Limitations of state estimation: absolute lower bound of minimum variance estimation/filtering, Gaussianity-whiteness measure (joint Shannon-Wiener entropy), and Gaussianing-whitening filter (maximum Gaussianity-whiteness measure principle)

TL;DR

This paper investigates fundamental performance limits of state estimation using information theory, introducing new measures like negentropy rate and Gaussianity-whiteness to analyze variance bounds and filtering principles.

Contribution

It proposes novel information-theoretic measures for analyzing the lower bounds of variance in state estimation and discusses the Gaussianing-whitening filter based on maximum Gaussianity-whiteness principles.

Findings

Derived absolute lower bounds for variance in state estimation.

Introduced negentropy rate and Gaussianity-whiteness measure for performance analysis.

Discussed the Gaussianing-whitening filter based on maximum Gaussianity-whiteness measure.

Abstract

This paper aims at obtaining performance limitations of state estimation in terms of variance minimization (minimum variance estimation and filtering) using information theory. Two new notions, negentropy rate and Gaussianity-whiteness measure (joint Shannon-Wiener entropy), are proposed to facilitate the analysis. Topics such as Gaussianing-whitening filter (the maximum Gaussianity-whiteness measure principle) are also discussed.