Joint state estimation and topology inference for graphical dynamical systems

In this paper, we consider the problem of joint state estimation and topology inference for a class of graphical dynamical systems, where the graph topology matrix is involved in the dynamical systems. A non-convex objective function, containing an equality constraint on the row sum of the topology matrix, is established with respect to the state and the topology, in which the estimated node states and observations at the historical time steps are used to infer the graph topology, and a regularization term is designed to enhance the sparsity of the graph topology. Then, the state estimation and topology inference are obtained by solving two convex subproblems in manner of using the Kalman filtering and the alternating direction method of multipliers (ADMM) algorithms, respectively. Specially, by separating the non-differentiable regularization term and utilizing a proximity operator, we derive an iterative solution with high computational efficiency to infer the graph topology in the ADMM algorithm. To verify the effectiveness of the proposed algorithm, simulation with a car-following model is carried out.