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A technique is presented for estimating the covariance matrix due to underwater ambient noise by enforcing frequency- and angle-smoothness on the power-angle spectrum underlying an observed sample covariance matrix. This smoothing is achieved through a combination of least-squares fitting procedures and explicit suppression of contributions from discrete broadband emitters. The process preserves contributions from diffuse broadband sources whereby the resulting covariance matrix is dominated by ambient noise. Possible applications include adaptive beamforming and measuring the vertical/horizontal directionality of diffuse broadband ambient noise sources such as wind and rain.