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In emerging tracking systems using large-scale wireless sensor networks, sensor management is an essential task in order to balance the tracking performance and costs subject to limited network resources in terms of energy, communication bandwidth, and sensing range. This paper considers the sensor allocation problem for multi-target tracking (MTT), in which a group of sensors are dynamically selected and allocated to track each of the multiple targets and collaborate within the group via track data fusion. The sensor assignments evolve over time as targets move, and are accomplished by solving a constrained optimization problem that is formulated to maximize the overall tracking performance for all targets, while conserving network energy and providing tracking coverage guarantee. The original integer-valued optimization problem is relaxed to a convex program for computational tractability, and then implemented in a distributed manner for network scalability and reduced communication costs. Through local one-hop communication with neighboring nodes, each sensor autonomously decides on whether to participate in data collection and how to contribute to track fusion. The proposed distributed sensor allocation algorithm, implemented via iterative subgradient search, is shown to converge to the global optimum of the centralized relaxed problem, and is near optimal for the original integer programming problem.