IEEE Transactions on Automatic Control, Vol.55, No.7, 1615-1626, 2010
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.
Keywords:Asymptotical analysis;kernel estimation;local polynomial estimation;nonlinear system identification;optimal estimator