The absence of a globally nonsingular three-parameter representation of the rotation group forces attitude Kalman filters to estimate either a singular or a redundant attitude representation. We compare two filtering strategies using simplified kinematics and measurement models. Our favored strategy estimates a three-parameter representation of attitude deviations from a reference attitude specified by a higher-dimensional nonsingular parameterization. The deviations from the reference are assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. We point out some disadvantages of the other strategy, which directly estimates the four-component quaternion representation.