The tracking of objects is an important practical application of sensor networks. A key challenge in this domain is to track multiple targets accurately and to disambiguate them correctly in case of temporary interference. In our work, we present a novel object tracking mechanism for binary proximity sensors, where sensors are grouped into cliques based on the objects they are tracking. The use of cliques allows for effective disambiguation in case of target interference since overlaps in cliques can be separated as long as each clique has at least one unique sensor. While prior work has made use of clique-based object tracking techniques, our work is the first to perform such object tracking in a fully distributed fashion. Using distributed approach makes our solution simpler, more robust to sensor failure, and less energy-consuming due to lower communication overhead. In addition, our simulations show that tracking accuracy and multiple-target location disambiguation accuracy is higher than in other approaches.