Acceleration from device's coordinate system into absolute coordinate system

Question

From my Android device I can read an array of linear acceleration values (in the device's coordinate system) and an array of absolute orientation values (in Earth's coordinate system). What I need is to obtain the linear acceleration values in the latter coord. system.

How can I convert them?

EDIT after Ali's reply in comment:

All right, so if I understand correctly, when I measure the linear acceleration, the position of the phone completely does not matter, because the readings are given in Earth's coordinate system. right?

But I just did a test where I put the phone in different positions and got acceleration in different axes. There are 3 pairs of pictures - the first ones show how I put the device (sorry for my Paint "master skill") and the second ones show readings from data provided by the linear acc. sensor:

1. device put on left side

2. device lying on back

3. device standing

And now - why in the third case the acceleration occurs along the Z axis (not Y) since the device position doesn't matter?

Answer 1

I finally managed to solve it! So to get acceleration vector in Earth's coordinate system you need to:

1. get rotation matrix (float[16] so it could be used later by android.opengl.Matrix class) from SensorManager.getRotationMatrix() (using SENSOR.TYPE_GRAVITY and SENSOR.TYPE_MAGNETIC_FIELD sensors values as parameters),
2. use android.opengl.Matrix.invertM() on the rotation matrix to invert it (not transpose!),
3. use Sensor.TYPE_LINEAR_ACCELERATION sensor to get linear acceleration vector (in device's coord. sys.),
4. use android.opengl.Matrix.multiplyMV() to multiply the rotation matrix by linear acceleration vector.

And there you have it! I hope I will save some precious time for others.

Thanks for Edward Falk and Ali for hints!!

Answer 2

Based on @alex's answer, here is the code snippet:

private float[] gravityValues = null; private float[] magneticValues = null;   @Override     public void onSensorChanged(SensorEvent event) {         if ((gravityValues != null) && (magneticValues != null)              && (event.sensor.getType() == Sensor.TYPE_ACCELEROMETER)) {              float[] deviceRelativeAcceleration = new float[4];             deviceRelativeAcceleration[0] = event.values[0];             deviceRelativeAcceleration[1] = event.values[1];             deviceRelativeAcceleration[2] = event.values[2];             deviceRelativeAcceleration[3] = 0;              // Change the device relative acceleration values to earth relative values             // X axis -> East             // Y axis -> North Pole             // Z axis -> Sky              float[] R = new float[16], I = new float[16], earthAcc = new float[16];              SensorManager.getRotationMatrix(R, I, gravityValues, magneticValues);              float[] inv = new float[16];              android.opengl.Matrix.invertM(inv, 0, R, 0);             android.opengl.Matrix.multiplyMV(earthAcc, 0, inv, 0, deviceRelativeAcceleration, 0);            Log.d("Acceleration", "Values: (" + earthAcc[0] + ", " + earthAcc[1] + ", " + earthAcc[2] + ")");                          } else if (event.sensor.getType() == Sensor.TYPE_GRAVITY) {             gravityValues = event.values;         } else if (event.sensor.getType() == Sensor.TYPE_MAGNETIC_FIELD) {             magneticValues = event.values;         }     }