Kalman filters are so interesting. As far as I can tell they are one of the very simplest things one can do that requires a real understanding of math. It doe

Kalman filters are so interesting. As far as I can tell they are one of the very simplest things one can do that requires a real understanding of math. It doesn't seem like you can just drop in a library, in the general case, or if you can, it doesn't seem to be common practice. Usually things that need an actual understanding are either totally novel, or solved problems with existing tools. Kalman filters are where you find out that you really did need math all along, if you're like me and don't really see math in everyday life. I suspect there's still a way to fake your way through if you need to and have a day or two to study, but the first time you see it it really shows what you don't know. It's like when you see non physicists talking about physics and feel amazed at how they managed to seemingly understand maxwells equations just for fun.