Bayesian Sonar Detection Performance Prediction With Source Position Uncertainty Using SWellEx-96 Vertical Array Data

Predicting sonar detection performance is important for the development of sonar systems. The classical sonar equation cannot accurately predict sonar detection performance because it does not incorporate the effect of ocean environmental and source position uncertainty. We propose an analytical receiver operating characteristic (ROC) expression that characterizes the performance of the optimal Bayesian detector in the presence of ocean environmental and source position uncertainty. The approach is based on a statistical model of the environment and a physical model of acoustic propagation, which translates ocean environmental and source position uncertainty to signal wavefront uncertainty. The analytical ROC expression developed in this paper is verified for source position uncertainty due to source motion using both simulated data and real data collected during the Shallow Water Evaluation Cell Experiment (SWellEx-96). The results showed that the primary effect of source position uncertainty on optimal sonar detection performance is captured by the rank that corresponds to the significant eigenvalues of the signal matrix, an ensemble of replica signal wavefronts (normalized acoustic pressure vector) at the receiving array. The results also showed that the proposed ROC expression provides a realistic detection performance prediction for the Bayesian detector for source position uncertainty using real data. The proposed approach to sonar detection performance prediction is much simpler and faster than those using conventional Monte Carlo approaches