Bayesian fault-tolerant protection level for multi-constellation navigation from integrity perspective

The multi-constellation is anticipated to enhance navigation performance by providing abundant satellites in view. However, with this comes the necessity of considering simultaneous fault events in integrity risk assessment when applying the receiver autonomous integrity monitoring. Meanwhile, the integrity monitoring efficacy remains vulnerable to the uncertainty of prior fault probability in multi-constellation navigation. In this regard, this paper proposes a Bayesian approach for the multi-constellation navigation at the user segment to strengthen the evaluation robustness of integrity risk. We bound the Bayesian posterior probability of fault hypotheses that comprise multiple concurrent faults (satellite or constellation faults) without assuming an optimistic prior fault distribution. This posterior probability bound leads to an associated Bayesian integrity risk. Following that, a fault-tolerant estimate accounting for multiple faults and nominal biases is derived to minimize the Bayesian integrity risk. Finally, we establish a Bayesian fault-tolerant protection level to bound the position estimate error and assess the integrity availability, resisting the uncertainty in the prior fault probability. Results validate the robustness improvement the proposed Bayesian approach fulfills compared with the advanced receiver autonomous integrity monitoring in four cases. In addition, the Bayesian approach can lower the protection level at the cost of an offset from the least-square estimate while maintaining the same position accuracy.