A Recursive Local Linear Estimator for Identification of Nonlinear ARX Systems: Asymptotical Convergence and Applications

In this paper, we propose a recursive local linear estimator (RLLE) for nonparametric identification of nonlinear autoregressive systems with exogenous inputs (NARX). First, the RLLE is introduced. Next, the strong consistency as well as the asymptotical mean square error properties of the RLLE are established, and then an application of the RLLE to an additive nonlinear system is discussed. The RLLE provides recursive estimates not only for the function values but also their gradients at fixed points. A simulation example is provided to confirm the theoretical analysis.