l1-optimal estimation for discrete-time linear systems

A linear multichannel estimation problem with discrete-time linear shift-invariant models is formulated in the time domain as a minimum l¹ 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 l¹ -optimal design versus l²- or H^∞-optimal designs is presented. A sample problem is solved to illustrate the computational procedure, as well as to compare the relative performances of the l¹-, l² and H^∞-optimal estimators in a practical situation