A Chi-square test for fault-detection in Kalman filters

A test for real-time detection of soft failures in navigation systems using Kalman filters has been proposed by Kerr. The test is based on the overlap between the confidence regions associated with two estimates, one obtained from a Kalman filter using on-line measurements, and the other based solely on a priori information. An alternate computational technique is presented which is based on constructing a chi-square test statistic from the difference between the two estimates and comparing it to a precomputed threshold. The chi-square test avoids the iterative computations required by the two-ellipsoid method for dimensions of two and higher.