Kalman Filter from the Mutual Information Perspective

TL;DR

This paper derives the Kalman filter from a mutual information perspective, extending it to Rényi mutual information, and highlights the measurement update as key to minimizing state uncertainty.

Contribution

It provides the first detailed derivation of the Kalman filter from mutual information and extends the concept to Rényi mutual information.

Findings

Measurement update minimizes state uncertainty

Kalman filter derived from mutual information principles

Extension to Rényi mutual information

Abstract

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.