The development of effective passive sonar systems depends upon the ability to accurately predict the performance of sonar detection algorithms in realistic ocean environments. Such environments are typically characterized by a high degree of uncertainty, thus limiting the usefulness of performance prediction approaches that assume a deterministic environment. Here we derive closed-form receiver operating characteristic (ROC) expressions for an optimal Bayesian detector and for several typical suboptimal detectors, based on a statistical model of environmental uncertainty. Various scenarios extended from an NRL benchmark shallow-water model were used to check the analytical ROC expressions and to illustrate the effect of environmental uncertainty on detection performance. The results showed that (1) optimal detection performance in an uncertain environment in diffuse noise depends primarily on the signal-to-noise ratio at the receivers and the rank of the signal matrix, where the rank is an effective representation of the scale of environmental uncertainty; (2) the ROC expression for the optimal Bayesian detector provides a more realistic performance upper bound than that obtained from conventional sonar equations that do not incorporate environmental uncertainty; and (3) detection performance predictions can be performed much faster than with commonly used numerical methods such as Monte Carlo performance evaluations.
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