Geometric integration of quaternions

The accuracy of quaternion estimates obtained using RK methods is compared with those obtained using the Crouch Grossman (CG) method. Additionally, an RK method with brute-force quaternion normalizations at each time step will be considered. This will permit the determination of any impact these operations have on result accuracy and, more importantly, the comparison of the new approach with that typically employed in practice. Accurate tracking of all Earth-orbiting objects is important because their presence can be extremely hazardous to current space missions as well as disruptive for any future mission. One method currently used to estimate the attitude of such objects makes use of light-curve data. A clear advantage was observed in using the fourth-order Crouch Grossman algorithm. For larger time steps, significant improvements in accuracy were observed, and the quaternion norm was preserved to within high precision.