The traditional approach in sensor fusion is to use high accuracy, high drift sensors like the phone's accelerometer to provide accurate short term data and the

The traditional approach in sensor fusion is to use high accuracy, high drift sensors like the phone's accelerometer to provide accurate short term data and then correct for the drift using less accurate but low drift sensors like GPS. Just integrating the accelerometers will work on short time spans, but you also double integrate the noise of the accelerometer, so that measurement of position blows up quickly unless you correct for it.