Equivalence Proof and Performance Analysis of Weighted Least Squares Residual Method and Weighted Parity Vector Method in RAIM

Abstract

Besides accuracy, integrity is another important performance measure of GNSS. The classical least-squares-residual (LSR) method and parity vector (PV) method are often used in the receiver autonomous integrity monitoring (RAIM). The two fault detection methods assume that the observation errors of different satellites are the same, ignoring possible variations of accuracy between observations. In this study, the mathematical models of the weighted least-squares-residual (WLSR) method and the weighted parity vector (WPV) method are derived in detail. The equivalence of the two methods is established with statistical tests. The WPV method is applied to detect those faults based on both GPS and BDS observations collected at Wuhan JiuFeng Station (JFNG). The theoretical results show that this method has lower computational complexity than the WLSR method, hence more suited for cases requiring fast fault detection. The fault detection rate increases as the deviation of the pseudorange observation increases. Thus, using the threshold value T d of the posterior unit weight errorσ 0 , the WPV achieves a higher fault detection rate than using a priori unit weight error σ 0 . The experiments show that these two methods can detect relatively large faults, it is possible to detect them in GPS observations if σ 0 is more than 12×bias (1×bias=8 m) andσ 0 superior to 4×bias, whereas the faults detection in BDS observations requires a deviation bigger than 8×bias and 6×bias, respectively. But these two methods are insensitive when the deviation is smaller.INDEX TERMS Weighted least-squares-residual, weighted parity vectors, receiver autonomous integrity monitoring (RAIM), fault detection.

Euclidean Distance Matrix-Based Rapid Fault Detection and Exclusion

“…For solution separation, the most time-consuming part of the algorithm is the least-squares position estimate (Blanch et al, 2012;Joerger et al, 2014;Ma et al, 2019;Pullen & Joerger, 2021;Zhu et al, 2018). For the fault detection step of solution separation, the least-squares position estimate is calculated using all measurement subset combinations with a single measurement removed.…”

“…The most time-consuming part of residual-based FDE is calculating the differce between the measured and expected pseudoranges (Ma et al, 2019;Parkinson & Axelrad, 1988;Pullen & Joerger, 2021). This step runs only once for residual-based fault detection, resulting in a time complexity approximation of ( ) 1 .…”

“…Residual-based methods calculate the difference between measured and expected pseudorange values (Ma et al, 2019;Parkinson & Axelrad, 1988;Pullen & Joerger, 2021). If the normalized difference is larger than the pre-determined threshold, then a fault is detected.…”

Research on Satellite Selection Strategy for Receiver Autonomous Integrity Monitoring Applications

“…The RAIM monitoring technique has been commonly implemented especially in aerial navigation and air transport area for keeping the safety of the flight [10][11][12][13][14][15], while also being investigated in the maritime navigation field [16][17][18]. The snapshot RAIM process only needs the satellite signals in current epoch for operating and requires no additional aid information beyond the receiver, thus has been widely investigated and employed for the last decades [19][20][21]. Along with the modernization of GNSS and the combination of different constellation navigation systems, the significant increase in operating satellites in view greatly improves the accuracy of navigation solution and the availability of the RAIM process.…”

Integrity monitoring of satellite-based positioning for railway trackside augmentation network

“…In the first layer of integrity detection, it is to detect and eliminate faults caused by errors originating from the propagation environment [3] [4]. The algorithm basically eliminates the tropospheric error and ionospheric error in the propagation environment, so that the residual error caused by information propagation may cause errors such as multipath effects of faults.…”