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In this paper we address the problem of tracking of multiple targets in a wireless sensor network using particle filtering. This methodology approximates the probability distributions of the objects of interest by using random measures composed of particles and associated weights. An important challenge of the resulting algorithms is the need for very large number of particles when the dimensions of the states are even moderately large. We propose to combat this problem by alternative particle filtering implementations where we partition the state space of the system into different subspaces and run a separate particle filter for each subspace. The performance of the considered algorithm is illustrated through computer simulations that show considerable advantage of the proposed method over the standard particle filter.