  A deterministic attitude estimation problem for a rigid body in a potential
field, with bounded attitude and angular velocity measurement errors is
considered. An attitude estimation algorithm that globally minimizes the
attitude estimation error is obtained. Assuming that the initial attitude, the
initial 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 the size of the uncertainty ellipsoid measures
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 attitude and angular velocity estimates are
optimal in the sense that the sizes of the uncertainty ellipsoids are
minimized.
