Mathematical Derivation of the Bayes and Kalman filters

I read a lot of technical documents, but sometimes I just don’t get them without a lot of extra work. In particular, I’m prone to getting stuck on mathematical conclusions that I don’t follow (usually because there is a step or two that the author assumed without proving). I’ve found that if I work through the details, and write up them up as clearly as possible, the writeup itself has value for me down the line when I need to remember the fine points.

I’m going to start posting some of these writeups here, where they can unstick someone else. This first writeup was written earlier this year when I was studying Probabilistic Robotics by Sebastian Thrun, Wolfram Burgard, and Dieter Fox; I think that book has the best, most intuitive treatment of the Kalman Filter I’ve ever read.

This is a “level 3” writeup: for grad students and hardcore practitioners.

A mathematical derivation of the Bayes and Kalman filterDownload