Low-Rank Structured Covariance Matrix Estimation

The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persy...

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Bibliographic Details
Published in:IEEE signal processing letters 2019-05, Vol.26 (5), p.700-704
Main Authors: Shikhaliev, Azer P., Potter, Lee C., Chi, Yuejie
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian MAP
Clutter
Covariance matrices
Covariance matrix
Economic models
Eigenvalues
Eigenvalues and eigenfunctions
Estimating techniques
Iterative methods
low rank
maximum likelihood
Maximum likelihood estimation
Optimization
persymmetry
Thermal noise
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Summary:The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2019.2906405