Distance moved by Accelerometer

You get position by integrating the linear acceleration twice but the error is horrible. It is useless in practice.

Here is an explanation why (Google Tech Talk) at 23:20. I highly recommend this video.

However the gyro mouse might work for your application, see between 37:00-38:25 in the video.

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Not easy to do accurately. An accelerometer only reports acceleration, not movement. You can try (numerically) integrating the acceleration over time, but you're likely to end up with cumulative errors adding up and leading to unintended motion.

Pseudocode, obviously untested:

init:
    loc = {0, 0, 0}    ; location of object on screen
    vel = {0, 0, 0}    ; velocity of object on screen
    t = 0              ; last time measured

step:
    t0 = time          ; get amount of time since last measurement
    dt = t0 - t
    accel = readAccelerometer()
    vel += accel * dt  ; update velocity
    loc += vel * dt    ; update position
    displayObjectAt(loc)

Why don't you use the acceleration itself instead distance moved? For example; If your acceleration is 1.4G east, your object should move to east 14pixels per second until your acceleration changes.

So that object's movement is will be like it is under a relative force and I think it's more realistic. Faster moving device, bigger force to effect object.

Also look:

http://www.freescale.com/files/sensors/doc/app_note/AN3397.pdf

and

Using accelerometer, gyroscope and compass to calculate device's movement in 3D world