I succeeded in understanding the Kalman filter only when I found a text that took a similar approach. It was this invaluable article, which presents the Kalman filter from a Bayesian perspective:
Meinhold, Richard J., and Nozer D. Singpurwalla. 1983. "Understanding the Kalman Filter." American Statistician 37 (May): 123–27.
Meinhold, Richard J., and Nozer D. Singpurwalla. 1983. "Understanding the Kalman Filter." American Statistician 37 (May): 123–27.