You’re correct. The Kalman gain in the linear case can be computed offline since it’s only a function of model parameters. The P matrix is updated at every iter

You’re correct. The Kalman gain in the linear case can be computed offline since it’s only a function of model parameters. The P matrix is updated at every iteration, but it is also only a function of Q and R (which is determined offline) and the previous P, which at time 0 is initialized with diagonals. P does represent the covariance of (xpred - xact) but it doesn’t take in inputs at every iteration. I appreciate that call out. Like most things, in practical implementations there’s a bunch of extra things that go beyond the basic theory you have to do like reestimating the initial P every few iterations as well as reestimating Q and R with online data. It’s not magic and yes it is a form of recursive linear regression but it does work in real life.