Abstract
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 Cramer-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.
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