Non-Parametric Nonlinear System Identification: An Asymptotic Minimum Mean Squared Error Estimator

This paper studies the problem of the minimum mean squared error estimator for non-parametric nonlinear system identification. It is shown that for a wide class of nonlinear systems, the local linear estimator is a linear (in outputs) asymptotic minimum mean squared error estimator. The class of the systems allowed is characterized by a stability condition that is related to many well studied stability notions in the literature. Numerical simulations support the analytical analysis.