How to determine absolute orientation

Question

I have a xyz accelerometer and magnetometer. Now I want to determine the orientation of the device using both. The problem I see is that depending on the device orientation, I'd need to use the sensors in different order.

Let me give an example. If I have the device facing me then changes in both the roll and pitch can be determined with the accelerometer. For yaw I use the magnetometer.

But if I put the device horizontally (ie. turn it 90º, facing the ceiling) then any change in the up vector (now horizontal) isn't notice, as the accelerometer doesn't detect any change. This can now be detected with the magnetometer.

So the question is, how to determine when to use one or the other. Is this enough with both sensors or do I need something else?

Thanks

Answer 1

The key is to use the cross product of the two vectors, gravity and magnetometer. The cross product gives a new vector perpendicular to them both. That means it is horizontal (perpendicular to down) and 90 degrees away from north. Now you have three orthogonal vectors which define orientation. It is a little ugly because they are not all perpendicular but that is easy to fix. If you then cross this new vector back with the gravity vector that gives a third vector perpendicular to the gravity vector and the magnet plane vector. Now you have three perpendicular vectors which defines your 3D orientation coordinate system. The original accelerometer (gravity) vector defines Z (up/down) and the two cross product vectors define the east/west and north/south components of the orientation.