A kernel-based PEM estimator for forward models
Abstract
This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with a high-order stable ARX model. However, such choice induces a certain undesired prior information in the system that we want to estimate. To overcome this issue, we propose a new kernel-based paradigm which is formulated directly in terms of the impulse responses of the forward model and leading to the identification of a high-order MAX model. The most challenging step is the estimation of the kernel hyperparameters optimizing the marginal likelihood. The latter, indeed, does not admit a closed form expression. We propose a method for evaluating the marginal likelihood which makes possible the hyperparameters estimation. Finally, some numerical results showing the effectiveness of the method are presented.
Cite
@article{arxiv.2409.09679,
title = {A kernel-based PEM estimator for forward models},
author = {Giulio Fattore and Marco Peruzzo and Giacomo Sartori and Mattia Zorzi},
journal= {arXiv preprint arXiv:2409.09679},
year = {2024}
}