Double Rodrigues Parameters method and its application in attitude determination

A method was proposed to present the attitude of a rigid body using an ordered pair of Rodrigues Parameters. We proved that any attitude of a rigid body could be described by an ordered pair consist of two Rodrigues parameters whose two-norm were no more than unit. We reduced variables of the ordered pair from six to three (the freedom of attitude motion) by "freezing" the first Rodrigues parameters. The relationship between an ordered pair of Rodrigues parameters and other attitude representations were presented. Then, the attitude kinematics based on the ordered pair of Rodrigues parameters was provided. Finally, we discussed the application of the presented attitude representation in attitude determination for flight vehicles. Simulation computation results showed that the presented algorithm had better precision than quaternion-based algorithm.