Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

This paper studies 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.