[aktenlage]

Figured I can save you a click and put the main point here, as few people will be interested in the rest:

The Kalman filter is adding the precision (inverse of covariance) of the measurement and the precision of the predicted state, to obtain the precision of the corrected state. To do so, the respective covariance matrices are first inverted, to obtain precision matrices. To have both in the same space, the measurement precision matrix is projected to the state space using matrix H. The resulting sum is converted back to a covariance matrix, by inverting it.

[tj_astro]

That is super helpful, thanks! I'm used to calling the inverse of the covariance the information matrix.

[aktenlage]

Yeah, that's the correct term! I think precision is mainly used for 1D. But I like the term, as I feel it has a better intuition.