Robust ANMF test using Huber's M-estimator

In many statistical signal processing applications, the quality of the estimation of parameters of interest plays an important role. We focus in this paper, on the estimation of the covariance matrix. In the classical Gaussian context, the Sample Covariance Matrix (SCM) is the most often used, since it is the Maximum Likelihood estimate. It is easy to manage and has a lot of well-known statistical properties. However it may exhibit poor performance in context of non-Gaussian signals, contaminated or missing data. In that case M-estimators provide a good alternative. In this paper, we extend to the complex data case, a theoretical result already proposed by Tyler in the real data case, deriving the asymptotical distribution of any homogeneous functional of degree 0 of the M-estimates. Then, applying this result to the Adaptive Normalized Matched Filter (ANMF), we obtain a robust ANMF and give the relationship between its Probability of False Alarm (P-fa) and the detection threshold.