Robust Bayesian estimation of nonlinear parameters on SE(3) Lie group

Abstract

The basic challenge in autonomous robotic exploration is to safely interact with natural environments. An essential part of that challenge is 3D map building. In robotics research this problem is addressed as simultaneous localization and mapping (SLAM). In computer vision it is termed structure from motion (SFM). The common underlying problem is the accurate estimation of the camera pose. Uncertainty information about the pose estimates is essential for a recursive inference scheme. We show that the pose parametrization plays an important role for the finite parametric representation. In the case of sparse observations (weak evidence) the full exponential Lie Cartan coordinates of 1.st kind are most suitable, when assuming a Gaussian noise model on the measurements. Further, we address the pose estimation from a sequence of images and introduce the marginalized MAP estimator, which is numerically more stable and efficient than the joint estimate (bundle‐adjustment) used in computer vision.