Performance analysis of the recursive parameter estimation algorithms for multivariable Box–Jenkins systems

Abstract

Two auxiliary model based recursive identification algorithms, a generalized extended stochastic gradient algorithm and a recursive generalized extended least squares algorithm, are developed for multivariable Box–Jenkins systems. The basic idea is to use the auxiliary models to estimate the unknown noise-free outputs of the system and to replace the unmeasurable terms in the information vectors with their estimates. We prove that the estimation errors given by the proposed algorithms converge to zero under the persistent excitation condition. Finally, an example is provided to show the effectiveness of the proposed algorithms.