Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals
Résumé
A central limit theorem for bilinear forms of the type a * ˆ C N (ρ) −1 b, where a, b ∈ C N are unit norm deterministic vectors and C N (ρ) a robust-shrinkage estima-tor of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of a * ˆ C N (ρ) −1 b are found to be of order N − 1 2 and to be the same as those of a * ˆ S N (ρ) −1 b for S N (ρ) a matrix of a theoretical tractable form. This result is exploited in a classical signal detection problem to provide an improved detector which is both robust to elliptical data observations (e.g., impulsive noise) and optimized across the shrinkage parameter ρ.
Origine : Accord explicite pour ce dépôt
Loading...