Bayesian Upper Bound on GNSS Posterior Integrity Risk

Quantifying navigation integrity is crucial for safety-critical applications of Global Navigation Satellite Systems (GNSS). Traditional receiver autonomous integrity monitoring (RAIM) and advanced RAIM (ARAIM) methods evaluate integrity risk solely based on prior information, such as measurement models and prior fault probabilities. For exploring the benefits of incorporating measurements, previous studies introduced the concept of Bayesian RAIM to evaluate posterior integrity risk. On this basis, this paper proposes a Bayesian RAIM approach that offers a guaranteed upper bound on the posterior integrity risk under arbitrary distributions of measurement faults. This is achieved by (a) deriving the posterior probability density of the true state, (b) establishing a formula to evaluate the posterior integrity risk, (c) searching the worst-case fault distributions that maximize the posterior integrity risk. The key difference between our approach and the existing method lies in step (c): the latter searches the worst-case faults to maximize the posterior probabilities of each hypothesis. Simulation results suggest that the proposed Bayesian RAIM approach offers comparable performance to the ARAIM method in terms of the predictive integrity risk and continuity risk. Meanwhile, the real-time measurement-dependent posterior integrity risk from our approach is lower than the ARAIM integrity risk in most cases.