Bayesian recursive estimation on the rotation group

Tracking of the orientation of a rigid body based on directional measurements is a key issue in many applications. Configurations in this sense are precisely representable as elements of the rotation group SO(3), and the issue devolves to one of tracking on this group, for which and algorithm is described here. Its novelty derives from the use of maximum entropy distributions on these groups as models for the priors, and from the approximation algorithms that permit numerical implementation of such a model. These solutions can be written in a recursive form. While the general ideas apply in all dimensions, the focus of this paper is on the important 3-dimensional case. It is impossible to compute the exact solution; instead, obtained here is a highly effective approximation. It is shown that, in contrast with other approaches, the algorithm described here produces outputs which are both very accurate and statistically meaningful.