If Q and R are constant (as is usually the case), the gain quickly converges, such that the Kalman filter is just an exponential filter with a prediction step. For many people this is a lot easier to understand, and even matches how it is typically used, where Q and R are manually tuned until it “looks good” and never changed again. Moreover, there is just one gain to manually tune instead of multiple quantities Q and R.
This is really what I have never understood about Kalman Filters. As to how you pick Q and R. Do you just adjust them until the result looks right? How does that end up working for anything not completely over-fit?
For example, if I'm tracking birds from video footage, I might choose a certain Q, but depending on the time of day the noise statistics might change. What do you do then?
