  A class of robust estimators of scatter applied to information-plus-impulsive
noise samples is studied, where the sample information matrix is assumed of low
rank; this generalizes the study of (Couillet et al., 2013b) to spiked random
matrix models. It is precisely shown that, as opposed to sample covariance
matrices which may have asymptotically unbounded (eigen-)spectrum due to the
sample impulsiveness, the robust estimator of scatter has bounded spectrum and
may contain isolated eigenvalues which we fully characterize. We show that, if
found beyond a certain detectability threshold, these eigenvalues allow one to
perform statistical inference on the eigenvalues and eigenvectors of the
information matrix. We use this result to derive new eigenvalue and eigenvector
estimation procedures, which we apply in practice to the popular array
processing problem of angle of arrival estimation. This gives birth to an
improved algorithm based on the MUSIC method, which we refer to as robust
G-MUSIC.
