Bounds on estimation errors of discrete-time filters under modeling uncertainty

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a designer can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices are available.