Given a set of 3D points with their coordinates in 2 different coordinate systems, what is the correct algorithm to use in order to estimate the relative rotation and translation of the coordinate systems. Explored until now :
Any help of guidance is appreciated!
2D -->2D, 2D-->3D both are not for your application.
ICP -> Yes. It's overkill if your data is noiseless
Your problem is called rigid body registration. There is a closed-form solution.
See page 3 (Paired Point Methods) https://www.yanivresearch.info/writtenMaterial/rigidRegistrationIGIBook.pdf