Auxiliary Model Hierarchical Generalized Extended Recursive Parameter Estimation for Autoregressive Output‐Error Autoregressive Moving Average Systems

ABSTRACT This paper considers recursive parameter identification for autoregressive output‐error autoregressive moving average (AR‐OE‐ARMA) systems from the perspective of computational efficiency. By means of the hierarchical identification principle, we propose an auxiliary model hierarchical generalized extended stochastic gradient algorithm (AM‐HGESG), an auxiliary model hierarchical multi‐innovation generalized extended stochastic gradient (AM‐HMI‐GESG) algorithm, an auxiliary model hierarchical generalized extended recursive gradient algorithm (AM‐HGERG), an auxiliary model hierarchical multi‐innovation generalized extended recursive gradient (AM‐HMI‐GERG) algorithm, an auxiliary model hierarchical generalized extended least squares algorithm (AM‐HGELS), and an auxiliary model hierarchical multi‐innovation generalized extended least squares (AM‐HMI‐GELS) algorithm by using the multi‐innovation identification theory. The proposed hierarchical identification methods can be extended to other linear and nonlinear multivariable stochastic systems with colored noises.