A Bayes factor for high frequency broadband active acoustic detection

A Bayes Factor (BF) inference processor is developed for high frequency broadband active monostatic sonar in shallow water environments with a vertical aperture. Relevant information regarding the refractive media, rough surface and volume reverberation are incorporated to build the marginal likelihoods under each of the composite hypotheses of null and alternative. Acoustic scattering from a mobile object of interest under considerable depth uncertainty characterizes the compound alternative hypothesis. Approximations are presented such that inferences regarding the presence of the mobile body of interest can be determined in closed form against a composite null hypothesis of reverberation and ambient acoustic noise. Reverberation is modeled via Lambert rough surface scattering.The BF processor is shown to be a time-varying quadratic form of array observations over the beam-delay space. We discuss the structure of the quadratic form relative to the expected angle-delay spectra of target and reverberation. We illustrate the BF inferential approach by considering various refractive waveguides as well as the iso-velocity case. The BF inference structure can be employed for decision theoretic loss functions in order to establish processors that optimally incorporate vertical arrival structure for decision making.