A Generalized GraphEM for Sparse Time-Varying Dynamical Systems

We consider the problem of joint parameter estimation and smoothing in structured linear systems using the expectation maximization (EM) framework. Specifically, we explore how partially known sparsity structures in the estimation model can be leveraged to improve the computation speed and performance of the considered EM approaches. We use these ideas to generalize a recently proposed GraphEM algorithm to a linear time-varying setting, where the sparsity structures may vary in time. We obtain a biconvex form of the majorizing function in the M-step, which is minimized subject to an l1-regularization using a Douglas-Rachford proximal splitting algorithm. Numerical results using a satellite positioning example shows significant improvements in the estimation errors and an F1-score that quantifies model sparsity.