A Kullback-Leibler Divergence Variant of the Bayesian Cramér-Rao Bound
Document Type
Article
Publication Date
6-1-2023
Abstract
This paper proposes a Bayesian Cramér-Rao type lower bound on the minimum mean square error. The key idea is to minimize the latter subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback–Leibler divergence ball centered at a Gaussian reference distribution. The bound is tight and is attained by a Gaussian distribution whose mean is identical to that of the reference distribution and whose covariance matrix is determined by a scalar parameter that can be obtained by finding the unique root of a simple function. Examples of applications in signal processing and information theory illustrate the usefulness of the proposed bound in practice.
Identifier
85147198241 (Scopus)
Publication Title
Signal Processing
External Full Text Location
https://doi.org/10.1016/j.sigpro.2023.108933
ISSN
01651684
Volume
207
Recommended Citation
Fauß, Michael; Dytso, Alex; and Poor, H. Vincent, "A Kullback-Leibler Divergence Variant of the Bayesian Cramér-Rao Bound" (2023). Faculty Publications. 1697.
https://digitalcommons.njit.edu/fac_pubs/1697
