H2 Optimal Robust Filtering

Abstract

In this paper, a design procedure for H 2 optimal robust filtering is presented. The robust filter is determined from the equilibrium solution of a minimax programming problem where the H 2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all full order, linear, rational and causal filters. As the main contribution, it is shown that for the class of parameter uncertainty considered, the equilibrium solution of the aforementioned minimax problem can be exactly determined. In contrast to the design methods available in the literature to date, dealing with norm bounded or convex bounded parameter uncertainty, which naturally provide suboptimal solutions to the robust filtering problem, the one presented in this paper does not present any degree of conservatism due to the particular parameter uncertainty model taken into consideration. However, the price to be payed to reach robust optimality is that the order of the optimal robust filter is, in general, very high. The classical static linear approximation problem as well as the filter design problem corresponding to continuous and discrete time linear systems are considered. In the last section, an illustrative example is presented to make clear the main features of the reported results.