H2 optimal robust filtering

In this seminar, a new design procedure for H2 optimal robust filtering is presented. The robust filter is determined from the equilibrium solution of a minimax programming problem where the H2 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. 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, the proposed one does not include any degree of conservatism. The classical static linear approximation problem as well as the filter design problem corresponding to continuous and discrete time linear systems are considered. An illustrative example is presented. The seminar ends with a discussion on a problem still unsolved.