PHD filter with approximate multiobject density measurement update

The PHD filter is a popular approach to the multiple target tracking problem, however, it suffers from the Poisson assumption which yields a cardinality estimate with too high variance. In recent work Le and Kaplan proposed to improve the performance of the PHD filter using a particle approximation of the predicted multiobject density and updating it using the multiobject measurement pdf. Following the work by Le and Kaplan, in this paper we use the predicted PHD to construct a particle approximation of the predicted multiobject density. Using joint probabilistic data association, the multiobject particle approximation can then be updated using the multiobject measurement likelihood, resulting in a particle approximation of the posterior multiobject density. The posterior multiobject particles are then used to approximate the posterior PHD, which is subsequently predicted using the standard PHD prediction. The proposed filter is implemented using a Gaussian mixture approximation of the PHD intensity, and a simulation study shows a significant performance improvement compared to using the standard PHD measurement update, especially in terms of the cardinality estimate.