Distributed processing algorithms are attractive alternatives to centralized algorithms for target tracking applications in sensor networks. In this paper, we determine an initial probability distribution of multiple target states in a distributed manner to initialize distributed trackers. Our approach is based on Monte-Carlo methods, where the state distributions are represented as a weighted set of discrete state realizations. The filter state vector consists of the target positions and velocities on the 2D plane. Our approach can determine the state vector distribution even if the individual sensors alone are not capable of observing it. The only condition is that the network as a whole be able to observe the state vector. A robust weighting strategy is formulated to account for missed detections and clutter. To demonstate the effectiveness of the algorithm, we simulate a network with direction-of-arrival nodes and range-doppler nodes.