On Filtering and Smoothing

In this paper we consider the problems of optimal ti smoothing and sub-optimal t1 filtering. We show that the optimal smoother is a finite dimensional, non-causal system and that it can be obtained by solving a fixed finite linear programming problem the order of which is determined by the Mchfillan degree of the plant. In the case of > 0, there is a finite linear programming problem the solution of which yields a finite dimensional filter that achieves performance within 6 of optimal. The order of this associated linear programming problem can be bounded, albeit conservatively, by an explicit function of E.