Data filtering based maximum likelihood gradient estimation algorithms for a multivariate equation-error system with ARMA noise

In this paper, we use the maximum likelihood principle and the data filtering technique to study the identification issue of the multivariate equation-error system whose outputs are contaminated by an ARMA noise process. The key is to break the system into several regressive identification subsystems based on the number of the outputs. Then a multivariate equation-error subsystem is transformed into a filtered model and a filtered noise model, and a filtering based maximum likelihood extended stochastic gradient algorithm is derived to estimate the parameters of these two models. The filtering based maximum likelihood extended stochastic gradient algorithm has higher parameter estimation accuracy than the maximum likelihood generalized extended stochastic gradient algorithm and the maximum likelihood recursive generalized extended least squares algorithm. The simulation examples indicate that the proposed methods work well.