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Target tracking is investigated using particle filtering of data collected by distributed sensors. In lieu of a fusion center, local measurements must be disseminated across the network for each sensor to implement a centralized particle filter (PF). However, disseminating raw measurements incurs formidable communication overhead as large volumes of data are collected by the sensors. To reduce this overhead and thus enable distributed PF implementation, the present paper develops a set-membership constrained (SMC) PF approach that i) exhibits performance comparable to the centralized PF; ii) requires only communication of particle weights among neighboring sensors; and iii) can afford both consensus-based and incremental averaging implementations. These attractive attributes are effected through a novel adaptation scheme, which is amenable to simple distributed implementation using min- and max-consensus iterations. The resultant SMC-PF exhibits high gain over the bootstrap PF when the likelihood is peaky, but not in the tail of the prior. Simulations corroborate that for a fixed number of particles, and subject to peaky likelihood conditions, SMC-PF outperforms the bootstrap PF, as well as recently developed distributed PF algorithms, by a wide margin.