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Least-squares parameter estimation algorithm for a class of input nonlinear systems. (English) Zbl 1251.62036
Summary: We study least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.
MSC:
62M10Time series, auto-correlation, regression, etc. (statistics)
62F12Asymptotic properties of parametric estimators
65C60Computational problems in statistics