On l/sub 1/ filtering and smoothing

摘要

The problems of optimal l/sub 1/ smoothing and suboptimal l/sub 1/ filtering are considered. It is shown that the optimal smoother is a finite-dimensional, noncausal system, and that it can be obtained by solving a fixed finite linear programming problem whose order is determined by the McMillan degree of the plant. In the case of l/sub 1/ filtering, it is shown that, given any in 0, there is a finite linear programming problem whose solution yields a finite-dimensional filter that achieves performance within in of optimal. The order of this associated linear programming problem can be bounded, albeit conservatively, by an explicit function of in .