Optimal linear filtering under parameter uncertainty
Author:
- 1 January 1999
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 47 (1) , 168-175
Abstract
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.Keywords
This publication has 9 references indexed in Scilit:
- Multiplier-free realizations for FIR multirate converters based on mixed-radix number representationIEEE Transactions on Signal Processing, 1997
- Robust minimum variance filteringIEEE Transactions on Signal Processing, 1995
- Decentralized control through parameter space optimizationAutomatica, 1994
- Robust Kalman filtering for uncertain systemsSystems & Control Letters, 1994
- Linear Matrix Inequalities in System and Control Theory1994
- 2 guaranteed cost control for uncertain continuous-time linear systemsSystems & Control Letters, 1992
- On a Convex Parameter Space Method for Linear Control Design of Uncertain SystemsSIAM Journal on Control and Optimization, 1991
- Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen—Hollot boundsSystems & Control Letters, 1987
- Guaranteed error estimation in uncertain systemsIEEE Transactions on Automatic Control, 1975