Multiple target counting and tracking using binary proximity sensors: bounds, coloring, and filter

Binary proximity sensors (BPS) provide extremely low cost and privacy preserving features for tracking mobile targets in smart environment, but great challenges are posed for track- ing multiple targets, because a BPS cannot distinguish one or multiple targets are in its sensing range. In this paper, we at first address the counting problem by presenting a maxi- mum clique partition model on unit disk graph, which leads to a tight lower bound for estimating the number of targets by a snapshot of sensor readings. Then, to more accurately count and track the multiple targets by sequential readings of sensors, we state the key is to comprehensively infer the states behind the events. Therefore, at each event we infer which target may trigger the event via a dynamic coloring technique (DEC) and predict the potential regions of the multiple targets by a colorful area shrinking and expanding approach. Such an approach generates multiple potential scenarios containing different colors to interpret the sequen- tial events, where the number of colors indicates the different estimations of the target number. Then we designed multi- color particle filter (MCPF), which is run in parallel in each scenario to enumerate and evaluate the potential trajecto- ries of the targets under the color constraint. The likelihoods of the trajectories are evaluated by each target's movement consistence. The overall best trajectory over all scenarios is voted to provide not only the most possible target number, but also the trajectories of the targets. Extensive simula- tions were conducted using a multi-agent simulator which show good accuracy of the proposed multi-target tracking algorithms.