Tracking Rotations using Maximum Entropy Distributions

Tracking on the rotation group is a key component of many modern systems for estimation and tracking of the orientation of rigid bodies. To address this problem, here, we describe a Bayesian algorithm that relies on directional measurements, acquired, for example, by an inertial measurements unit (IMU), for tracking on the special orthogonal (rotation) group. Its novelty lies in the use of maximum entropy distributions on these groups as models for the priors, and justifiable relaxation algorithms that permit the recursive implementation of such a model to provide a filter. We provide the solutions in a recursive closed form. In the two-dimensional case, the parameters of the prior and posterior distributions can be computed exactly and the solution has low complexity. Adoption of this approach eliminates the problem of angle wrapping. In higher dimensions, the exact solution cannot be computed, and it is necessary to make appropriate relaxations, which is done here. We demonstrate in simulations that, in contrast with some other approaches, our algorithm produces very accurate and statistically meaningful outputs. Pseudocode, specific to the IMU measurements is also provided.