A review on non iterative closed form configuration matching and rotations estimation

Orthonormal matrices, Procrustes and quaternion analysis are closed form solutions of the configuration matching problem, common in geodesy as in the datum transformation problem. Literature reports more Procrustes based geodetic applications than Quaternions, which are more used in other application fields, such as aerospace navigation, robotics and computer vision. The large popularity of Procrustes in geodesy is mainly due to its capability to take into account a priori observation weighting in a simple way.