  This paper considers a batch solution to the multi-object tracking problem
based on sets of trajectories. Specifically, we present two offline
implementations of the trajectory Poisson multi-Bernoulli mixture (TPMBM)
filter for batch data based on Markov chain Monte Carlo (MCMC) sampling of the
data association hypotheses. In contrast to online TPMBM implementations, the
proposed offline implementations solve a large-scale, multi-scan data
association problem across the entire time interval of interest, and therefore
they can fully exploit all the measurement information available. Furthermore,
by leveraging the efficient hypothesis structure of TPMBM filters, the proposed
implementations compare favorably with other MCMC-based multi-object tracking
algorithms. Simulation results show that the TPMBM implementation using the
Metropolis-Hastings algorithm presents state-of-the-art multiple trajectory
estimation performance.
