How should I calculate azimuth, pitch, orientation when my Android device isn't flat?

Question

I\'m using the Android gravity and magnetic field sensors to calculate orientation via SensorManager.getRotationMatrix and SensorManager.getOrientation. This gives me the a

Answer 1

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 (E_x, E_y, E_z), (N_x, N_y, N_z) and (G_x, G_y, G_z) are vectors pointing due East, North, and in the direction of Gravity. Then the azimuth angle that you want is given by

Answer 2

When the device is not flat, you have to call remapCoordinateSystem(inR, AXIS_X, AXIS_Z, outR); before calling getOrientation.

The azimuth returns by getOrientation is obtained by orthogonally project the device unit Y axis into the world East-North plane and then calculate the angle between the resulting projection vector and the North axis.

Now we normally think of direction as the direction where the back camera is pointing. That is the direction of -Z where Z is the device axis pointing out of the screen. When the device is flat we do not think of direction and accept what ever given. But when it is not flat we expect it is the direction of -Z. But getOrientation calculate the direction of the Y axis, thus we need to swap the Y and Z axes before calling getOrientation. That is exactly what remapCoordinateSystem(inR, AXIS_X, AXIS_Z, outR) does, it keep the X axis intact and map Z to Y.

Now so how do you know when to remap or not. You can do that by checking

float inclination = (float) Math.acos(rotationMatrix[8]);
if (result.inclination < TWENTY_FIVE_DEGREE_IN_RADIAN 
            || result.inclination > ONE_FIFTY_FIVE_DEGREE_IN_RADIAN)
{
    // device is flat just call getOrientation
}
else
{
    // call remap
}

The inclination above is the angle between the device screen and the world East-North plane. It shows how much the device is tilting.