Systems and methods are provided for tracking moving objects from a set of measurements. An estimate of a posterior probability distribution for a plurality of track states is determined from an estimate of the posterior probability distribution for a plurality of possible assignments of the set of measurements to a set of tracks representing trajectories of the plurality of moving objects and the set of measurements. A new estimate of the posterior probability distribution for the assignments is determined from the measurements and the estimate of a posterior probability distribution for the track states. A variational lower bound is determined from the new estimate of the posterior probability distribution for the assignments, the estimate of the posterior probability distribution for the track states, and the set of measurements. These steps are iteratively repeated until the variational lower bound is less than a threshold value.