Regularized Covariance Estimation for Polarization Radar Detection in Compound Gaussian Sea Clutter

TL;DR

This paper introduces a robust regularized covariance matrix estimator for polarization radar in sea clutter environments, improving performance with limited data by leveraging Kronecker structure and shrinkage techniques.

Contribution

It develops the RSKE method combining Kullback-Leibler regularization, shrinkage, and iterative algorithms for better covariance estimation in complex sea clutter scenarios.

Findings

RSKE outperforms existing methods with limited training data.

The iterative algorithm converges reliably.

Simulations validate high performance on real sea data.

Abstract

This paper investigates regularized estimation of Kronecker-structured covariance matrices (CM) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex, elliptically symmetric (CES) distributions with a Kronecker-structured CM. To obtain a well-conditioned estimate of the CM, we add penalty terms of Kullback-Leibler divergence to the negative log-likelihood function of the associated complex angular Gaussian (CAG) distribution. This is shown to be equivalent to regularizing Tyler's fixed-point equations by shrinkage. A sufficient condition that the solution exists is discussed. An iterative algorithm is applied to solve the resulting fixed-point iterations and its convergence is proved. In order to solve the critical problem of tuning the shrinkage factors, we then introduce two methods by exploiting oracle approximating shrinkage (OAS) and cross-validation (CV). The proposed estimator, referred to as the robust shrinkage Kronecker estimator (RSKE), is shown to achieve better performance compared with several existing methods when the training samples are limited. Simulations are conducted for validating the RSKE and demonstrating its high performance by using the IPIX 1998 real sea data.