The Bayes factor (BF) provides an optimal inference scheme for high-frequency broadband discrimination from relatively short vertical arrays by properly accounting for environmental information regarding the refractive media, as well as surface and volume reverberation models. The BF addresses acoustic scatterer depth uncertainty through proper marginalization rather than maximization as employed in the generalized likelihood ratio test. BF operates as proper aggregation of a set of time-varying quadratic forms in beam-delay space, optimally balancing target, reverberation, and noise subspaces. The BF minimizes average risk by attenuating reverberation subspaces while preserving the target subspace, effectively increasing Signal-to-Reverberation+Noise Ratios (SRNR) despite target depth uncertainty. Depth-invariant modes are leveraged for a computationally fast BF expansion. Performance across various refractive and shallow water environments lends credence to the approach via probabilty of detection and probability of false alarm. Funded by the Office of Naval Research.
Gendron et al. (Wed,) studied this question.