CFAR assessment of covariance matrix estimators for non-Gaussian clutter

In the non-Gaussian clutter modeled as independent and identically distributed spherically invariant random vectors, three estimators of sample covariance matrix (SCM), normalized sample covariance matrix (NSCM) and the corresponding recursive estimator (NSCM-RE) are analyzed. Based on the uniform theorem, three corresponding adaptive normalized matched filters (ANMF) are evaluated from the standpoint of constant false alarm rate (CFAR) property. The theoretical results demonstrate that the SCM-ANMF is only CFAR to the normalized clutter covariance matrix (NCCM); the NSCM-ANMF is only CFAR to the clutter power level; and the NSCM-RE-ANMF with finite number of iterations is still not CFAR to the NCCM. To ensure CFAR property of ANMF, an adaptive estimator (AE) is devised. Moreover, with AE as the initialization matrix for the iterations, the AE-RE is proposed. With finite number of iterations, the corresponding AE-REANMF guarantees CFAR property to both of the NCCM and the clutter power level. Finally, the performance assessment conducted by Monte Carlo simulation confirms the effectiveness of the proposed detectors.