Particle PHD forward filter-backward simulator for targets in close proximity

In this work, we introduce the particle PHD forward filter - backward simulator (PHD-FFBSi) capable of dealing with uncertainties in the labeling of tracks that appear when tracking two targets in close proximity with measurements that do not discriminate between them. The Forward Filter Backward Simulator is a smoothing technique based on rejection sampling for the calculation of the probabilities of association between targets and tracks. The forward filter is a particle implementation of the Probability Hypothesis Density (PHD) filter that presents advantages over an SIR filter. Difficulties that arise due to the presence of target birth and death processes are addressed through modifications to the fast FFBSi. Simulations show the new particle filter of asymptotically linear complexity in the number of particles calculates correct target label probabilities at varying levels of measurement noise.