This paper addresses asymptotically minimum variance (AMV) algorithms within the class of algorithms based on second-order statistics for estimating direction-of-arrival (DOA) parameters of possibly spatially correlated (even coherent) narrowband noncircular sources impinging on arbitrary array structures. To reduce the computational complexity due to the nonlinear minimization required by the matching approach, the covariance matching estimation technique (COMET) is included in the algorithm. Numerical examples illustrate the performance of the AMV algorithm