Abstract
Tracking an underwater mobile object by means of a continuous wave transmission is challenging in part due to the difficulty of drawing inferences on closely spaced tones associated with target depth and speed. Considered here is a bistatic sonar arrangement employed to infer the depth, speed and range of an oncoming submerged object. Computation of the full posterior probability distribution of the returned amplitudes and frequencies from both the prior distribution and a finite duration window of the received waveform is made by Markov-chain Monte Carlo sampling. A Gibbs sampler is employed to construct the posterior joint density of all parameters by taking full advantage of the analytic tractability of the conditional and marginal densities of the received amplitudes while those of the ordered frequencies are constructed numerically by either an inverse quantile sampling or a Metropolis-Hastings sampler. The inferred density of depth, range, and speed of the target is accomplished by constructing a numerical inverse-transformation of the forward propagation model.