No matter how much I read about the topic, I just could not grok it. The whole "state update" algorithm and sheer amount of different variables threw me off. Does anyone else feel the same way?
What worked for me in the end, was to first understand state observers (e.g. Luenberger observers) and then consider a Kalman filter as an optimal observer, where the observer gain is the steady-state Kalman gain.
The whole duality between state-feedback design and observer design -- and LQR and Kalman filters. Then it made sense :-)
Imo it starts with the name, it tells nothing and probably implies something different. It is the dynamic programming of control theory.