ANALYSIS OF THE GAUSS-BINGHAM DISTRIBUTION FOR ATTITUDE UNCERTAINTY PROPAGATION

Attitude uncertainty quantification typically requires a small angle assumption, and thus an inherent small uncertainty assumption, to be made. This small angle assumption can be eliminated by employing the Bingham distribution to represent the attitude uncertainty in the attitude quaternion directly. Moreover, an extension to the Bingham distribution, termed the Gauss-Bingham distribution, can be used to represent correlated attitude quaternion and angular velocity uncertainty to enable attitude uncertainty propagation. In order to evaluate the potential accuracy gain using the Gauss-Bingham distribution for attitude uncertainty quantification, the Gauss-Bingham distribution method for attitude uncertainty propagation is compared to the propagation step of the multiplicative extended Kalman filter, which requires a small angle assumption to be made. The attitude uncertainty quantified by each method is discretely sampled and mapped to a common attitude parameterization in order to make accurate comparisons between each method.