  In this paper, we propose a novel algorithm for the identification of
Hammerstein systems. Adopting a Bayesian approach, we model the impulse
response of the unknown linear dynamic system as a realization of a zero-mean
Gaussian process. The covariance matrix (or kernel) of this process is given by
the recently introduced stable-spline kernel, which encodes information on the
stability and regularity of the impulse response. The static non-linearity of
the model is identified using an Empirical Bayes approach, i.e. by maximizing
the output marginal likelihood, which is obtained by integrating out the
unknown impulse response. The related optimization problem is solved adopting a
novel iterative scheme based on the Expectation-Maximization (EM) method, where
each iteration consists in a simple sequence of update rules. Numerical
experiments show that the proposed method compares favorably with a standard
algorithm for Hammerstein system identification.
