Kalman Filter Innovation-Based Optimal Integrity Monitoring Against Unknown Bias in Time Updates

Abstract Kalman-filter-based multi-sensor navigation systems are promising for future mobility but vulnerable to sensor faults, necessitating integrity monitoring (IM). This paper proposes an optimal innovation-based IM approach that minimizes the integrity risk against dynamic sensor faults using current-time information and a single filter. While the solution separation (SS) concept provides an optimal solution yielding the snapshot-based SS IM, we approach this problem through innovation-domain optimization. We formulate a min-max problem, reparametrize it to apply the Neyman–Pearson lemma, and obtain the position-domain projection of the innovation as the optimal statistic. We prove that this solution is mathematically equivalent to the snapshot-based SS statistic. Performance evaluation of the innovation-based position-domain IM method under IMU faults demonstrates superior integrity performance compared with innovation-based range-domain IM. Comparison with the full SS IM approach using parallel filters shows the advantages of the proposed approach in improving computational efficiency while narrowing the integrity performance gap as measurement redundancy increases.