correct exclusion probability and computational efficiency as well as a lower possibility of false exclusion in the case of multiple faults.

RAIM Algorithm Based on Fuzzy Clustering Analysis

With the development of various navigation systems (such as GLONASS, Galileo, BDS), there is a sharp increase in the number of visible satellites. Accordingly, the probability of multiply gross measurements will increase. However, the conventional RAIM methods are difficult to meet the demands of the navigation system. In order to solve the problem of checking and identify multiple gross errors of receiver autonomous integrity monitoring (RAIM), this paper designed full matrix of single point positioning by QR decomposition, and proposed a new RAIM algorithm based on fuzzy clustering analysis with fuzzy c-means(FCM). And on the condition of single or two gross errors, the performance of hard or fuzzy clustering analysis were compared. As the results of the experiments, the fuzzy clustering method based on FCM principle could detect multiple gross error effectively, also achieved the quality control of single point positioning and ensured better reliability results.

Analyses of the sensitivity of multi-constellation advanced receiver autonomous integrity monitoring vertical protection level availability to error parameters and a failure model over China

The availability of advanced receiver autonomous integrity monitoring for vertical guidance down to altitudes of 200 ft (LPV-200) is discussed using real satellite orbit/ephemeris data collected at eight international global navigation satellite system service stations across China. Analyses were conducted for the availability of multi-constellation advanced receiver autonomous integrity monitoring and multi-fault advanced receiver autonomous integrity monitoring, and the sensitivity of availability in response to changes in error model parameters (i.e. user range accuracy, user range error, Bias-Nom and Bias-Max) was used to compute the vertical protection level. The results demonstrated that advanced receiver autonomous integrity monitoring availability based on multiple constellations met the requirements of LPV-200 despite multiple-fault detections that reduced the availability of the advanced receiver autonomous integrity monitoring algorithm; the advanced receiver autonomous integrity monitoring availability thresholds of the user range error and Bias-Nom used for accuracy were more relevant to geographic information than the user range accuracy and Bias-Max used for integrity at the eight international global navigation satellite system service stations. Finally, the possibility of using the advanced receiver autonomous integrity monitoring algorithm for a Category III navigation standard is discussed using two sets of predicted errors, revealing that the algorithm could be used in 79% of China.

BDS/GPS combined navigation receiver autonomous integrity monitoring algorithm

BDS/GPS combined navigation receiver autonomous integrity monitoring algorithm

Particle Filtering Approach for GNSS RAIM and FPGA Implementation

The integrity monitoring system, as an integral part of aviation navigation system for global navigation satellite system (GNSS), should detect and isolated Failures or faults caused by system failures to maintain the integrity of the GNSS. The pseudorange residual noise of navigation satellites does not completely follow the Gaussian distribution, the performance of traditional filtering algorithms (such as the Kalman filtering) may be reduced due to non-Gaussian noise. The particle filter algorithm has great advantage to dealing with the nonlinear and non-Gaussian system. in this paper, the particle filter algorithm is applied to GNSS receiver autonomous integrity monitoring(RAIM) to detect the fault of navigation satellite. Firstly, Log likelihood ratio (LLR) testing is established; and then, the consistency between the state estimation of the main particle filter and the auxiliary particle filter is checked to determine whether the navigation satellite has failed; finally, the novel RAIM algorithm is undertaken by field programmable gate array (FPGA), the modules of the proposed RAIM algorithm is implemented. The effectiveness of the proposed approach is illustrated in a problem of GPS (Global Positioning System) autonomous integrity monitoring system, the algorithm and its implementation can be embeded in GNSS receiver.

GNSS receiver autonomous integrity monitoring (RAIM) algorithm based on robust estimation

Integrity is significant for safety-of-life applications. Receiver autonomous integrity monitoring (RAIM) has been developed to provide integrity service for civil aviation. At first, the conventional RAIM algorithm is only suitable for single fault detection, single GNSS constellation. However, multiple satellite failure should be considered when more than one satellite navigation system are adopted. To detect and exclude multi-fault, most current algorithms perform an iteration procedure considering all possible fault model which lead to heavy computation burden. An alternative RAIM is presented in this paper based on multiple satellite constellations (for example, GPS and BeiDou (BDS) etc.) and robust estimation for multi-fault detection and exclusion, which can not only detect multi-failures, but also control the influences of near failure observation. Besides, the RAIM algorithm based on robust estimation is more efficient than the current RAIM algorithm for multiple constellation and multiple faults. Finally, the algorithm is tested by GPS/BeiDou data.

Galileo: The Added Value for Integrity in Harsh Environments.

A global navigation satellite system (GNSS)-based navigation is a challenging task in a signal-degraded environments where GNSS signals are distorted by multipath and attenuated by fading effects: the navigation solution may be inaccurate or unavailable. A possible approach to improve accuracy and availability is the joint use of measurements from different GNSSs and quality check algorithms; this approach is investigated here using live GPS and Galileo signals. A modified receiver autonomous integrity monitoring (RAIM) algorithm, including geometry and separability checks, is proposed to detect and exclude erroneous measurements: the multi-constellation approach provides redundant measurements, and RAIM exploits them to exclude distorted observations. The synergy between combined GPS/Galileo navigation and RAIM is analyzed using live data; the performance is compared to the accuracy and availability of a GPS-only solution. The tests performed demonstrate that the methods developed are effective techniques for GNSS-based navigation in signal-degraded environments. The joint use of the multi-constellation approach and of modified RAIM algorithms improves the performance of the navigation system in terms of both accuracy and availability.

Research on GPS Receiver Autonomous Integrity Monitoring Algorithm In the Occurrence of Two-satellite Faults

Reliability is an essential factor for GPS navigation system. Therefore, an integrity monitoring is considered as one of the most important parts for a navigation system. GPS receiver autonomous integrity monitoring (RAIM) technique can detect and isolate fault satellite. Based on particle filter, a novel RAIM method was proposed to detect two-satellite faults of the GPS signal by using hierarchical particle filter. It can deal with any system nonlinear and any noise distributions. Because GNSS measurement noise does not follow the Gaussian distribution perfectly, the particle filter can estimate the posterior distribution more accurately. In order to detect fault, the consistency test statistics is established through cumulative log-likelihood ratio (LLR) between the main and auxiliary particle filters (PFs).Specifically, an approach combining PF with the hierarchical filter is used in the process of two-satellite faults. Through GPS real measurement, the performance of the proposed GPS two-satellite faults detection algorithm was illustrated. Some simulation results are given to evaluate integrity monitoring performance of the algorithm. Validated by the real measurement data, the results show that the proposed algorithm can successfully detect and isolate the faulty satellite in the case of non-Gaussian measurement noise.