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Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. (English) Zbl 1165.65308

Summary: An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein-Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
93E10 Estimation and detection in stochastic control theory
62F10 Point estimation
62H12 Estimation in multivariate analysis
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