Reproducing Table 1 (Orientation RMSE)

[jhultman]

Hi, I am trying to reproduce the iOS CoreMotion result from this table in the paper:

Can you explain more what is meant by "direct angular distance"? Do you mean the angle required to rotate one quaternion q1 to another q2? Is the error defined on the yaw angle, three-axis euler angles, unit quaternions? Do you unwrap the angles to avoid 0 / 2pi discontinuity?

I cannot reproduce the number, so I think I am misunderstanding something. If helpful I can share the code I have written to compute the error.

[scottsun95]

We use the formula θ = 2 arccos(|<q₁, q₂>|), where θ is the angle of rotation between two unit quaternions q₁ and q₂ by the shortest arc. There are a few other variants of this formula that are equivalent. So in this case, one of the quaternions is the prediction, and the other is the ground truth. We then take the RMS for all such corresponding pairs in the sequence.