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.