A deterministic attitude estimation problem for a rigid body in an attitude
dependent potential field with bounded measurement errors is studied. An
attitude estimation scheme that does not use generalized coordinate
representations of the attitude is presented here. Assuming that the initial
attitude, angular velocity and measurement noise lie within given ellipsoidal
bounds, an uncertainty ellipsoid that bounds the attitude and the angular
velocity of the rigid body is obtained. The center of the uncertainty ellipsoid
provides point estimates, and its size gives the accuracy of the estimates. The
point estimates and the uncertainty ellipsoids are propagated using a Lie group
variational integrator and its linearization, respectively. The estimation
scheme is optimal in the sense that the attitude estimation error and the size
of the uncertainty ellipsoid is minimized at each measurement instant, and it
is global since the attitude is represented by a rotation matrix.Comment: IEEE Conference on Decision and Control, 2006. 6 pages, 6 figure