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) |
Keywords:
Recursive identification; Parameter estimation; Convergence properties; Stochastic gradient; Least squares; Hammerstein models; Wiener models; Martingale convergence theoremReferences:
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