Bayes Factor test for the discrimination of a submerged mobile object from a continuous wave transmission

Abstract

Detection of an underwater mobile object by means of a continuous wave transmission is a challenging problem in part due to the difficulty of making inferences on closely spaced tones that provide clues regarding the objects' depth and speed. Considered here is a bistatic sonar arrangement to detect the presence of an oncoming submerged object. The optimal receiver computes the Bayes factor associated with the hypothesis test. The analytic intractability of the marginalization associated with the composite nature of the hypothesis leads to numerical methods of integration. The prior density on the target present scenario is constructed by an inverse image transformation through the forward propagation model. Computation of the Bayes factor is accomplished by Markov-chain Monte Carlo sampling with a Gibbs sampler. Analytically tractable conditional and marginal densities of the tone amplitudes are exploited while the conditional density of the ordered frequencies are constructed numerically by an inverse quantile sampler. Detection performance of a receiver against a mobile target are illustrated and discussed.