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 com ni uni cat! on 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 geneigte own local tracking estimates. Our approach introduces the concepts of active node set and connectivity graph to ch a l'acte rize such a network, and by mei'ging tliese two, an effective network graph is obtained. Then we propose a distributed tracking-with-consens us algorithm for such a network model. We establish the conditions on (II· connectivity graph so that distributed consensus can I» 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 spa re-home objects in a hybrid space surveillance network (SSN) I'm un il 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 |h ilium-, almost the same as the distributed local Kaiman filtering with centralized fusion on a noisy time-varying graphs with incomplete data, while the proposed algorithm has (lie additional advantages of flexibility and scalability.