Advanced Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both stra...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 70; no. 12; p. 1
Main Authors Aubry, Augusto, Babu, Prabhu, Maio, Antonio De, Rosamilia, Massimo
Format Journal Article
LanguageEnglish
Published IEEE 01.12.2024
Subjects
Adaptive radar signal processing
Array processing
Banded Toeplitz
Block-Toeplitz
Computational complexity
Convergence
Covariance matrices
Estimation
Iterative methods
Maximum likelihood estimation
Minimization
Optimization
Radar applications
Spectral estimation
Toeplitz covariance matrix
Toeplitz-block-Toeplitz
Vectors
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Summary:This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2024.3474977