Identification of polynomial input/output recursive models with simulation error minimisation methods

Polynomial input/output (I/O) recursive models are widely used in nonlinear model identification for their flexibility and representation capabilities. Several identification algorithms are available in the literature, which deal with both model selection and parameter estimation. Previous works have shown the limitations of the classical prediction error minimisation approach in this context, especially (but not only) when the disturbance contribution is unknown, and suggested the use of a simulation error minimisation (SEM) approach for a better selection of the I/O model. This article goes a step further by integrating the model selection procedure with a simulation-oriented parameter estimation algorithm. Notwithstanding the algorithmic and computational complexity of the proposed method, it is shown that it can sometimes achieve great performance improvements with respect to previously proposed approaches. Two different parameter estimation algorithms are suggested, namely a direct SEM optimisation algorithm, and an approximate method based on multi-step prediction iteration, which displays several convenient properties from the computational point of view. Several simulation examples are shown to demonstrate the effectiveness of the suggested SEM approaches.