Directional data emerge in many scientific disciplines due to the nature of the observed phenomena or the working principles of a sensor. The problem of tracking with direction-only sensors is challenging since the motion of the target typically resides either in 3D or 2D Euclidean space, while the corresponding measurements reside either on the unit sphere or the unit circle, respectively. Furthermore, in multitarget tracking there is the need to deal with the problem of pairing sensors measurements with targets in the presence of clutter (the data association problem). In this paper we propose to approach multitarget tracking in clutter with direction-only data by setting it on the unit hypersphere, 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 estimation on the unit hypersphere. The final PDA and JPDA filter equations are derived with respect to the Kullback-Leibler divergence by preserving the first moment of the hyperspherical distribution. Although the fundamental equations are given for the hyperspherical case, we focus on the filters on the unit 1-sphere (circle in R²) and the unit 2-sphere (surface of the unit ball in R³). The proposed approach is validated through synthetic data experiments on 100 Monte Carlo runs simulating multitarget tracking with noisy directional measurements and clutter.