Testing the Covariance Matrix of the Innovation Sequence in Application to Aircraft Sensor Fault Detection

Operative methods of 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 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 the elements of the matrix is used for the scalar measure of the Wishart matrix being tested, while in the second algorithm the maximal eigenvalue of this matrix is used. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model is considered, and detection of pitch rate gyro failures, which affect the covariance matrix of the innovation sequence, are examined. Some recommendations for the fastest detection of failure are given.