Filtering on the Unit Sphere Using Spherical Harmonics

For manifolds with topologies that strongly differ from the standard topology of Rn, using common filters created for linear domains can yield misleading results. While there is a lot of ongoing research on estimation on the unit circle, higher-dimensional problems particularly pose a challenge. One important generalization of the unit circle is the unit hypersphere. In this paper, we propose a recursive Bayesian estimator for the unit sphere S-2 based on spherical harmonics for arbitrary likelihood functions and rotationally symmetric system noises. In our evaluation, the proposed filter outperforms the particle filter in a target tracking scenario on the sphere.