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This paper considers a problem of distributed tracking with consensus on a time-varying graph with noisy communications links. A distributed tracking with consensus algorithm is proposed to handle a time-varying network topology in which every node generates own local tracking estimates and communicates over noisy links. The conditions on the connectivity graph are established so that distributed consensus can be achieved in the presence of noisy communication links when the graph topology is time-varying. The steady-state performance of the proposed distributed tracking with consensus algorithm is analyzed and compared with that of distributed local Kalman filtering with centralized fusion. Simulation results and performance analysis of the proposed algorithm are also given.