Convergence of the auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm for Box–Jenkins systems

Abstract

This paper focuses on the parameter estimation problem of Box–Jenkins systems. Using the multi-innovation identification theory, an auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm is derived. The convergence of the proposed algorithm is analyzed based on the stochastic martingale theory. It is proved that the parameter estimation errors converge to zero under persistent excitation conditions. Two simulation examples are provided to confirm the convergence results.