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We consider the problem of multiple mobile sensor agents tracking the position of one or more moving targets. In our formulation, each agent maintains a target estimate, and each agent moves so as to maximize the expected information from its sensor, relative to the current uncertainty in the estimate. The novelty of our approach is that each agent need only communicate with one-hop neighbors in a communication network, resulting in a fully distributed and scalable algorithm, yet the performance of the system approximates that of a centralized optimal solution to the same problem. We provide two fully distributed algorithms based on one-time measurements and a Kalman filter approach, and we validate the algorithms with simulations.