Considered here is an narrow band directed source and hydrophone receiver arrangement employed to infer the depth, speed, and range of an oncoming submerged object. Tracking the scattering body by means of a continuous wave transmission is challenging due to the difficulty of inferring the frequencies and angles of the two returned closely spaced wave vectors. Computation of the posterior pdf of these two wave vectors is accomplished by a judicious Gibbs sampling scheme that accounts for the uncertainty in the ambient acoustic noise level. Computational improvements are accomplished by taking full advantage of the prior distribution of the wave vectors associated with the specific target scenario. Very short duration observations of approximately 10 milliseconds are considered over which the Doppler rate of change of the two wave vectors can be considered negligible. This Bayesian scheme takes advantage of the analytic tractability of the conditional density of the received amplitudes and phases and of the noise powers. The conditional densities of the ordered wave vectors however are constructed numerically by 2 dimensional inverse quantile sampling. The inferred joint density of depth, range, and speed of the target is accomplished by constructing an inverse transformation of the acoustic propagation model.