Analog arrays with steerable beams can be capable of angle estimation and sometimes even adaptive beamforming based on power measurements taken at the outputs of multiple beam dwells. In the interesting case of a reflectarray, where beams are formed using a large collection of programmable, passive phase shifters, it is possible to use multiple dwells to estimate signal correlations among the phase shifters. These correlations form an estimated covariance matrix at the phase centers of the shifters. Adaptive beamforming and geolocation can be based on this covariance matrix. Various methods for estimating full-rank and approximately rank-deficient covariance matrices using power measurements from multiple dwells are introduced and evaluated. In some cases, the performance of an estimator can be shown to be optimal in the sense of achieving Cramer-Rao bounds for the estimated covariance parameters.