Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals

Publication Type:

Journal Article

Source:

Elsevier Journal of Multivariate Analysis, Volume 143, p.249-274 (2016)

Abstract:

A central limit theorem for bilinear forms of the type a∗CˆN (ρ)−1b, where a, b ∈CN are unit norm deterministic vectors and CˆN (ρ) a robust shrinkage estimator of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of a∗CˆN(ρ)−1b are found to be of order N−1 and to be the same as those of a∗Sˆ (ρ)−1b for Sˆ (ρ) a matrix of a 2NN 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.