Testing the covariance matrix of the innovation sequence with sensor/actuator fault detection applications

Operative methods for testing the covariance matrix of the innovation sequence of the Kalman filter are proposed. The quadratic form of the random Wishart matrix is used in this process as a monitoring statistic, and the testing problem is reduced to the classical problem of minimization of a quadratic form on the unit sphere. As a result, two algorithms for testing the covariance matrix of the innovation sequence are proposed. In the first algorithm, the sum of all elements of the matrix is used as the scalar measure of the Wishart matrix that is being tested, while in the second algorithm, the largest eigenvalue of this matrix is used. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model are considered, and the detection procedure of sensor/actuator faults, which affect the covariance matrix of the innovation sequence, is examined. Some recommendations for the fastest detection of the fault are given.