Linear System Identification via EM with Latent Disturbances and Lagrangian Relaxation

TL;DR

This paper introduces a novel approach to system identification using EM with latent disturbances and Lagrangian relaxation, improving convergence and handling singular models more effectively.

Contribution

It proposes using system disturbances as latent variables in EM, along with a Lagrangian relaxation technique via semidefinite programming, for better system identification.

Findings

Handles singular state space models effectively

Achieves faster convergence in EM iterations

Provides tighter likelihood bounds

Abstract

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.