How do you rotate 2 quaternions to their original position and then calculate the relative rotation?

Question

I have 2 IMU (Inertial Units) and I want to calculate their relative rotation. Unfortunately, the IMU result gives me both quaternions relatively global (I assume that quaternions work). However, I need measurements of the rotation of one of the sensors relative to the other. All this time, these two sensors have been rotated from their initial orientation on the global axis.

For example: I have one sensor attached to the chest, and the other attached to the arm. Both sensors are calibrated on the global axis. If I support this orientation, I can accurately calculate the rotations. However, when I rotate my body in a different orientation (90 degrees to the right) and perform the same movement, the sensors rotate around their local axis, but output quaternions about the global axis (rotation around the y axis of the sensors is displayed as rotation around the global x axis).

I want the same quaternions to make the same movements (and thereby show the same rotations), regardless of my orientation (laying, facing left, right, forward or backward)

Basically, I want to have one sensor will have a rotating "reference" axis and I want to measure the rotational changes from another sensor relative to the reference sensor (rotating the reference axis). p>

Answer 1

Converting from one Q1 to another Q2 frame is done simply as

Q1intoQ2 = q1.inversed() * q2;
// check it,  q2 = q1 * Q1intoQ2 == q1 * q1.inversed() * q2 == q2