Covariance Matrix Estimation With Kronecker Structure Constraint For Polarimetric Detection

With the Kronecker product structure constraint, this paper proposes a covariance matrix (CM) estimation method in the Compound-Gaussian (CG) sea clutter background. We assume the CG clutter in different polarization channels has different textures, which is different from the existing Kronecker structure-based CM estimation methods for polarimetric target detection. Based on the maximum likelihood (ML) criterion, we obtain the fixed point equation of the CM and solve it by an iterative algorithm. The proposed method is referred to as the Kronecker-based maximum likelihood estimate (KMLE), and the relevance of KMLE to the existing estimation methods is also discussed. For the performance assessment, we demonstrate the estimation accuracy of KMLE by presenting the normalized mean-square error (NMSE), and the detection performance is assessed by inserting the estimated CM into the test statistic of the texture-free generalized likelihood ratio test (TF-GLRT) detector. Through simulations with the synthetic and real sea clutter, we verify that KMLE outperforms other estimation methods when the training samples are limited.