A new probability distribution for simultaneous representation of uncertain position and orientation
Igor Gilitschenski, Gerhard Kurz, Simon Julier, Uwe D. Hanebeck · Repository KITopen (Karlsruhe Institute of Technology) · 2014
This work proposes a novel way to represent uncertainty on the Lie group of rigid-body motions in the plane.This is achieved by using dual quaternions for representation of a planar rigid-body motion and proposing a probability distribution from the exponential family of distributions that inherently respects the underlying structure of the representation.This is particularly beneficial in scenarios involving strong measurement noise.A relationship between the newly proposed distributional model and the Bingham distribution is discussed.The presented results involve formulas for computation of the normalization constant, the mode, parameter estimation techniques, and a closed-form Bayesian measurement fusion.