We consider the problem of tracking multiple objects with unknown state parameter information, time-dependent cardinality, and object identity. The problem becomes even more challenging when the unordered measurements have a large number of false alarms due to high noise or clutter. We propose a new approach that exploits the dependent Dirichlet process as the prior on the evolving object-state distributions. At each time step, a Dirichlet process mixture model, integrated with a Markov chain Monte Carlo method, is also used to learn the object-state identity from the measurements and infer the time- dependent object cardinality. A radar tracking example, with ten targets that are present in the observation scene at different times, is used to evaluate the new approach. We also compare it to the labeled multi-Bernoulli filter and demonstrate its improved tracking performance.