Acceleration from device's coordinate system into absolute coordinate system

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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

first position first readings

  1. device lying on back

second position second readings

  1. device standing

enter image description here enter image description here

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

coordinate-transformation coordinate-systems accelerometer vector android
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