Optimal Attitude Estimation and Filtering Without Using Local   Coordinates Part I: Uncontrolled and Deterministic Attitude Dynamics
  There are several attitude estimation algorithms in existence, all of which use local coordinate representations for the group of rigid body orientations. All local coordinate representations of the group of orientations have associated problems. While minimal coordinate representations exhibit kinematic singularities for large rotations, the quaternion representation requires satisfaction of an extra constraint. This paper treats the attitude estimation and filtering problem as an optimization problem, without using any local coordinates for the group of rotations. An attitude determination algorithm and attitude estimation filters are developed, that minimize the attitude and angular velocity estimation errors. For filter propagation, the attitude kinematics and deterministic dynamics equations (Euler's equations) for a rigid body in an attitude-dependent potential are used. Vector attitude measurements are used for attitude and angular velocity estimation, with or without angular velocity measurements. 
Amit K. Sanyal