Estimation of an N–L–N Hammerstein–Wiener model

Abstract

Estimation of a single-input single-output block-oriented model is studied. The model consists of a linear block embedded between two static nonlinear gains. Hence, it is called N–L–N Hammerstein–Wiener model. First, the model structure is motivated and the disturbance model is discussed. The paper then concentrates on parameter estimation. A relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear-in-parameters. This leads to a simple algorithm which minimizes the original loss function. The convergence and consistency of the algorithm are studied. In order to reduce the variance error, the obtained linear model is further reduced using frequency weighted model reduction. Simulation study will be used to illustrate the method.