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This paper considers the problem of tracking objects with sparsely located binary sensors. Tracking with a sensor network is a challenging task due to the inaccuracy of sensors and difficulties in sensor network localization. Based on the simplest sensor model, in which each sensor reports only a binary value indicating whether an object is present near the sensor or not, we present an optimal distributed tracking algorithm which does not require sensor network localization. The tracking problem is formulated as a hidden state estimation problem over the finite state space of sensors. Then a distributed tracking algorithm is derived from the Viterbi algorithm. We also describe provably good pruning strategies for scalability of the algorithm and show the conditions under which the algorithm is robust against false detections. The algorithm is also extended to handle non-disjoint sensing regions and to track multiple moving objects. Since the computation and storage of track information are done in a completely distributed manner, the method is robust against node failures and transmission failures. In addition, the use of binary sensors makes the proposed algorithm suitable for many sensor network applications.