In this paper, we present a Bayesian framework for the fully automatic tracking of a variable number of interacting targets using a fixed camera. This framework uses a joint multi-object state-space formulation and a trans-dimensional Markov Chain Monte Carlo (MCMC) particle filter to recursively estimates the multi-object configuration and efficiently search the state-space. We also define a global observation model comprised of color and binary measurements capable of discriminating between different numbers of objects in the scene. We present results which show that our method is capable of tracking varying numbers of people through several challenging real-world tracking situations such as full/partial occlusion and entering/leaving the scene.