Shrinkage covariance matrix estimator applied to STAP detection

Frédéric Pascal (1) , Yacine Chitour (2)

1 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)
2 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Traitement du signal et de l'image [eess.SP]

Frédéric Pascal, Yacine Chitour. Shrinkage covariance matrix estimator applied to STAP detection. SSP 2014, IEEE, Jun 2014, Gold Coast, Australia. pp.324 - 327, ⟨10.1109/SSP.2014.6884641⟩. ⟨hal-01104073⟩