A class of covariance matching estimation techniques (COMET) has recently attracted interest in the signal processing community. These techniques have their roots in the statistical literature where they are sometimes referred to as generalized least squares methods. Covariance matching is an alternative to maximum likelihood estimation, providing the same large sample properties often at a lower computational cost. Herein, we present a general framework for covariance matching techniques and show that they are well suited to solve several problems arising in array signal processing. A straightforward derivation of the COMET criterion from first principles is presented, which also establishes the large sample properties of the estimator. Closed form compact expressions for the asymptotic covariance of the estimates of the parameters of interest are also derived. Some detection schemes are reviewed and two COMET-based detection schemes are proposed. The main part of the paper treats three applications where the COMET approach proves interesting. First, we consider the localization of underwater sources using a hydro-acoustic array. The background noise is often spatially correlated in such an application and this must be taken into account in the estimation procedure. Second, the problem of channel estimation in wireless communications is treated. In digital communications, an estimate of the channel is often required to perform accurate demodulation as well as spatially selective transmission. Finally, a radar detection problem is formulated and the proposed detection schemes are evaluated. 1998 Academic Press