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An estimation-detection scheme is proposed for the estimation of signals with unknown parameters. The scheme is illustrated by considering the case of a signal with unknown but bounded variance. Two sets of bounds are used to determine two regions of signal uncertainty, and different linear estimators are used for each region. A detector is then used to select the appropriate estimator. Since no a priori information is assumed on the unknown parameters a weighted minimax criterion is used to optimize the detector and the estimators.