The Estimated Ocean Detector: Derivation and Predicted Performance under Gaussian Assumptions

This paper presents a derivation of the Maximum Likelihood (ML) detector for acoustic signals that have propagated through a random or uncertain ocean environment. The derivation requires probability distribution functions (pdfs) of relevant signal and noise parameters belonging to the exponential class. (A companion paper describes how available knowledge of the environment and the Maximum Entropy method can be used to calculate exponential class pdfs for signal and noise parameters.) The resultant ML detector operates on the observations to compute parameter means, referred to as conditional mean estimates (CMEs), and then correlates the CME with the observations to obtain a detection statistic. For this reason, the detector is referred to as an Estimated Ocean Detector (EOD). For Gaussian signal and noise, the EOD reduces to the weighted sum of a correlation detector (CD) and an energy detector (ED), which agrees with Van Trees' result. When the signal variance is low the weights strongly favor the CD, while for high signal variance the weights strongly favor the ED. A closed-form solution is not available for the Gaussian EOD. However, results obtained using a Monte Carlo simulation show that when the signal variance is low, EOD performance equals that of the CD, while under high signal variance, performance equals the ED. For intermediate signal variance, the simulation shows that the EOD weights the CD and ED outputs so as to perform better than either detector by itself. Finally, EOD robustness to incorrect estimates of received signal and noise parameters pdfs is investigated using the Monte Carlo simulation. The EOD is shown to be a promising method for improving passive sonar performance by directly incorporating available information about the ocean environment without sacrificing robustness to errors in the signal parameter distributions