Hierarchical generalized extended parameter identification for multivariable equation-error ARMA-like systems by using the filtering identification idea

Abstract

The filtering identification idea is an effective tool for handling the parameter identification of systems with colored noise. The hierarchical identification principle is an effective approach for addressing the identification of complex systems. For multivariable equation-error autoregressive moving-average-like (M-EEARMA-like) models with colored noise, which are also called multivariable controlled autoregressive autoregressive moving-average-like (M-CARARMA-like) models, this paper investigates and proposes the filtered hierarchical generalized extended stochastic gradient identification method, the filtered hierarchical multi-innovation generalized extended stochastic gradient identification method, the filtered hierarchical generalized extended recursive gradient identification method, the filtered hierarchical multi-innovation generalized extended recursive gradient identification method, the filtered hierarchical generalized extended least squares identification method, and the filtered hierarchical multi-innovation generalized extended least squares identification method by using the filtering identification idea and the hierarchical identification principle from available input–output data. These filtered hierarchical generalized extended identification methods can be extended to other linear and nonlinear multivariable stochastic systems with colored noise.