To your question about what filter should be used, be aware that it is impossible to remove noise entirely if the noise is random because it cannot be predicted, and therefore, at best, all you can do is reduce its mean and variance. For random noise, your objective might be to minimise the output noise variance, in which case a moving average filter is optimal, whose output noise distribution is:
$${\rm E}[\bar X] = \mu$$
$${\rm Var}\left[\bar X\right] = \frac{\sigma^2}{n}$$
Where $\bar X$ is the noise mean computed over $n$ samples, and $\mu$ and $\sigma^2$ are the noise mean and variance, respectively, and ${\rm E[\bar X]}$ and ${\rm Var[\bar X]}$ means the expected value and variance of $\bar X$, respectively.
Now, as comments have pointed out, unfortunately there is a high probability that you are not going to obtain satisfactory results estimating position from acceleration measurements due to rapidly growing uncertainty, which I will show analytically based on expected value and propagation of variance:
Firstly, the velocity is computed from the integrated acceleration signal, which is proportional to a cumulative sum in the discrete time domain, so this operation inherently minimises output noise variance since it equally weights all samples used, with the velocity noise distribution being:
$${\rm E}\left[T\sum X\right] = NT\mu$$
$${\rm Var}\left[T\sum X\right] = NT^2\sigma^2$$
Where $N$ is the number of samples used in a cumulative sum, and $T$ is the sample interval.
Then, the velocity is integrated to determine position, which, notably, no longer equally weights all samples used, meaning the output noise variance is no longer minimised, with the position noise distribution being:
$${\rm E}\left[T^2\sum\sum X\right] = \frac{N(N+1)}{2}T^2\mu$$
$${\rm Var}\left[T^2\sum\sum X\right] = \frac{N(N+1)(2N+1)}{6}T^4\sigma^2$$
Therefore, the noise's distribution in the position for large $N$ asymptotes to the following 95% confidence interval:
$$\frac{N^2}{2}T^2\mu\pm\frac{2}{\sqrt3}N^{1.5}T^2\sigma$$
As such, returning to my original statement, position uncertainty will grow with the number of samples, that is, time, with any non-zero noise mean eventually dominating as it grows as $N^2$, and whilst you might be able to zero your acceleration readings in an attempt to remove the noise mean, I can guarantee the noise mean will change over time due to sensor imperfections, and it still leaves the component of uncertainty due to noise variance that grows as $N^{1.5}$.
Finally, I will also mention that linearly interpolating your data can introduce significant undesirable artefacts because at one extreme it involves averaging two samples when the interpolation point is midway between two samples, and at the other extreme has no averaging when the interpolation point falls coincident with a sample. Therefore, just in case you're not aware, make sure your signal bandwidth is such that any artefacts introduced by this are within acceptable bounds.
