Robustness analysis of covariance matrix estimates

Standard covariance matrix estimation procedures can be very affected by either the presence of outliers in the data or some mismatch in their statistical model. In the Spherically Invariant Random Vectors (SIRV) framework, this paper proposes the statistical analysis of the Normalized Sample Covariance Matrix (NSCM) and the Fixed Point (FP) estimates in disturbances context. The main contribution of this paper is to theoretically derive the bias of the NSCM and the FP arising from disturbances in the data used to build these estimates. The superiority of these two estimates is then highlighted in Gaussian or SIRV noise corrupted by strong deterministic disturbances. This robustness can be helpful for applications such as adaptive radar detection or sources localization methods.