Kalman filtering in mobile consensus networks

In this paper, we design a Kalman filter for a mobile sensor network that tries to reach consensus based solely on relative measurements. We show, that this problem cannot be solved with state-of-the-art Kalman consensus filters because such a mobile consensus network is not observable. Hence, we propose a system transformation and the concept of a reference agent to obtain an asymptotically stable and observable system description. Based on the transformed system, we design a central Kalman filter and visualize the factorization details with Dynamic Bayesian Networks (DBN). Then, the Kalman filter is modified to obtain one decentral Kalman filter for each agent that uses delayed measurements propagated through the communication topology. This allows each agent to estimate the whole system state using only information sent by its neighbor agents defined by a communication topology. Simulation results demonstrate our method.