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The use of distributed particle filters for tracking in sensor networks has become popular in recent years. The distributed particle filters proposed in the literature up to now are only approximations of the centralized particle filter or, if they are a proper distributed version of the particle filter, their implementation in a wireless sensor network demands a prohibitive communication capability. In this work, we propose a mathematically sound distributed particle filter for tracking in a real-world indoor wireless sensor network composed of low-power nodes. We provide formal and general descriptions of our methodology and then present the results of both real-world experiments and/or computer simulations that use models fitted with real data. With the same number of particles as a centralized filter, the distributed algorithm is over four times faster, yet our simulations show that, even assuming the same processing speed, the accuracy of the centralized and distributed algorithms is practically identical. The main limitation of the proposed scheme is the need to make all the sensor observations available to every processing node. Therefore, it is better suited to broadcast networks or multihop networks where the volume of generated data is kept low, e.g., by an adequate local pre-processing of the observations.