Least squares and stochastic gradient parameter estimation for multivariable nonlinear Box‐Jenkins models based on the auxiliary model and the multi‐innovation identification theory

Abstract

PurposeThe purpose of this paper is to study the identification methods for multivariable nonlinear Box‐Jenkins systems with autoregressive moving average (ARMA) noises, based on the auxiliary model and the multi‐innovation identification theory.Design/methodology/approachA multi‐innovation generalized extended least squares (MI‐GELS) and a multi‐innovation generalized ex‐tended stochastic gradient (MI‐GESG) algorithms are developed for multivariable nonlinear Box‐Jenkins systems based on the auxiliary model. The basic idea is to construct an auxiliary model from the measured data and to replace the unknown terms in the information vector with their estimates (i.e. the outputs of the auxiliary model).FindingsIt is found that the proposed algorithms can give high accurate parameter estimation compared with existing stochastic gradient algorithm and recursive extended least squares algorithm.Originality/valueIn this paper, the AM‐MI‐GESG and AM‐MI‐GELS algorithms for MIMO Box‐Jenkins systems with nonlinear input are presented using the multi‐innovation identification theory and the proposed algorithms can improve the parameter estimation accuracy. The paper provides a simulation example.