Recursive parameter estimation of transfer function models

Abstract

A recursive technique to estimate the parameters of a general class of Box-Jenkins transfer function models is presented. This class of models allows multiple inputs, general ARMA noise and time-varying parameters. Both the system and noise parameters are simultaneously estimated, even when their dynamic structures are different. The recursive equations for parameter estimation are derived in closed form by using the extended Kalman filter technique. Convergence analysis is 1 performed Using Ljung's theory. Simulation results indicate that, with reasonable initial conditions, the estimates compare favourably with the common non-recursive least-square estimates. Accuracy and convergence rate are improved if the parameter update is delayed and if estimation of the noise variance is based on the most recent data rather than the whole past history. The method is readily applicable for on-line situations.