The partially wrapped normal distribution for SE(2) estimation

Abstract

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.

Directional Statistics and Filtering Using libDirectional

“…The first distribution is called the partially wrapped normal distribution (PWN) presented in Kurz, Gilitschenski, and Hanebeck (2014e) that was further discussed in Kurz (2015, Section 2.3.3) 2 . This distribution is defined on [0, 2π) × R 2 and is obtained from a normal distribution on R 3 where the first component is wrapped.…”

Extended information filter on matrix Lie groups

“…, and the motion model given by (23), which extracts only the Euclidean part of the state, we obtain…”

“…A state estimation method based on an observer and a predictor cascade for invariant systems on Lie groups with delayed measurements was proposed in [22]. Recently, some works have also addressed the uncertainty on the SE(2) group proposing new distributions [23,24]; however, these approaches do not yet provide a closed-form Bayesian recursion framework (involving both the prediction and update) that can include higher order motion and non-linear models. A least squares optimization and nonlinear KF on manifolds in the vein of the unscented KF was proposed in [25] along with an accompanying software library.…”

Directional Statistics and Filtering Using libDirectional

“…The first distribution is called the partially wrapped normal distribution (PWN) presented in Kurz et al (2014e) that was further discussed in Kurz (2015, Section 2.3.3) 2 . This distribution is defined on [0, 2π) × R 2 and is obtained from a normal distribution on R 3 where the first component is wrapped.…”