Invariance Approach to Integrity Monitoring Fault Detectors

This contribution explores the optimality properties of integrity monitoring fault detectors by exploiting the hypothesis testing invariance theory. The focus is on three fault detectors widely used in GNSS: the Generalized Likelihood Ratio Test (GLRT), the Least Squares (LS) residuals method, and the Solution Separation (SS) test statistics. The GLRT has been shown to be uniformly most powerful invariant for linear Gaussian models, and the single-state SS test statistic has been proven to be the optimal detector which minimizes the so-called worst-case integrity risk, if the LS estimator is used to estimate the unknown state vector. This work aims i) to make the connection between these two optimal detectors within the invariance framework, and ii) to establish the conditions for their equivalence in the case of a single alternative faulty hypothesis.