I have seen several questions regarding averaging multiple rotation matrices and the answer seems to be that there is no good way to do this. But maybe there is a good way to do the following. Suppose I have many vector pairs:
v11 - v12
v21 - v22
v31 - v32
...
Can I calculate a rotation matrix which approximates all vj1 vectors to their corresponding vj2 pairs?
Could I then also measure how good a fit this matrix is to the data?
As I note in my comment on the question, the Kabsch algorithm produces the answer to exactly the question described in this question.