Shrinkage covariance matrix estimator applied to STAP detection

In the context of robust covariance matrix estimation, this work generalizes the shrinkage covariance matrix estimator introduced in [1, 2]. The shrinkage method is a way to improve and to regularize the Tyler's estimator [3, 4]. This paper proves that the shrinkage estimator does not require any trace constraint to be well-defined, as it has been previously developed in [1]. The existence and the uniqueness of this estimator, defined through a fixed point equation, is given according to the values of the shrinkage parameter. Moreover, it is shown that the shrinkage estimator converges to a particular Tyler's estimator when the shrinkage parameter tends to 0. Then, results on real STAP data show the improvement of using such a robust estimator to perform target detection in cases where the data sample size is less than the dimension.

[1]  Olivier Besson,et al.  Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case , 2012, IEEE Trans. Signal Process..

[2]  James Ward,et al.  Space-time adaptive processing for airborne radar , 1998 .

[3]  Olivier Besson,et al.  Covariance matrix estimation in complex elliptic distributions using the expected likelihood approach , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[4]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .

[5]  A. Hero,et al.  Robust shrinkage estimation of high-dimensional covariance matrices , 2010 .

[6]  Jean-Yves Tourneret,et al.  Parameter Estimation For Multivariate Generalized Gaussian Distributions , 2013, IEEE Transactions on Signal Processing.

[7]  Philippe Forster,et al.  Asymptotic Properties of Robust Complex Covariance Matrix Estimates , 2012, IEEE Transactions on Signal Processing.

[8]  Philippe Forster,et al.  Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis , 2008, IEEE Transactions on Signal Processing.

[9]  L. Scharf,et al.  The CFAR adaptive subspace detector is a scale-invariant GLRT , 1998, Ninth IEEE Signal Processing Workshop on Statistical Signal and Array Processing (Cat. No.98TH8381).

[10]  Ami Wiesel,et al.  Unified Framework to Regularized Covariance Estimation in Scaled Gaussian Models , 2012, IEEE Transactions on Signal Processing.

[11]  H. Vincent Poor,et al.  Complex Elliptically Symmetric Distributions: Survey, New Results and Applications , 2012, IEEE Transactions on Signal Processing.

[12]  David E. Tyler.  A Distribution-Free $M$-Estimator of Multivariate Scatter , 1987 .

[13]  H. Vincent Poor,et al.  IEEE Workshop on Statistical Signal Processing, SSP 2014, Gold Coast, Australia, June 29 - July 2, 2014 , 2014, Symposium on Software Performance.

[14]  R. Maronna.  Robust $M$-Estimators of Multivariate Location and Scatter , 1976 .

[15]  Yacine Chitour,et al.  Generalized Robust Shrinkage Estimator and Its Application to STAP Detection Problem , 2013, IEEE Transactions on Signal Processing.