Htykuut

I have researched this topic extensively, here on stack and all over the internet, and I can't seem to come across a solution. A lot of people on stack have asked similar questions, and people have provided responses but I don't think anyone has provided a good solution yet.

Problem: When using CoreMotion to report attitude, all 4 options for reference frame they provide have the Z axis oriented opposite of gravity (vertical). The app I am developing needs to use rotation data relative to the phones coordinate system, as defined in the photo here:
Coordinate Systems

How I am hoping the solution would work: the first reading can be used to establish the phone reference frame, as that will give us the rotation from apples reference frame to the phone reference frame. All the following rotation readings can then be calculated using a transformation, so that the attitude reported is relative to the new reference frame.

Note 1: I am aware of the issues with using Euler Angles (Gimbal lock, as well as ordering) and as such would like to avoid using these.

Note 2: A solution using quaternions would be preferred, but a solution using the rotation matrix would also work.

Note 3: Many people have suggested in other posts using multiplyByInverseOfAttitude as shown in the apple example here: (https://developer.apple.com/documentation/coremotion/getting_processed_device-motion_data/understanding_reference_frames_and_device_attitude). However, this seems only to reset your first readings to 0, but still reports all following readings relative to apples standard reference frame.