In this contribution, we propose a kernel-based method for the identification
of linear systems from noisy and incomplete input-output datasets. We model the
impulse response of the system as a Gaussian process whose covariance matrix is
given by the recently introduced stable spline kernel. We adopt an empirical
Bayes approach to estimate the posterior distribution of the impulse response
given the data. The noiseless and missing data samples, together with the
kernel hyperparameters, are estimated maximizing the joint marginal likelihood
of the input and output measurements. To compute the marginal-likelihood
maximizer, we build a solution scheme based on the Expectation-Maximization
method. Simulations on a benchmark dataset show the effectiveness of the
method.Comment: 16 pages, submitted to IEEE Conference on Decision and Control 201