Robust H_2 Filtering For Structured Uncertainty: The Performance Of Probabilistic And Minimax Schemes.

Abstract

: A probabilistic approach to the robustification of Kalman filters is presented. It results in a higher order model, in which the uncertainty can be taken into account by simply modifying the noise covariance matrices. The proposed method provides a systematic way of performing this transformation. The performance of the robustified Kalman filter is compared to that of a recently proposed minimax H 2 scheme, based on two coupled Riccati equations and a one--dimensional numerical search. It is concluded that such methods should be used with care, since their guaranteed performance may be worse than that obtained by doing no filtering at all. 1 Introduction The aim of this paper is to discuss two recently proposed design techniques for robust filtering: 1. to minimize the worst case mean square error by utilizing two coupled Riccati equations, see e.g. [17]; 2. obtaining modified Wiener or Kalman filters by averaging over stochastic model uncertainties, as described in [16] and [13]. T..