Abstract
We evaluate the performance of a Bayes factor active acoustic inference detection scheme under various refractive and shallow water waveguides. The Bayes factor (BF) scheme makes use of a time-varying quadratic form over a beam-delay space which in turn offers a simplified approach for the user. The quadratic form is one that is able to reject strong reverberation and noise features while passing aprior highly probable target signature returns. The BF processor exploits the apriori known physical characteristics of the waveguide, such as ambient noise levels and the sound speed profile, to provide prior environmental information to aid detection. The probability distribution of the detection scheme under the composite null hypothesis, the case in which no target is present, is shown to be a superposition of weighted central chi-squared variates with the degrees of freedom being the number of in-phase and quadrature channels of the return path impulse response. The distribution under the composite alternative is a weighted sum of non-central chi-squared variates. These distributions are not simple closed forms but can be well approximated. We consider two such methods of computation and evaluate a number of refractive and scattering regimes. The probability of detection as a function of probability of false alarm under conventional fixed threshold and cost rules are provided to demonstrate the advantage of prior environmental information for the purpose of sonar detection.