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This paper develops a novel approach for multitarget tracking, called box-particle probability hypothesis density filter (box-PHD filter). The approach is able to track multiple targets and estimates the unknown number of targets. Furthermore, it is capable to deal with three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. The box-PHD filter reduces the number of particles significantly, which improves the runtime considerably. The small particle number makes this approach attractive for distributed computing. A box-particle is a random sample that occupies a small and controllable rectangular region of non-zero volume. Manipulation of boxes utilizes methods from the field of interval analysis. The theoretical derivation of the box-PHD filter is presented followed by a comparative analysis with a standard sequential Monte Carlo (SMC) version of the PHD filter. To measure the performance objectively three measures are used: inclusion, volume and the optimum subpattern assignment metric. Our studies suggest that the box-PHD filter reaches similar accuracy results, like a SMC-PHD filter but with much considerably less computational costs. Furthermore, we can show that in the presence of strongly biased measurement the box-PHD filter even outperforms the classical SMC-PHD filter.