Abstract
We explore the performance of a Bayes Factor (BF) active acoustic inference approach under various refraction and rough surface scattering regimes that typify diverse ocean waveguides. The BF processor, a time varying quadratic form over beam-angle observations, enables various user risk minimization strategies. The nature of the BF quadratic form is shaped by the expected ambient noise, reverberation and target angle-delay spectra. The structure of the BF processor provides intuition regarding the role of prior environmental and bathymetric information on detection in shallow water ocean waveguides with rough boundary scattering. The distribution of the BF under the composite null hypothesis when target and reverberation are well approximated as uncorrelated is shown to be a superposition of heteroskedastic gamma densities with the degree of freedom being the dimension of the target hypothesis scattering sub space. The distribution of the BF under the composite alternative is a superposition of heteroskedastic scaled non-central chi-square distributions. These distributions do not admit simple closed forms but can be well approximated. We consider a number of refractive and scattering regimes and relate the probability of detection as a function of probability of false alarm under conventional fixed threshold and cost rules. [This work supported by the Office of Naval Research.]