Covariance Matrix Estimation of Texture Correlated Compound-Gaussian Vectors for Adaptive Radar Detection

Abstract

Covariance matrix estimation of compound-Gaussian vectors with texture-correlation (spatial correlation for the adaptive radar detectors) is examined. The texture parameters are treated as hidden random parameters whose statistical description is given by a Markov chain. States of the chain represent the value of texture coefficient and the transition probabilities establish the correlation in the texture sequence. An Expectation-Maximization (EM) method based covariance matrix estimation solution is given for both noiseless and noisy snapshots. An extension to the practically important case of persymmetric covariance matrices is developed and possible extensions to other structured covariance matrices are described. The numerical results indicate that the benefit of utilizing spatial correlation in the covariance matrix estimation can be significant especially when the total number of snapshots in the secondary data is small. From applications viewpoint, the suggested model is well suited for the adaptive target detection in sea-clutter where some spatial correlation between range cells has been experimentally observed. The performance improvements of the suggested approach for small number of snapshots can be particularly important in this application area.