Missed detection probability is a critical metric for the integrity performance of receiver autonomous integrity monitoring (RAIM) in the presence of faults. The traditional missed detection probability evaluation method for RAIM is limited by impractical time consumption because of the absence of accurate searching interval for the magnitude of a worst-case fault. To address this issue, the searching interval for the magnitude of a worst-case fault is constructed by the combination of minimum detectable magnitude and minimum hazardous magnitude, and the searching interval adjustment is designed to avoid the absence of worst-case fault magnitude so that the maximum missed detection probability can be accurately evaluated. The simulation result indicates that the proposed method can achieve higher accuracy for the worst-case fault magnitude searching. Furthermore, the accuracy of worldwide evaluated missed detection rate can achieve an improvement of 57·66% at most by the proposed method for the different classical RAIM algorithms.

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 the w-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 the w-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.

This paper is the second part of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). Part 1 shows that for realistic navigation requirements, the solution separation RAIM method can approach the optimal detection region when using a least-squares estimator. This paper constitutes Part 2. It presents new methods to design Non-Least-Squares (NLS) estimators, which, in exchange for a slight increase in nominal positioning error, can substantially lower the integrity risk. A first method is formulated as a multi-dimensional minimisation problem, which directly minimises integrity risk, but can only be solved using a time-consuming iterative process. Parity space representations are then exploited to develop a computationally-efficient, near-optimal NLS-estimator-design method. Performance analyses for an example multi-constellation Advanced RAIM (ARAIM) application show that this new method enables significant integrity risk reduction in real-time implementations where computational resources are limited.

This paper describes the first of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). In this first part, a new method is established to determine a piecewise linear approximation of the optimal detection region in parity space. The paper presents examples suggesting that the optimal detection boundary lays in between that obtained using chi-squared residual-based RAIM, and that provided by Solution Separation (SS) RAIM, as one varies the alert limit requirement. In addition, these examples indicate that for realistic navigation requirements, the SS RAIM method approaches the optimal detection region. The SS RAIM detection tests will be employed in the second part of this work, which focuses on the design of non-least-squares estimators to reduce the integrity risk in exchange for a slight increase in nominal positioning error.

A method to compute the minimum Horizontal Protection Level (HPL) using the test statistic of normal distribution, which will exploit advances in computational power to meet the requirement of Time to Alert (TTA), is proposed to improve service availability. To obtain the minimum solution, two approximations used in traditional algorithms need exact solutions: the distribution of the horizontal position error and the determination of the worst case to ensure that the resulting HPL is able to accommodate all possible bias. This is validated with results such that the optimal solution is achieved with a pre-defined accuracy and sufficient computational efficiency. Also, the new HPL is used to determine if current approximated methods are conservative, where one of the methods does not meet the integrity requirement with given test statistics, error model and integrity risk definition.

A new Bayesian approach for multiple satellite faults detection and exclusion is proposed by introducing a classification variable to each satellite observation. If we treat this classification variable as random and assume a prior distribution for it, then a rule for satellite fault detection and exclusion based on the posterior probabilities of the classification variables is constructed under the framework of Bayesian hypothesis testing. Secondly, the Gibbs sampler is introduced to compute the posterior probabilities of the classification variables. Then the implementation for a Bayesian Receiver Autonomous Integrity Monitoring (RAIM) algorithm is designed with the Gibbs sampler. Finally, different schemes are designed to evaluate the performance of the new Bayesian RAIM algorithm in the case of multiple faults. We compare the method in this paper with the Range Consensus (RANCO) method. Experiments illustrate that the proposed algorithm in this paper is capable of detecting and eliminating multiple satellite faults, and the probability of correctly detecting faults is high.

The advent of multiple Global Navigation Satellite System (GNSS) constellations will result in a considerable increase in the number of satellites for positioning worldwide. This substantial improvement in measurement redundancy has the potential to radically advance receiver autonomous integrity monitoring (RAIM) performance. However, regardless of the number of satellites, the performance of existing RAIM methods is sensitive to the assumed prior probabilities of individual fault hypotheses. In this paper, a new method is developed using Bayes’ theorem to generate upper bounds on posterior probabilities of individual fault hypotheses given current user measurements. These bounds are used in a Bayesian fault-tolerant position estimator (FTE) that minimizes integrity risk. The detection test statistic is a measurement-based integrity risk bound, which is directly compared with a pre-specified risk requirement. The associated challenge of quantifying continuity risk is resolved using a bounding approach, which is also detailed in this work. The new Bayesian FTE method is shown to be more robust to uncertainty in prior probability of fault occurrence than existing RAIM methods.

Four methods to calculate the Vertical Protection Level (VPL) can be used in Advanced Receiver Autonomous Integrity Monitoring (A-RAIM), among which the ideal method is the strictest one. To obtain the ideal VPL satisfying the exact required integrity risk, the worst case bias with the maximum integrity risk is searched for. This investigation has found that the correct worst case highly depends on the choice of the input VPL. To gain the correct result, the computation becomes complex and the accuracy of the result is compromised. Therefore, a new procedure is designed with a new search: the maximum VPL is searched to encompass all possible bias sizes. Since VPL is calculated with a given integrity risk for each bias size, the uncertainty of the arbitrary VPL input in the ideal method is avoided. Also, an optimisation algorithm is adopted to improve computational efficiency. It is shown that the new method is more reliable and efficient than the current best method. Simulation results worldwide also show that the new approach has improved A-RAIM availability from 32%–38% to 74% with GPS and from 44%–43% to 85% with Galileo.

Receiver Autonomous Integrity Monitoring (RAIM) is a method, used by an aircraft's receiver, for detecting and isolating faulty satellites of the Global Navigation Satellite System (GNSS). In order for a receiver to be able to detect and isolate a faulty satellite using a RAIM algorithm, a couple of conditions must be met: a minimum number of satellites, and an adequate satellite geometry. Due to the highly predictable orbits of the GPS satellites, a RAIM availability prediction can be done easily. A number of RAIM methods exist; however, none of them takes into account the precise terrain masking of the satellites for the specific location. They consider a uniform fixed mask angle over the whole horizon. This paper will introduce the variable mask RAIM algorithm in order to show to what extent the terrain can affect the RAIM availability and how much it differs from the conventional algorithms.

With more satellite systems becoming available there is currently a need for Receiver Autonomous Integrity Monitoring (RAIM) to exclude multiple outliers. While the single outlier test can be applied iteratively, in the field of statistics robust methods are preferred when multiple outliers exist. This study compares the outlier test and numerous robust methods with simulated GPS measurements to identify which methods have the greatest ability to correctly exclude outliers. It was found that no method could correctly exclude outliers 100% of the time. However, for a single outlier the outlier test achieved the highest rates of correct exclusion followed by the MM-estimator and the L1-norm. As the number of outliers increased MM-estimators and the L1-norm obtained the highest rates of normal exclusion, which were up to ten percent higher than the outlier test.

Global Navigation Satellite System (GNSS) Receiver Autonomous Integrity Monitoring (RAIM) is essential for safety-of-life and liability critical applications. This paper discusses two fundamentally different ways to assess the integrity risk of an operation with RAIM, based on a different amount of information available: the expected (or average) performance that is computed using the GNSS models only and the real-time (or actual) performance, which also uses information on the internal status of a GNSS receiver. It is shown both theoretically and by simulation that the real-time integrity risk significantly exceeds the expected risk after the detection and exclusion of a failing satellite. Therefore, while most published RAIM algorithms base their performance assessment on the expected performance only, this is only correct when the requirements allow the risk evaluation to be averaged over multiple operations. However, when the GNSS integrity requirement is to be applied on a ‘per operation’ basis, real-time integrity measures are more appropriate.

With conventional snapshot RAIM algorithms, it is difficult to detect small errors and simultaneous multiple faults. Assuming that we know the system dynamics, filtering algorithms, such as the Kalman filter, can provide better integrity-monitoring performance than the snapshot algorithms because the filter reduces the noise level of measurements. However, because the Kalman filter presumes that measurement noise and disturbance follow the Gaussian distribution, its performance might degrade if the assumption is wrong. To address this problem, we propose a fault detection and exclusion algorithm using Gaussian sum filters. Because GNSS measurement noise does not follow the Gaussian distribution perfectly, the Gaussian sum filter can estimate the posterior distribution more accurately; therefore it has better integrity-monitoring performance. This paper describes the detailed algorithms and shows simulation results to evaluate the integrity-monitoring performance of the algorithms. The proposed algorithms detect about 30% smaller faults and generate 35% lower protection levels than the conventional methods. The results show that the proposed algorithms can provide better accuracy and availability performance.