The best presentation that I&#x27;ve ever seen on what a Kalman filter really is comes from a SIAM Review article, &quot;A Fresh Look at the Kalman Filter&quot; by Jeffrey Humpherys, Preston Redd, and Jeremy West<p><a href="http:&#x2F;&#x2F;epubs.siam.org&#x2F;doi&#x2F;abs&#x2F;10.1137&#x2F;100799666" rel="nofollow">http:&#x2F;&#x2F;epubs.siam.org&#x2F;doi&#x2F;abs&#x2F;10.1137&#x2F;100799666</a><p>It sets up the discrete-time linear system and then uses a minimization principle to show what&#x27;s going on.  I can highly recommend it especially for people coming to Kalman filters from a math or optimization background.