AUTOREGRESSIVE MODELS IN STOCHASTIC-APPROXIMATION ALGORITHMS FOR PARAMETER-ESTIMATION

This paper describes an on-line procedure for estimating the parameters of linear discrete time systems when input and output are subjected to measurement noise of unknown statistics. The algorithm is derived through stochastic approximation, To ensure unbiased parameter estimates, the correlated part of the residuals are first estimated by modelling the residuals as an autoregressive series, and then subtracted from the estimated residuals. The algorithm estimates the system parameters and noise parameters simultaneously. Three gain expressions are derived for the estimation algorithm. They are (a) scalar gain, (b) diagonal matrix gain, and (c) square matrix gain. © 1979 Taylor & Francis Group, LLC.