Calculate speed and distance using accelerometer

Apparently, it is impossible to measure speed and distance using the accelerometer; it is prohibited by the fundamental physical principles: all phenomena in different reference system moving at uniform speeds go in the same way, so you cannot detect any difference between them from inside the system. In other words, you would detect the same acceleration in systems at different coordinates and speeds, it is principally impossible to tell one from another.

In principle, you can assume that, for example, at the moment of the start of your program, the device's coordinates and speed equal to zero, and integrate the accelerations starting from this point, adding estimated coordinates and speeds to this initial point, but the accuracy of this will be extremely low, and the errors can accumulate with time greatly. First of all, you can only take the measurements at some time interval, loosing the acceleration values in between. For any given accuracy and interval between measurements and given requirements for final accuracy, it is possible to design such motion plan which will cause the system to to fail to deliver required accuracy.

—SA