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

ABSTRACT 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. Copyright © 2013 Institute of Navigation.