A novel Multiplicative Polynomial Kernel for Volterra series identification

Volterra series is especially useful for nonlinear system identification, also thanks to its capability to approximate a broad range of input-output maps. However, its identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularization strategies can be useful for this task. In this paper, we propose a new regularization network for Volterra models identification. It relies on a new kernel given by the product of basic building blocks. Each block contains some unknown parameters that can be estimated from data using marginal likelihood optimization or cross-validation. In comparison with other algorithms proposed in the literature, numerical experiments show that our approach allows to better select the monomials that really influence the system output, much increasing the prediction capability of the model. The method immediately extends also to polynomial NARMAX models.