Grid-Based Quaternion Filter for SO(3) Estimation

A novel discrete Bayesian filtering scheme is proposed on the manifold of unit quaternions for rotation estimation. Existing quaternion filters rely on specific distributions (typically the Bingham distribution) to model the uncertainty in a parametric form. The scheme proposed in this paper allows non-parametric modeling of the underlying uncertainty using Dirac mixtures located on a hyperspherical grid. The grid is generated by first discretizing the tangent space layer-wise w.r.t. spherical coordinates. Then, the on-tangent-space grid is mapped back to the manifold via the exponential map. The on-manifold grid of quaternions is deployed in a discrete Bayesian filtering scheme. We evaluate the proposed grid-based quaternion filter for recursive rotation estimation with simulations. Results show that the tracking performance of the proposed approach is superior to Bingham-based quaternion filters.