Hyperspherical Unscented Particle Filter for Nonlinear Orientation Estimation

We propose a novel quaternion particle filter for nonlinear SO(3) estimation. For importance sampling, the proposal distribution is designed to incorporate newly observed evidence. For that, the unscented Kalman filtering is performed particle-wise on the tangent plane of the unit quaternion manifold via gnomonic projection/retraction based on hyperspherical geometry. As prior particles are driven towards high-likelihood regions on the manifold, computational efficiency of quaternion particle filtering is significantly improved. The resulting hyperspherical unscented particle filter (HUPF) is evaluated for nonlinear orientation estimation in simulations. Results show that it gives superior tracking performance compared with the conventional particle filter and other existing quaternion filtering schemes relying on parametric modeling.