Extended objects generate a variable number of multiple measurements. In contrast with point targets, extended objects are characterized with their size or volume, and orientation. Multiple object tracking is a notoriously challenging problem due to complexities caused by data association. This paper develops a box particle filter (box PF) method for multiple extended object tracking, and for the first time, it is shown how interval-based approaches can deal efficiently with data association problems and reduce the computational complexity of the data association. The box PF relies on the concept of a box particle. A box particle represents a random sample and occupies a controllable rectangular region of nonzero volume in the object state space. A theoretical proof of the generalized likelihood of the box PF for multiple extended objects is given based on a binomial expansion. Next, the performance of the box PF is evaluated using a challenging experiment with the appearance and disappearance of objects within the area of interest, with real laser rangefinder data. The box PF is compared with a state-of-the-art particle filter with point particles. Accurate and robust estimates are obtained with the box PF, both for the kinematic states and extent parameters, with significant reductions in computational complexity. The box PF reduction of computational time is atleast 32% compared with the particle filter working with point particles for the experiment presented. Another advantage of the box PF is its robustness to initialization uncertainty.
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