Linear prediction, filtering, and smoothing: An information-theoretic approach

Abstract

Information-theoretic concepts are used to derive some fundamental principles for the general estimation problem. With these basic principles, a minimal-error entropy estimator for linear systems disturbed by Gaussian random processes is easily derived, which is identical to the Kalman filter. Under non-Gaussian disturbances it is shown that the Kalman filter is a minimax-error-entropy linear estimator.