How a Kalman filter works, in pictures

I have to tell you about the Kalman filter, because what it does is pretty damn amazing.

Surprisingly few software engineers and scientists seem to know about it, and that makes me sad because it is such a general and powerful tool for combining information in the presence of uncertainty. At times its ability to extract accurate information seems almost magical— and if it sounds like I’m talking this up too much, then take a look at this previously posted video where I demonstrate a Kalman filter figuring out the orientation of a free-floating body by looking at its velocity. Totally neat!