An Equivariant von Mises-Gaussian distribution on SE(n) for Unscented Kalman Filtering

The characterization and propagation of uncertainties on the Special Euclidean Lie groups SE(2) and SE(3) are crucial in robotics and state estimation. Applications such as navigation and SLAM require accurate modeling of pose uncertainty involving both position and attitude. Lie groups offer a structured state space that preserves system properties and improves consistency in nonlinear estimation. Kalman filters on Lie groups improve robustness but rely on a Gaussian assumption, which fails for large uncertainties. To overcome these limitations, we used an alternative probability density function, based on a maximum entropy criterion, leading to a filter that we call vMG-UKF-LG. The resulting method is validated on experimental datasets against four benchmark filters and indicates improved accuracy when dealing with complex trajectories and overestimating the process noise.