Intrinsic Cramér–Rao bounds for scatter and shape matrices estimation in CES distributions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IEEE Signal Processing Letters Année : 2019

Intrinsic Cramér–Rao bounds for scatter and shape matrices estimation in CES distributions

(1) , (2) , (3) , (4)
1
2
3
4

Résumé

Scatter matrix and its normalized counterpart, referred to as shape matrix, are key parameters in multivariate statistical signal processing, as they generalize the concept of covariance matrix in the widely used Complex Elliptically Symmetric distributions. Following the framework of [1], intrinsic Cramér-Rao bounds are derived for the problem of scatter and shape matrices estimation with samples following a Complex Elliptically Symmetric distribution. The Fisher Information Metric and its associated Riemannian distance (namely, CES-Fisher) on the manifold of Hermitian positive definite matrices are derived. Based on these results, intrinsic Cramér-Rao bounds on the considered problems are then expressed for three different distances (Euclidean, natural Riemannian, and CES-Fisher). These contributions are therefore a generalization of Theorems 4 and 5 of [1] to a wider class of distributions and metrics for both scatter and shape matrices.
Fichier principal
Vignette du fichier
[J29].pdf (304.45 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01975919 , version 1 (10-03-2020)

Identifiants

Citer

Arnaud Breloy, Guillaume Ginolhac, Alexandre Renaux, Florent Bouchard. Intrinsic Cramér–Rao bounds for scatter and shape matrices estimation in CES distributions. IEEE Signal Processing Letters, 2019, 26 (2), pp.262-266. ⟨10.1109/LSP.2018.2886700⟩. ⟨hal-01975919⟩
159 Consultations
198 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More