Iterative Update of the Pole Locations in a Wiener-Schetzen Model

A large variety of nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs), while the nonlinearity is modeled by a multivariate polynomial. The coefficients of the polynomial are the parameters of the model. The use of OBFs allows to incorporate prior knowledge about the system dynamics into the model, via user-specified pole locations. A mismatch between the poles used to construct the OBFs and the true poles of the underlying system can be handled by increasing the number of OBFs. Nevertheless, this results in a large number of parameters to be estimated, and eventually in a larger uncertainty of the estimated model. We propose an iterative method to update the pole locations of the model without making repeated experiments. An initial estimate of the pole locations is obtained from the best linear approximation (BLA) of the system. This paper analyzes the causes for the mismatch between the estimated and the true pole locations. Each of the error sources is tackled, resulting in the iterative method. The method is illustrated on a simulation example.