Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems

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Abstract

According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided.

Keywords

Iterative algorithm
Jacobi iteration
Matrix equation
Gradient search
Parameter estimation
Iterative identification
Hierarchical identification
Multivariable OEMA-like model
Multivariable CARMA-like model

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This work was supported in part by the National Natural Science Foundation of China (Nos. 60973043 and 50876093), International Cooperation and Exchange Project of Science and Technology (Department of Zhejiang Province, No. 2009C34008), and Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists (No. R4100133).