  This paper is focused on probabilistic estimation for the attitude dynamics
of a rigid body on the special orthogonal group. We select the matrix Fisher
distribution to represent the uncertainties of attitude estimates and
measurements in a global fashion without need for local coordinates. Several
properties of the matrix Fisher distribution on the special orthogonal group
are presented, and an unscented transform is proposed to approximate a matrix
Fisher distribution by selected sigma points. Based on these, an intrinsic,
global framework for Bayesian attitude estimation is developed. It is shown
that the proposed approach can successfully deal with large initial estimator
errors and large uncertainties over complex maneuvers to obtain accurate
estimates of the attitude.
