Bingham Distribution-Based Linear Filter for Online Pose Estimation

Pose estimation is central to several robotics applications such as registration, hand-eye calibration, SLAM, etc. Online pose estimation methods typically use Gaussian distributions to describe the uncertainty in the pose parameters. Such a description can be inadequate when using parameters such as unit-quaternions that are not unimodally distributed. A Bingham distribution can effectively model the uncertainty in unit-quaternions, as it has antipodal symmetry and is defined on a unit-hypersphere. A combination of Gaussian and Bingham distributions is used to develop a linear filter that accurately estimates the distribution of the pose parameters, in their true space. To the best of our knowledge our approach is the first implementation to use a Bingham distribution for 6 DoF pose estimation. Experiments assert that this approach is robust to initial estimation errors as well as sensor noise. Compared to state of the art methods, our approach takes fewer iterations to converge onto the correct pose estimate. The efficacy of the formulation is illustrated with a number of simulated examples on standard datasets as well as real-world experiments.