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In this paper, we consider the problem of tracking multiple targets using distributed active sensing networks (DASNs). The particle filter technique is adopted to estimate the trajectories of targets moving in the DASNs. We propose a novel joint measurement method, which allows the estimation of the states of targets as the estimation of a mixture of probability densities without labeling any specific targets. The method, therefore, avoids the process of data-to-target association, and provides robust performance in tracking multiple targets. Adaptive sample size is used to remove redundant particles, and thus greatly reduces the computation complexity. Extensive simulations on single and multiple targets demonstrate the robustness and accuracy of the proposed algorithm in estimating the number of targets and their trajectories.