Sensor fault detection by testing the largest eigenvalue of the innovation covariance using Tracy-Widom distribution

Abstract

Operative method of testing the innovation covariance of the Kalman filter is proposed. The maximal eigenvalue of the random Wishart matrix is used in this process as monitoring statistic, and the testing problem is reduced to determine the asymptotics for largest eigenvalue of the Wishart matrix. As a result, algorithm for testing the innovation covariance based on Tracy-Widom distribution is proposed. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model is considered, and detection of pitch rate gyro, air speed indicator and angle of attack sensor failures, which affect the innovation covariance, are examined.