Abstract
A Bayes factor active sonar (BFAS) discriminant is constructed for depth uncertain acoustic scattering bodies in refractive ocean waveguides for relatively high-frequency broadband reception along vertical arrays. The approach accounts for environmental information regarding the refractive media, as well as surface and volume reverberation models. Uncertainty in the reverberation field and the scatterers' depth, is incorporated through proper marginalization rather than maximization as in more conventional Generalized Likelihood Ratio Tests. The discriminant yields a set of time-varying quadratic forms in beam-delay space, optimally balancing uncertainty of the scatterer and reverberation and noise subspaces in the minimum average risk sense. Utilizing waveguide information, BFAS combines multi-path arrivals, optimally attenuating reverberation subspaces while preserving the target subspace, effectively increasing Signal-to-Reverberation plus Noise Ratios (SRNR) despite target depth uncertainty. Depth-Invariant Modes (DIMs) provide a valuable expansion of the discriminating information as the logarithm of the Bayes Factor, thereby providing lower bounds on the performance of the BFAS. These bounds illustrate that even with depth uncertainty, the BFAS outperforms a single specular arrival detector with perfect knowledge of the scattering body's depth. Performance across various refractive and shallow-water environments lends credence to the Bayesian multi-path combining approach. [Work supported by ONR]