  In the application of the Expectation Maximization algorithm to
identification of dynamical systems, internal states are typically chosen as
latent variables, for simplicity. In this work, we propose a different choice
of latent variables, namely, system disturbances. Such a formulation elegantly
handles the problematic case of singular state space models, and is shown,
under certain circumstances, to improve the fidelity of bounds on the
likelihood, leading to convergence in fewer iterations. To access these
benefits we develop a Lagrangian relaxation of the nonconvex optimization
problems that arise in the latent disturbances formulation, and proceed via
semidefinite programming.
