Identification of linear systems in canonical form through an EM framework

Least-squares estimation has always been the main approach when applying prediction error methods (PEM) in the identification of linear dynamical systems. Regardless of the estimation algorithm, if there are no restrictions on the form of the matrices we want to estimate, the matrices can be determined up to within a linear transformation and thus the result may be different than the true solution and the convergence of iterative algorithms may be affected. In this paper, we apply a new identification procedure based on the Expectation Maximization framework to a family of identifiable state-space models. To our knowledge, this is the first complete solution of Maximum-Likelihood estimation for general linear state-space models.