Simultaneous Detection and Estimation under Multiple Hypotheses.
Technical rept. Feb-Sep 69,
JOHNS HOPKINS UNIV BALTIMORE MD CARLYLE BARTON LAB
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The report treats the problem of simultaneous detection and estimation under multiple hypotheses when data from only one observation interval is available. The analysis is based on statistical decision theory. In the past, parameter estimation was always performed under the assumption that the desired signal was present with probability one. Since detection is meaningful only when some uncertainty exists as to the presence or absence of the desired signal it is apparent that classical estimation theory must be modified if the two operations are to be performed simultaneously. In addition, this report considers the case when the operations of detection and estimation are coupled. Specific detector and estimator structures are determined for the case where the two operations are strongly coupled and where the cost of estimation is given by a quadratic cost function. It is found that the detector structures are complex nonlinear functions of the received data, but nevertheless the one case considered in detail resulted in a type of correlation detector, where the basic operation is correlation of the received data with the various least squares estimators of the possible signals in the absence of uncertainty. The associated optimum estimator structures are determined for this case, and found to be weighted sums of the various least squares estimators in the absence of uncertainty. Author