A Simple Iterative Procedure for the Identification of the Unknown Parameters of a Linear Time Varying Discrete System

Abstract

A new “steepest descent” approach to the “adaptive control system” problem of the determination of the process dynamics of a time varying system is analyzed in considerable detail. The unknown parameters are the parameters of the impulse response of a linear discrete system. The identification procedure is a first-order iterative process and is designed to operate with the natural inputs of the system to be identified. After each new (single) input, new estimates of all the unknown parameters are computed. The method is computationally simple and, in its analysis, the effects of additive noise in the observations (of both input and output), random drift with time, or neglected parameters of the impulse response are handled with relative ease and become transparent. Time variations are taken directly into account, thus eliminating the necessity of the assumption of stationarity over a period of time.