I want to compute the stationary Kalman filter algorithm but I haven't found any information about that algorithm ( not even the pseudo code ) so, I wonder what is the difference between the Kalman filter algorithm and the stationary Kalman filter algorithm and how I can derive it from the Kalman filter algorithm. Could someone point me out resources I can read about it?
I just found this post:
How to derive the stationary Kalman filter predictor?
and this document:
http://www.uh.edu/~bsorense/kalman.pdf on page 5.
Basically what I understand is that you calculate beforehand ( before the recursive process ) the Kalman gain and the state covariance matrix when the Kalman gain goes to infinite using these two equations:
$$\bar{P} = A\bar{P}A^T - A\bar{P}C^T ( C\bar{P}C^T + R )^{-1}C\bar{P}A^T + Q$$ $$\bar{K} = \bar{P}C^T(C\bar{P}C^T+R)^{-1}$$
and in the recursive function, this equation:
$$\hat{x}(t+1|t) = (A-A\bar{K}C)\hat{x}(t|t-1) + A\bar{K}y(t)$$
Is that correct?
Notes:
Yes, it is a question from a DSP book ( https://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf excercise 4.6 on page 83 ) but there is no information in that book about the stationary Kalman filter algorithm.