  Kalman filter is a best linear unbiased state estimator. It is also
comprehensible from the point view of the Bayesian estimation. However, this
note gives a detailed derivation of Kalman filter from the mutual information
perspective for the first time. Then we extend this result to the R\'enyi
mutual information. Finally we draw the conclusion that the measurement update
of the Kalman filter is the key step to minimize the uncertainty of the state
of the dynamical system.
