Dual Quaternion Sample Reduction for SE(2) Estimation

We present a novel sample reduction scheme for random variables belonging to the SE(2) group by means of Dirac mixture approximation. For this, dual quaternions are employed to represent uncertain planar transformations. The Cramér-von Mises distance is modified as a smooth metric to measure the statistical distance between Dirac mixtures on the manifold of planar dual quaternions. Samples of reduced size are then obtained by minimizing the probability divergence via Riemannian optimization while interpreting the correlation between rotation and translation. We further deploy the proposed scheme for nonparametric modeling of estimates for nonlinear SE(2) estimation. Simulations show superior tracking performance of the sample reduction-based filter compared with Monte Carlo-based as well as parametric model-based planar dual quaternion filters.