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Identification of Hammerstein nonlinear ARMAX systems. (English) Zbl 1086.93063

Summary: Two identification algorithms, an iterative least-squares and a recursive least-squares, are developed for Hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by ARMAX/CARMA models. The basic idea is to replace unmeasurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. Convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition. The simulation results validate the algorithms proposed.

MSC:

93E12 Identification in stochastic control theory
93E10 Estimation and detection in stochastic control theory
93E24 Least squares and related methods for stochastic control systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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