Optimal linear filtering under parameter uncertainty

This paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state, output, and input matrices. The design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty. The results provided generalize the ones available in the literature to date in several directions. First, all system matrices can be corrupted by parameter uncertainty, and the admissible uncertainty may be structured. Assuming the order of the uncertain system is known, the optimal robust linear filter is proved to be of the same order as the order of the system. In the present case of convex bounded parameter uncertainty, the basic numerical design tools are linear matrix inequality (LMI) solvers instead of the Riccati equation solvers used for the design of robust filters available in the literature to date. The paper that contains the most important and very recent results on robust filtering is used for comparison purposes. In particular, it is shown that under the same assumptions, our results are generally better as far as the minimization of a guaranteed error variance is considered. Some numerical examples illustrate the theoretical results.