On the design of multiple kernels for nonparametric linear system identification

It has been recently shown that regularization methods for system identification have, under certain circumstances, advantages over classical parametric methods. This advantage is mainly due to the fact that the regularization term, which have a well known Bayesian interpretation, is an effective and flexible mean to control model complexity. In this paper we take a principled approach to the design of kernels and, using a well known decomposition of the so called “stable spline” kernel, we show that it provides a natural description for impulse responses of linear systems. Motivated by this decomposition we introduce a new family of multiple kernels which yields a remarkable improvement over state-of-the-art kernels when it comes to modeling resonant systems.