The partially wrapped normal distribution for SE(2) estimation

We introduce a novel probability distribution on the group of rigid motions SE(2) and we refer to this distribution as the partially wrapped normal distribution. Describing probabilities on SE(2) is of interest in a wide range of applications, for example, robotics, autonomous vehicles, or maritime navigation. We derive some important properties of this novel distribution and propose an estimation scheme for its parameters based on moment matching. Furthermore, we provide a qualitative comparison to a recently published approach based on the Bingham distribution, and show that there are complementary advantages and disadvantages of the two approaches.