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It was a surprisingly light read. I really liked the strong intuition based reasoning in each step.

When I was playing with different compass implementations in F-droid I recognized many of them uses Kalman filter for reducing the noise from the raw sensor data. Some of them (maybe only one) had some problems near the angle 0, where the sensor data jumps between almost 2pi and slightly above 0 frequently. The problem that the assumption that the measurement uncertanity is gauss-distributed is breaking there badly, since it will be a half gauss near 0 and an other half near 2pi. I don't know what is the general approach to solve this. I would solve this with either:

- Convert the angle into a unit vector and use that as measurement input. Then predict the actual vector and use its orientation for the compass. - Move the periodic window boundaries with a slow relaxation. So if I hold my compass in 0 angle direction, then all angle data is transformed into the [-pi,pi) range. If I hold it to pi direction then the raw data transformed to [0,2pi) range.

TL;DR: Be careful when applying a Karman filter on angles (or more generally R/Z).

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