Continuity risk evaluation of the Bayesian posterior integrity monitoring against multiple faults

Abstract

Compared to the prior integrity monitoring of global navigation satellite system (GNSS), the posterior integrity monitoring incorporates the used GNSS measurements into the computation of integrity risk, thereby providing a more accurate representation of the reliability of position solution. However, the continuity risk evaluation in posterior integrity monitoring remains an unresolved issue. After formulating the posterior integrity risk of each event hypothesis as a parity function, we propose a method to evaluate the posterior continuity risk by computing the cumulative probability of false alarm within a sphere constructed in the parity space. This approach guarantees a conservative estimate of the probability of false alarm, thereby establishing an upper bound for posterior continuity risk. Experiment and analysis based on positioning cases involving GPS, Galileo, and BeiDou satellites suggest that the posterior integrity monitoring can achieve a lower probability of false alarm compared to prior integrity monitoring under certain integrity monitoring configurations. Furthermore, the evaluation accuracy of probability of false alarm inversely correlates with the severity of the differences in solution separation variances.