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An efficient algorithm is presented for estimating a covariance matrix consisting of a low-rank signal term and a full-rank noise term, known apart from a scalar factor. For each sample of the vector of sensor outputs, the algorithm approximates, in the least-squares sense, a rank-one update of the covariance matrix, under the side condition that the rank of the signal term remains bounded. If the model noise is spatially colored, the least-squares approximation is preceded by spatial prewhitening, It is shown that if the rank of the signal term is small compared to the number of sensors, then the proposed algorithm requires substantially less computational work than conventional averaging. Some simulation results are included, indicating that the proposed algorithm reduces the variance of some commonly used spectral estimators in off-target directions, without impairing their detection and resolution properties.