My question was closed as "unfocused". At the same time it didn't receive any kind of feedback to describe what is unfocused about it.
That's while the question has a specific and focused question right in it: "3. Ideas for how to filter the data to get rid of the dependance between samples? Would using something like an unscentend Kalman filter be a good idea?".The other data is provided to create a context for it, the previous two (no.1 and no.2) are there just to show that I'm open to the possibility that "I'm holding it wrong" and that my whole approach is incorrect.