Linearized two-hydrophone localization of a pulsed acoustic source in the presence of refraction: Theory and...

This paper develops an efficient three-dimensional localization method for transient acoustic sources, with uncertainty estimation, based on time differences between direct and surface-reflected arrivals at two hydrophones. The localization method accounts for refraction caused by a depth-dependent sound-speed profile using a ray-theoretic approach for calculating eigenray travel times and partial derivatives. Further, the method provides localization error estimates accounting for uncertainties of the arrival times and hydrophone locations, as well as for depth-dependent uncertainties in the sound-speed profile. In the first of two steps, source depth and range to each hydrophone are estimated using an iterative, linearized Gauss-Markov inversion scheme. In the second step, the estimated source ranges are combined with the hydrophone locations to obtain the source location in the horizontal. Localization performance is analyzed in a simulation study, and the linearized localization estimates and uncertainties are validated by comparison with a fully nonlinear (but numerically intensive) Markov-chain Monte Carlo inversion.