# What is the difference between Kalman filter algorithm and stationary Kalman filter algorithm?

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.

If that is the same thing, then you just solve for the Kalman gain at $t=\infty$ and apply the normal Kalman filter equations.