Distributionally Robust Optimization for STAP With Finite Samples

Drawing on the minimization of worst-case maximum likelihood (ML) estimation, this article develops a robust inverse clutter-plus-noise covariance matrix (CNCM) estimator for space-time adaptive processing against Gaussian clutter background at low sample support without any prior knowledge. Leverag...

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Bibliographic Details
Published in:IEEE transactions on aerospace and electronic systems Vol. 61; no. 5; pp. 11420 - 11436
Main Authors: Wang, Yalong, Zhang, Xuejing, Wang, Zhihang, Li, Jun, He, Zishu
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Closed form solutions
Clutter
Computational complexity
Covariance matrices
Covariance matrix
Distributionally robust optimization (DRO)
Eigenvalues
Eigenvalues and eigenfunctions
finite samples
Gaussian process
inverse clutter-plus-noise covariance matrix estimation
Maximum likelihood estimation
Optimization
Robustness
Robustness (mathematics)
space–time adaptive processing (STAP)
Training
Uncertainty
Vectors
ISSN:0018-9251, 1557-9603
Online Access:Get full text
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Summary:Drawing on the minimization of worst-case maximum likelihood (ML) estimation, this article develops a robust inverse clutter-plus-noise covariance matrix (CNCM) estimator for space-time adaptive processing against Gaussian clutter background at low sample support without any prior knowledge. Leveraging the nonconvex uncertainty set for CNCMs, we formulate a distributionally robust optimization-based ML estimation problem with the Wasserstein metric. We validate that the resulting nonconvex problem is algorithmically tractable. To achieve this, we reformulate the problem as a finite-dimensional semidefinite program. To pursue lower computational complexity, we establish a closed-form solution framework by imposing the rotation-equivariant property. We theoretically prove the existence and uniqueness of the solution and address the challenge of adaptively choosing the uncertainty set size. Importantly, the solution composes a nonlinear shrinkage estimator that inherently preserves the order of sample eigenvalues without additional operations. Experiments with both simulated and measured clutter data confirm the superiority of the proposed estimator in terms of estimation accuracy and robustness.
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ISSN:0018-9251
1557-9603
DOI:10.1109/TAES.2025.3566360