Sequential Monte Carlo implementation and state extraction of the group probability hypothesis density filter for partly unresolvable group targets-tracking problem

Abstract

This study proposes a sequential Monte Carlo (SMC) implementation to the Mahler's group probability hypothesis density filter (PHDF) for partly unresolvable group targets tracking problem. A potential limitation of the group PHDF is that it cannot be used to determine the number of groups. Therefore we have to jointly extract the group number and states from the proposed group SMC-PHDF at each time step. We propose to fit the resampled particles of the group SMC-PHDF by application of Gaussian mixture models with unknown component number. In the mixture, the number and parameters of the components correspond to the number and states of the groups over the observation region. The Markov chain Monte Carlo (MCMC) algorithm is proposed to estimate the component parameters of the mixture. The estimate of component number of the mixture can be derived by a component management strategy. In simulation, the proposed group SMC-PHDF with the expectation maximum (EM) and MCMC extractions are, respectively, used to detect and track the groups. Hundred Monte Carlo simulation results show that the latter outperforms the former a lot in estimating the group number and states, although the computational requirement of the MCMC extraction is more expensive than the EM extraction.