A multilevel homotopy MCMC sequential Monte Carlo filter for multi-target tracking

In this paper, we propose an enhanced sequential Monte Carlo filter through the design of a sophisticated Markov chain Monte Carlo (MCMC) procedure. This MCMC procedure is appended after the resampling step of the generic sequential Monte Carlo filter to efficiently resolve the degeneracy of the algorithm. In this work, we use the effective sample size as a learning criterion to monitor the levels of homotopy in the MCMC procedure at each time instant so that the computational cost is reduced without undermining the accuracy of estimation. We test the algorithm on a multi-target tracking problem and compared to other contemporary approaches such as the bootstrap particle filter and the auxiliary particle filter (APF). Based on two scenarios, the proposed algorithm is administrated to have a significant increase in accuracy.