Summary: An optimal batch estimator and smoother based on the minimum model error (MME) approach is developed for a three-axis stabilized spacecraft. The formulation is shown using only attitude sensors, e.g., three-axis magnetometers, sun sensors, star trackers. This algorithm accurately estimates the attitude of a spacecraft and substantially smoothes noise associated with attitude sensor measurements. The general functional form of the optimal estimation approach involves the solution of a nonlinear two-point-boundary-value problem that can be solved only by using computationally intense methods. A linearized solution also is shown that is computationally more efficient than methods that solve the general form.