A mixed GM/SMC implementation of the probability hypothesis density filter

The Probability Hypothesis Density (PHD) filter is a recent solution for tracking an unknown number of targets in a multi-object environment. The PHD filter cannot be computed exactly, but popular implementations include Gaussian Mixture (GM) and Sequential Monte Carlo (SMC) based algorithms. GM implementations suffer from pruning and merging approximations, but enable to extract the states easily; on the other hand, SMC implementations are of interest if the discrete approximation is relevant, but are penalized by the difficulty to guide particles towards promising regions and to extract the states. In this paper, we propose a mixed GM/SMC implementation of the PHD filter which does not suffer from the above mentioned drawbacks. Due to the SMC part, our algorithm can be used in models where the GM implementation is unavailable; but it also benefits from the easy state extraction of GM techniques, without requiring pruning or merging approximations. Our algorithm is validated on simulations.