Approximate SEM identification of polynomial input-output models

Achieving accurate long range prediction and simulation performance in the identification of nonlinear polynomial input-output models requires both careful model selection and accurate parameter estimation. The simulation error minimization (SEM) identification approach has been shown to provide significant advantages over the standard prediction error minimization (PEM) approach for these modelling objectives, but has been generally limited to the model selection task for computational reasons. A computationally efficient scheme is here proposed for the parameter estimation task, that suitably fits in the model selection scheme. The presented approach extends to the nonlinear case a method, based on iterative predictor estimation with increasing prediction horizon, previously developed for linear models. The effectiveness of the proposed algorithm is demonstrated by means of simulation examples. A benchmark for nonlinear identification is also analyzed.