Umeyama alignment and scaling for computing ATE-5

[hemangchawla]

Hello,

Why is the standard Umeyama algorithm not used for alignment and scaling of 5-frame trajectories when computing the ATE-5?

[adizhol]

I would also like to understand that.
The Umeyama algorith uses the SVD of the covariance matrix to calculate the alignment between two trajectories.
http://rpg.ifi.uzh.ch/docs/IROS18_Zhang.pdf

edit
One possible reason is that finding alignment of the entire trajectory estimation will give you a different error (kind of an "average"), but if the alignment is done on the first frame pose, the errors are accumulated over the entire trajectory.
Correct me if I'm wrong.