Bayesian estimation and the Kalman filter

In this tutorial article, we give a Bayesian derivation of a basic state estimation result for discrete-time Markov process models with independent process and measurement noise and measurements not affecting the state. We then list some properties of Gaussian random vectors and show how the Kalman filtering algorithm follows from the general state estimation result and a linear-Gaussian model definition. We give some illustrative examples including a probabilistic Turing machine, dynamic classification, and tracking a moving object.