How should I calculate azimuth, pitch, orientation when my Android device isn't flat?
I'm using the Android gravity and magnetic field sensors to calculate orientation via SensorManager.getRotationMatrix and SensorManager.getOrientation. This gives me the azimuth, pitch and orientation numbers. The results look sensible when the device is lying flat on a table.
However, I've disabled switches between portrait and landscape in the manifest, so that getWindowManager().getDefaultDisplay().getRotation() is always zero. When I rotate the device by 90 degrees so that it's standing vertical I run into trouble. Sometimes the numbers seem quite wrong, and I've realised that this relates to Gimbal lock. However, other apps don't seem to have this problem. For example, I've compared my app against two free sensor test apps (Sensor Tester (Dicotomica) and Sensor Monitoring (R's Software)). My app agrees with these apps when the device is flat, but as I rotate the device into the vertical position there can be significant differences. The two apps seem to agree with each other, so how do they get around this problem?
I think the best way of defining your orientation angles when the device isn't flat is to use a more appropriate angular co-ordinate system that the standard Euler angles that you get from SensorManager.getOrientation(...). I suggest the one that I describe here on math.stackexchange.com. I've also put some code that does implements it in an answer here. Apart from a good definition of azimuth, it also has a definition of the pitch angle which is exactly the angle given by Math.acos(rotationMatrix[8]) that is mentioned in another answer here.
You can get full details from the two links that I've given in the first paragraph. However, in summary, your rotation matrix R from SensorManager.getRotationMatrix(...) is
where (Ex, Ey, Ez), (Nx, Ny, Nz) and (Gx, Gy, Gz) are vectors pointing due East, North, and in the direction of Gravity. Then the azimuth angle that you want is given by
