Behavior of the discrete-time Kalman filter under incorrect noise covariances

In this paper, we study the behavior of the discrete-time Kalman filter under incorrect noise covariances. In particular, we are interested in the characteristic of the actual performance of the Kalman filter. The filter performance is quantified by the actual one-step predictor error covariance. Convergence and divergence analyses of the actual one-step predictor error covariance are given. The results developed in the paper provide useful insights in the behavior of the Kalman filter when the noise covariances used in designing the filter are inexact.