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The problem of finding maximum-likelihood estimates of the partially or completely unknown autocorrelation function of a zero-mean Gaussian stochastic signal corrupted by additive, white Gaussian noise is analyzed. It is shown that these estimates can be found by maximizing the output of a Wiener estimator-correlator receiver biased by a smoothed version of the output noise-to-signal ratio of the Wiener estimator over the class of admissible autocorrelation functions. For the case where the autocorrelation function is known except for an amplitude scale parameter, an illuminating expression for the Cramer-Rao minimum estimation variance is derived. Detailed study of this expression yields, among other results, an interpretation of the maximum-likelihood estimator as an adaptive processor.