I don't know what it is about the Kalman filter but so many explanations including the OP have this format: "It's very simple! <complicated obtuse explanation listing the computation steps>"
Your comment is the first I've seen actually providing intuition about what is happening. It doesn't help perhaps that the name itself is misleading as heck to computer people like me: it's not a filter as in stream processing or SQL.
- simple to predict / understand what it would do: Easily explained with pictures and hardly no math
- simple to understand at a higher level / see why it works: Not easily explained without math and fraught with bayesian vs optimization vs EE-type approaches
- simple to understand well enough to use: Not easily done without other relevant math that is not covered in KF explanation, e.g., controls, matrix analysis, Jacobians, etc
- simple to understand why the equations are named what they are, and why they work: Not easily explained without math and historical context that takes a page or so to explain.
> it's not a filter as in stream processing
As you say "filter" means 'remove noise', but it also means 'process in order of arrival', so it's similar to your def of filter.
I recall reading a very intuitive explanation including animations of a point cloud to show how it works. I've had no luck finding the article again though.
Your comment is the first I've seen actually providing intuition about what is happening. It doesn't help perhaps that the name itself is misleading as heck to computer people like me: it's not a filter as in stream processing or SQL.