The Effect of Uncertain Covariance on a Chi-Square Integrity Monitor

This paper presents a method for overbounding integrity risk for chi-square monitors, which detect anomalies by analyzing the two-norm of a vector of input signals. Aircraft navigation examples of chi-square monitors include many Receiver Autonomous Integrity Monitoring (RAIM) algorithms as well as fault-specific detection algorithms in space-based and ground-based augmentation systems for GNSS (e.g., signal deformation monitoring and ionosphere gradient monitoring). Simple inflation of the noise model for the input-data vector does not always ensure conservative bounding, particularly for unfavorable fault cases. To ensure integrity in such fault cases, this paper introduces a conservative modeling approach for replacing a generalized chi-square distribution with a conventional chi-square distribution. This conservative model relies on bracketing the range of variation of the input-data covariance matrix between an upper and a lower bound.