  This paper studies a rigid body attitude tracking control problem with
attitude measurements only, when angular velocity measurements are not
available. An angular velocity observer is constructed such that the estimated
angular velocity is guaranteed to converge to the true angular velocity
asymptotically from almost all initial estimates. As it is developed directly
on the special orthogonal group, it completely avoids singularities,
complexities, or discontinuities caused by minimal attitude representations or
quaternions. Then, the presented observer is integrated with a
proportional-derivative attitude tracking controller to show a separation type
property, where exponential stability is guaranteed for the combined observer
and attitude control system.
