l/sup 1/-optimal estimation for discrete-time linear systems

摘要

A linear multichannel estimation problem with discrete-time linear shift-invariant models is formulated in the time domain as a minimum l/sup 1/ norm approximation problem. It is shown, using some key results from optimization theory, that solving the approximation problem is equivalent to solving a sequence of linear programming problems which terminates when an optimal or near-optimal solution is reached. The motivation for considering an l/sup 1/-optimal design versus l/sup 2/- or H/sup infinity /-optimal designs is presented. A sample problem is solved to illustrate the computational procedure, as well as to compare the relative performances of the l/sup 1/-, l/sup 2/ and H/sup infinity /-optimal estimators in a practical situation.