Abstract
Performance metrics of a Bayes Factor (BF) active sonar detection scheme is developed for various refractive and shallow water waveguides for the noise limited, uncorrelated scattering regime. The BF, a time-varying quadratic form, attenuates apriori reverberation and noise subspaces while passing apriori probable target returns. The BF processor makes use of the physical characteristics of the waveguide to increase signal-to-noise and reverberation ratios for uncertain environment and uncertain target depths. The distribution of the log of the BF when no target, the composite null, is a superposition of weighted central chi-squared variates with the degrees of freedom associated with the uncertain target depth subspace. Similarly, under the composite alternative, when a target is present, the distribution is a weighted superposition of noncentral chi-squared variates. These distributions do not permit simple closed form solutions but are computable with the asymptotic method of Davies or via moment matching. Performance for each of the considered waveguides with target uncertainty is summarized by receiver operating characteristic curves and is compared to a single specular arrival benchmark for the certain depth target. The BF active sonar with uncertain target depth and multipath combining demonstrates improved performance over the known depth single specular detector.