Abstract
A narrowband source ensonifies an area of interest in a refractive undersea environment. A small aperture vertical array is employed to infer the depth, range and speed of the acoustic scatterer by resolving the scattered direct and surface interacting wave fronts. Tracking the target 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. The propagation of sound in a refractive medium presents additional challenges for inversion of the wave vectors to range, depth, and speed. Joint posterior inference is made possible with a computational Bayesian Gibbs sampling scheme over all track parameters taking full advantage of the analytic tractability of the conditional densities of the received amplitudes and phases and of the ambient acoustic noise power. The conditional densities of the ordered wave vectors however are constructed numerically by 2-dimensional inverse quantile sampling. The inferred joint posterior density of the target state is obtained by constructing a numerical inverse transformation of the acoustic propagation model and provides posterior confidence intervals over speed, depth, and range. Simulation results demonstrate the approach at received signal to noise ratios (SNR) well below -9 dB and illuminate the limits of depth and speed estimation as a function of both depth and SNR.