This paper presents an estimator-based attitude tracking control scheme that uses feedback of attitude and angular velocity estimates constructed by an optimal state estimation scheme. The tracking control scheme gives almost global convergence to a desired attitude and angular velocity profile with perfect state feedback. The estimation scheme consists of measurement, filtering and state propagation stages, and the measurements are assumed to have deterministic error bounds. These error bounds are ellipsoidal and are referred to as uncertainty ellipsoids. Each measurement is followed by a filtering stage, which obtains the minimum-volume ellipsoid that contains the intersection of uncertainty ellipsoids corresponding to the estimated states and the measured states. The state estimates are propagated between measurements using a variational integrator that discretizes the equations of motion. This estimator-based tracking control scheme is applied to the model of a satellite in circular Earth orbit. Numerical simulation results with realistic error bounds on attitude and angular velocity measurements show the good performance of this estimator-based control scheme.