The results of this paper show how randomness and/or uncertainty of medium, boundary conditions, source characterization, and source and receiver motion affects the probability of detection of a narrow band, high frequency source. Using ray acoustic model, we derive expressions for loss of time coherency and its dual, spectral spreading that is caused motion through a medium with random boundary conditions and inhomogeneities. Spectral spreading decreases probability of detection of a narrowband signals. In this analysis both the usual knowledge and the essential uncertainty are incorporated into problem formulation by separating propagation models and boundary conditions into deterministic and random parts. Maximum entropy method (MEM) is used to incorporate essential uncertainty into model. Maximum entropy method uses what is known in its model, but models what is not known with maximum uncertainty. It does not make any unwarranted assumptions about unknown parameters. MEM is used to calculate confidence intervals and mean values of receiver operating characteristics of high-frequency passive and active sonar detectors when signal to noise ratio is a random variable.
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