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Volterra series are especially useful for nonlinear system identification,also thanks to their capability to approximate a broad range of input-outputmaps. However, their identification from a finite set of data is hard, due tothe curse of dimensionality. Recent approaches have shown how regularizedkernel-based methods can be useful for this task. In this paper, we propose anew regularization network for Volterra models identification. It relies on anew kernel given by the product of basic building blocks. Each block containssome unknown parameters that can be estimated from data using marginallikelihood optimization. In comparison with other algorithms proposed in theliterature, numerical experiments show that our approach allows to betterselect the monomials that really influence the system output, much increasingthe prediction capability of the model.

A novel Multiplicative Polynomial Kernel for Volterra series identification