Direction-only tracking of moving objects on the unit sphere via probabilistic data association

Directional data can emerge in many scientific disciplines due to the nature of the observed phenomena or the working principles of a sensor. Such direction-only sensors can be used in applications with the aim of tracking multiple moving objects. One of the reasons why multiple moving object tracking can be challenging is because of the need to deal with the problem of pairing sensors measurements with tracked objects in the presence of clutter (the data association problem). In this paper we propose to approach the problem of multiple object tracking in clutter with direction-only data by setting it on the unit sphere, thus tracking the objects with a Bayesian estimator based on the von Mises-Fisher distribution and probabilistic data association. To achieve this goal we derive the probabilistic data association (PDA) filter and the joint probabilistic data association (JPDA) filter for the Bayesian von Mises-Fisher estimator on the unit sphere. The final PDA and JPDA filter equations are derived with respect to the Kullback-Leibler divergence by preserving the first moment of the spherical distribution. The performance of the proposed approach is demonstrated in experiments with synthetic data where moving object trajectories were simulated and noisy observations obtained along with the clutter simulated as a Poisson process on the unit sphere.