The accelerometer (and gyrometer) noise is the reason for the 9-DOF sensor fusion, adding a magnetometer:

• The magentometer is not very useful regarding assessing linear and/or rotational accelerations, but it is quite good in terms of assessing whether the position of the sensor has changed. Thus, its signal is used when the signals from acceleration are near-zero.
• Accelerometers (and gyrometers as well) have significant noise, which usually does not zero-out via integration. (It tends to be somewhat asymmetrical overall.)
• Dual integration (once for speed, twice to get the displacement) does nothing good to you when fed with a noisy signal which is not perfectly symmetrical.

You can try to apply some better calibration for the zero-acceleration offset, but some error will remain --- a well-known challenge with the attempt to use accelerometers for displacement "measurements" (better: "assessments").

U. Dreher: Thank you very much for the given answer. I calculated the offset value for the three axis and subtracted it before the integration process to obtain displacement. I will try the sensor fusion.

Can you please recommend me some noise filters which can be used to minimize the noise in the accelerometer readings.

I think in order to block out some of the noise by filtering, there need to be a measurable difference in the properties of noise and signal (frequency range, signal following a predictable pattern etc.).

As far as I can see, in principle, the signal could look exactly like the noise. So, regardless of the kind of filtering, the signal to noise ratio will remain the same.

It would be another matter, if you knew that the acceleration will always match a certain pattern.

Subhashini De Silva

Some sliding-average filter (as long as acceptable - longer is better) might improve your position estimates (basically reducing the extreme excursions that cause significant dislocations due to double-integration), although the effects of noise cannot be cancelled completely.