A distributed set-membership-constrained particle filter (SMC-PF) is developed for decentralized tracking applications using wireless sensor networks. Unlike existing PF alternatives, SMC-PF offers reduced overhead for inter-sensor communications because it requires only particle weights to be exchanged among sensors, instead of raw measurements or parameters of a Gaussian mixture model. SMC-PF relies on a novel distributed adaptation scheme based on successive set intersections that can afford reduced number of particles without sacrificing performance. Conditions are provided to quantify the variance reduction of the SMC-PF-based state estimator. Simulations corroborate the ability of the SMC-PF to considerably outperform the bootstrap PF for a fixed number of particles.