Invariant mode factorizations of a Bayes Factor high active sonar discriminant

A Bayes factor active sonar (BFAS) processor for high-frequency broadband inference on vertical arrays in shallow water waveguides is presented. Relevant information regarding the refractive media, rough surface and volume reverberation is incorporated to build the marginal likelihood under the composite null while the alternative hypothesis must account for scattering from an object of uncertain depth. The processor is contrasted with the generalized likelihood ratio test (GLRT), where maximization is a surrogate for proper marginalization. The processor aggregates a set of time-varying quadratic forms over the array observations over beam-delay and we present an invariant mode factorization that is particularly insightful in terms of the eigenrays of the waveguide. We illustrate the approach by considering various refractive waveguides and demonstrate how prior information regarding the waveguide attenuates reverberant and noise subspaces weighing favorably target subspaces, effectively increasing signal-to-noise and reverberation ratios under uncertain target depths. The distribution of the BFAS under each hypothesis, while not admitting a simple closed form, does allow a lower bound through an approximation via moments. Bounds on receiver operating characteristic curves under depth uncertainty show the potential to outperform a direct path arrival detector with known target depth. [This work is supported by ONR.]