  We propose a new method for blind system identification. Resorting to a
Gaussian regression framework, we model the impulse response of the unknown
linear system as a realization of a Gaussian process. The structure of the
covariance matrix (or kernel) of such a process is given by the stable spline
kernel, which has been recently introduced for system identification purposes
and depends on an unknown hyperparameter. We assume that the input can be
linearly described by few parameters. We estimate these parameters, together
with the kernel hyperparameter and the noise variance, using an empirical Bayes
approach. The related optimization problem is efficiently solved with a novel
iterative scheme based on the Expectation-Maximization method. In particular,
we show that each iteration consists of a set of simple update rules. We show,
through some numerical experiments, very promising performance of the proposed
method.
