New properties for Tyler’s covariance matrix estimator

Gordana Draskovic (1) , Frédéric Pascal (1)

1 L2S - Laboratoire des signaux et systèmes

In this paper, we deal with covariance matrix estimation in complex elliptically symmetric (CES) distributions. We focus on Tyler's estimator (TyE) and the well-known sample covariance matrix (SCM). TyE is widely used in practice, but its statistical behavior is still poorly understood. On the other hand, under Gaussian assumption, the SCM is Wishart-distributed, but its properties degrade in non-Gaussian environments. The main contribution is the derivation of new properties of TyE under CES framework, in order to approximate its behavior with a simpler one, the Wishart one. Finally, Monte-Carlo simulations support that claims and demonstrate the interest of this result.

Mots clés: Index Terms-Covariance matrix estimation; Complex Ellipti- cally Symmetric distributions; Sample Covariance Matrix; Tyler's estimator; robust estimation

Domaines: Traitement du signal et de l'image [eess.SP]; Autres [stat.ML]; Applications [stat.AP]

Gordana Draskovic, Frédéric Pascal. New properties for Tyler’s covariance matrix estimator. 50th Asilomar Conference on Signals, Systems and Computers, Nov 2016, Pacific Grove, CA, United States. ⟨10.1109/acssc.2016.7869161⟩. ⟨hal-01634293⟩