Distributed tracking with consensus on noisy time-varying graphs: Convergence results and applications

In this paper we consider the problem of distributed tracking with consensus on a time-varying graph with noisy communication s links and sensing constraints. We develop a framework to handle the time-varying network topology in which not every node has local observations to generate own local tracking estimates. Our approach introduces the concepts of active node set and connectivity graph to characterize such a network, and by merging these two, an effective network graph is obtained. Then we propose a distributed tracking-with-consensus algorithm for such a network model. We establish the conditions on the connectivity graph so that distributed consensus can be achieved in the presence of noisy communication links when the effective network graph is time-varying. We also discuss how this problem is motivated by the problem of distributed tracking of spare-home objects in a hybrid space surveillance network (SSN) formed by both ground and satellite nodes. Simulation results of the proposed distributed tracking with consensus algorithm are given for a two-dimensional hybrid sensor network. They show that our algorithm perform, almost the same as the distributed local Kalman filtering with centralized fusion on a noisy time-varying graphs with incomplete data, while the proposed algorithm has the additional advantages of flexibility and scalability.