Inference regarding the state of mobile underwater object from a small aperture vertical array

Abstract

A narrowband source ensonifies an area of interest with an oncoming submerged target in a refractive undersea environment. A vertical linear hydrophone array is employed to infer the depth, range, and speed of the target by resolving a direct path and one interacting surface path. 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 complex propagation of sound in a refractive medium presents additional challenges for inversion of the wave vectors to range and depth. A Gibbs sampler is employed to construct the posterior joint density of all 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 an inverse transformation of the acoustic propagation model that accounts for the depth dependent sound speed. Simulation results demonstrate the approach at received signal to noise ratios below −3dB.