I have data from a sensor that quite noisy. I have determined the sensor's error distribution and found it to be normally distributed.
My question is: Can this distribution be used in some way to smooth the data? Ideally some discrete function or method.
I will need to integrate it twice, and the sharp spikes get out of control the more it is integrated. In my project, I measure acceleration and integrate to velocity and displacement. The acc values are (as an average) close to 0. However, the displacement turns out to be $\pm60\text{ m}$ on a stationary sensor. I tried a first order filter that produced better results, but nowhere near $0 \text{ m}$.
EDIT: For some reason I confused differentiation with integration...