On the relative performance of the Kalman and Wiener filters

Upper and lower bounds on the error covariance matrices of the Kalman and Wiener filters for linear finite state time-invariant system are derived. These bounds yield a measure of the relative estimation accuracy of these filters and provide a practical tool for determining when the implementational complexity of a Kalman filter can be justified. The calculation of these bounds requires little more than the determination of the corresponding Wiener filter.