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

摘要

A central limit theorem for bilinear forms of the type a*(C) over cap (N) (rho)(-1) b, where a, b is an element of C-N are unit norm deterministic vectors and (C) over cap (N)(rho) a robust-shrinkage estimator of scatter parametrized by rho and built upon n independent elliptical vector observations, is presented. The fluctuations of a*(C) over cap (N)(rho)(-1) b are found to be of order N-1/2 and to be the same as thoSe of a*(S) over cap (N)(rho)(-1)b for (S) over cap (N) (rho) 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 rho. (C) 2015 Elsevier Inc. All rights reserved.