The filtering based auxiliary model generalized extended stochastic gradient identification for a multivariate output-error system with autoregressive moving average noise using the multi-innovation theory

This paper studies the parameter estimation algorithms of multivariate output-error autoregressive moving average (M-OEARMA) systems. By means of the filtering technique and the auxiliary model identification idea, this paper gives an auxiliary model generalized extended stochastic gradient (AM-GESG) algorithm for identifying the M-OEARMA system as a comparison. In order to enhance the performance of the AM-GESG algorithm, a modified filtering based AM-GESG algorithm and a filtering based auxiliary model multi-innovation generalized extended stochastic gradient algorithm are proposed. Compared with the AM-GESG algorithm, the proposed two algorithms can generate highly accurate parameter estimates. The simulation examples demonstrate that the proposed algorithms are effective for identifying the M-OEARMA systems.