Initialization and model reduction for Wiener model identification

The identification of nonlinear systems by the minimization of a prediction error criterion suffers from the problem of local minima. To get a reliable estimate we need good initial values for the parameters. In this paper we discuss the class of nonlinear Wiener models, consisting of a linear dynamic system followed by a static nonlinearity. By selecting a parameterization where the parameters enter linearly in the error, we can obtain an initial estimate of the model via linear regression. An example shows that this approach may be preferential to trying to estimate the linear system directly form input-output data, if the input is not Gaussian. We discuss some of the user’s choices and how the linear regression initial estimate can be converted to a desired model structure to use in the prediction error criterion minimization. The method is also applied to experimental data.