Recent developments in system identification have brought attention to
regularized kernel-based methods. This type of approach has been proven to
compare favorably with classic parametric methods. However, current
formulations are not robust with respect to outliers. In this paper, we
introduce a novel method to robustify kernel-based system identification
methods. To this end, we model the output measurement noise using random
variables with heavy-tailed probability density functions (pdfs), focusing on
the Laplacian and the Student's t distributions. Exploiting the representation
of these pdfs as scale mixtures of Gaussians, we cast our system identification
problem into a Gaussian process regression framework, which requires estimating
a number of hyperparameters of the data size order. To overcome this
difficulty, we design a new maximum a posteriori (MAP) estimator of the
hyperparameters, and solve the related optimization problem with a novel
iterative scheme based on the Expectation-Maximization (EM) method. In presence
of outliers, tests on simulated data and on a real system show a substantial
performance improvement compared to currently used kernel-based methods for
linear system identification.Comment: Accepted for publication in Automatic
