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I would like to control a system which orientation I measure with as quaternion based EKF in one degree of freedom. Obviously the simplest thing would be to convert the quaternion estimate to euler angles and take one of these. Unfortunately these euler angles are not stable. The other option I was thinking about was to use the so called quaternion error, where I specify another quaternion which I want my system to be controlled towards. Then I would have to specify all four values of this quaternion.

I'm wondering if there is a way to generate a quaternion error only for one of my angles?

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If your system has a fixed rotation about some axis, then you should be able to design your KF about a single angle of rotation. You should be able to tailor your equations of motion and measurements to be a function of that angle.

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