Convergence analysis of distributed Kalman filtering for relative sensing networks

We study the distributed Kalman filtering problem in relative sensing networks with rigorous analysis. The relative sensing network is modeled by an undirected graph while nodes in this network are running homogeneous dynamical models. The sufficient and necessary condition for the observability of the whole system is given with detailed proof. By local information and measurement communication, we design a novel distributed suboptimal estimator based on the Kalman filtering technique for comparison with a centralized optimal estimator. We present sufficient conditions for its convergence with respect to the topology of the network and the numerical solutions of n linear matrix inequality (LMI) equations combining system parameters. Finally, we perform several numerical simulations to verify the effectiveness of the given algorithms.