Theoretical Results on the Optimal Detection Statistics for Autonomous Integrity Monitoring

One of the most commonly used detection statistics in autonomous integrity monitoring is the solution separation statistic. In this paper, we show that the solution separation statistic is closely linked to the optimal detection statistics. More precisely, we show that in the case of one threat, even multi-dimensional, the optimal detection statistic is the solution separation, and that in the case of many one-dimensional threats, the optimal statistics can be expressed as a function of the solution separations corresponding to each threat. This is achieved by casting the search of the optimal detection region as a mini-max problem and by using the Neyman–Pearson lemma to limit the search of the detection regions to a class of regions parameterized by a bias. These results allow us to establish a lower bound on the minimum achievable integrity risk. Copyright © 2017 Institute of Navigation