Discrete-time Kalman filter under incorrect noise covariances

The optimum filtering results of Kalman filtering for linear dynamic systems require an exact knowledge of the process noise covariance matrix Q, the measurement noise covariance matrix R and the initial error covariance matrix P₀. In a number of practical solutions, Q, R and P₀, are either unknown or are known only approximately. In this paper the sensitivity due to class of errors in the statistical modeling employing a Kalman filter is discussed. In particular, we present a special case where it is shown that Kalman filter gains can be insensitive to scaling of covariance matrices. Some basic results are derived to describe the mutual relations among the three covariance matrices (actual and perturbed covariance matrices), their respective Kalman gain K_k and the error covariance matrices P_k. Experimental results using a tactical grade inertial measurement unit are presented to illustrate the theoretical results