A new probability distribution for simultaneous representation of uncertain position and orientation

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.