On Nonparametric Identification of Wiener Systems with Deterministic Inputs

The identification of nonlinear Wiener models (NWMs) for deterministic inputs and Gaussian noise is studied. We show that the nonparametric kernel regression estimation of the nonlinearity of a NWM (based on the Nadaraya-Watson kernel estimator) can be formulated as a parametric estimation problem leading to a Gaussian conditional observation model. This property allows us to derive the maximum likelihood estimators of the unknown parameters of the NWM, as well as the associated Cramér-Rao (CR) bounds. We finally derive a CR-like bound on the global mean squared error (MSE) of the estimated nonlinearity of a NWM. Numerical results obtained for a pulse wave input are presented and compared to the ones based on the Nadaraya-Watson kernel estimator.