Local polynomial approach for identification of nonparametric nonlinear systems: One dimensional case

In this study, we consider the local polynomial approach for the identification of the one dimensional nonparametric nonlinear systems. A kernel-based weighted least squares estimator is first introduced and then the strong consistency of the estimates is established. The algorithms provide recursive estimates not only for the function values but also their derivatives with specified orders at fixed points. Thus, from the local approximation point of view, the presented approach generates more accurate identification results compared with the classical approaches such as the local constant estimator and the local linear estimator.