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The attitude of a rigid-body in the three dimensional space has a unique andglobal definition on the Special Orthogonal Group SO (3). This paper gives anoverview of the rotation matrix, attitude kinematics and parameterization. Thefour most frequently used methods of attitude representations are discussedwith detailed derivations, namely Euler angles, angle-axis parameterization,Rodriguez vector, and unit-quaternion. The mapping from one representation toothers including SO (3) is given. Also, important results which could be usefulfor the process of filter and/or control design are given. The main weaknessesof attitude parameterization using Euler angles, angle-axis parameterization,Rodriguez vector, and unit-quaternion are illustrated. Keywords: SpecialOrthogonal Group 3, Euler angles, Angle-axis, Rodriguez Vector,Unit-quaternion, SO(3), Mapping, Parameterization, Attitude, Control, Filter,Observer, Estimator, Rotation, Rotational matrix, Transformation matrix,Orientation, Transformation, Roll, Pitch, Yaw, Quad-rotor, Unmanned aerialvehicle, Robot, spacecraft, satellite, UAV, Underwater vehicle, autonomous,system, Pose, literature review, survey, overview, comparison, comparativestudy, body frame, identity, origin, dynamics, kinematics, Lie group, inertialframe, zero, filter, control, estimate, observation, measurement, 3D, threedimensional space, advantage, disadvantage.

Special Orthogonal Group SO(3), Euler Angles, Angle-axis, Rodriguez Vector and Unit-Quaternion: Overview, Mapping and Challenges