I did some calibration measurements by rotating the knob only in one direction and doing a principal component analysis just using the first component for each of the measurements as a projection matrix
So how to solve it, in principle I have 9 measurements and 9 degrees of freedom (3 rotation and 3 displacements of the know respectively and 3 of the magnetic field). OK, since my sensors are not on the same position, one could argue that I even have 6 degrees of freedom of the whole device in space. How to continue:
- doing a highpass filter to remove the earth magnetic field
- adding 3 degrees of freedom to my calibration
- moving the magnets more closer that the induced field is much stronger than the earth field
- ...
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