Von Mises Mixture PHD Filter

TLDR: This letter proposes a novel mixture approximation of the probability hypothesis density filter based on the von Mises distribution, thus constructing a method that globally captures the non-Euclidean nature of the state and the measurement space.

Abstract: This letter deals with the problem of tracking multiple targets on the unit circle, a problem that arises whenever the state and the sensor measurements are circular, i.e. angular-only, random variables. To tackle this problem, we propose a novel mixture approximation of the probability hypothesis density filter based on the von Mises distribution, thus constructing a method that globally captures the non-Euclidean nature of the state and the measurement space. We derive a closed-form recursion of the filter and apply principled approximations where necessary. We compared the performance of the proposed filter with the Gaussian mixture probability hypothesis density filter on a synthetic dataset of 100 randomly generated multitarget trajectory examples corrupted with noise and clutter, and on the PETS2009 dataset. We achieved respectively a decrease of 10.5% and 2.8% in the optimal subpattern assignement metric (notably 16.9% and 10.8% in the localization component).