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)
For researchers in estimation theory, this work provides theoretical insights into performance bounds using information theory, but it is largely theoretical and incremental.
The paper proposes new information-theoretic measures (negentropy rate and Gaussianity-whiteness measure) to analyze fundamental performance limitations of state estimation, specifically the absolute lower bound of minimum variance estimation/filtering.
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.