Covariance Matrix Estimation for CFAR Detection in Correlated Heavy Tailed Clutter

This work addresses the problem of covariance matrix estimation for adaptive radar detection in correlated heavy tailed clutter. The clutter is modeled as a compound-Gaussian process with unknown statistics. An approximate maximum likelihood (AML) estimator is derived and compared to the maximum likelihood (ML) estimator; their calculation requires the iterative solution of a transcendental equation whose numerical convergence is obtained through the introduction of a constraint in the iteration. The performance of the two "constrained" algorithms is evaluated in terms of the Frobenius norm of the error matrix, of the computational complexity (i.e., the number of iterations), and of the constant false alarm rate (CFAR) property of the adaptive detector which makes use of them. Numerical results show that the AML estimator can be calculated with a very small number of iterations, it has a negligible performance loss with respect to the ML and less computational complexity. Finally, the AML guarantees the desired CFAR property to the detector.