The model equivalence based parameter estimation methods for Box–Jenkins systems

Abstract

This paper presents a model equivalence based recursive extended least squares algorithm for output-error autoregressive moving average (i.e., Box–Jenkins) systems. The key is to transform a Box–Jenkins system into a controlled autoregressive moving average system by the model equivalent transformation, to estimate the parameters of the new system, and to compute the parameter estimates of the original system by comparing coefficients of polynomials. In order to show advantages of the proposed algorithm, this paper gives an auxiliary model based recursive generalized extended least squares (AM-RGELS) algorithm for comparison. The simulation results indicate that the proposed algorithm can improve the parameter estimation accuracy compared with the AM-RGELS algorithm.