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

Abstract

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.

A Real-Time Acoustic Observatory for Sperm-Whale Localization in the Eastern Mediterranean Sea

“…(e) Source Range/Depth Estimation: The source ranges (horizontal distances from the hydrophones) and source depth, together with their respective uncertainties are estimated by applying a Bayesian iterative localization scheme (Skarsoulis and Dosso, 2015;Pavlidi and Skarsoulis, 2021). Depending on the arrival associations obtained in the previous step, whether between all three hydrophones or between two hydrophones only, the corresponding three-hydrophone (3H) or two-hydrophone (2H) localization scheme is applied, respectively.…”

“…(f) Source Localization in the Horizontal: The source ranges estimated in the previous step are combined with the hydrophone locations in the horizontal, estimated from the GPS fixes and taking into account the hydrophone depths, to obtain the source location in the horizontal as well (Skarsoulis and Dosso, 2015;Pavlidi and Skarsoulis, 2021). In the case where the localization is based on two hydrophones, there are two geometrically symmetric solutions, symmetric with respect to the line connecting the two hydrophones in the horizontal plane (left-right ambiguity); if one of the two falls in a shallow-water area or on land, it is ignored.…”

“…3D localization based on direct and surface-reflected arrivals was originally introduced in connection with receptions at two hydrophones separated in the horizontal, e.g. two-hydrophone towed arrays, first assuming homogeneous environments (Skarsoulis et al, 2004;Thode, 2004) and then generalizing for refractive environments using ray-theoretic approaches (Skarsoulis and Kalogerakis, 2005;Thode, 2005;Skarsoulis and Kalogerakis, 2006;Skarsoulis and Dosso, 2015). In those approaches source range and depth estimation only requires knowledge of hydrophone depths, not their location in the horizontal; if the latter is also known, then the source azimuth can be estimated too.…”

“…Two-hydrophone localization is subject to left-right ambiguity, and localization uncertainties are subject to angular dependence. Source locations close to the endfire result in large azimuth uncertainties, while source locations close to the broadside result in large range and depth uncertainties (Skarsoulis and Dosso, 2015;Skarsoulis et al, 2018). Those pitfalls can be addressed by adding a third hydrophone, not in line with the other two (Pavlidi and Skarsoulis, 2021).…”

Bayesian geoacoustic inversion of seabed reflection data at the New England mud patch

“…Although fully-nonlinear methods are often applied to solve Bayesian inverse problems, linearization can be applied to weakly nonlinear problems and can provide much more efficient approximate solutions [42,[46][47][48]. To present this approach, consider first the linear inverse problem 19) where d and m are vectors of data and model parameters, respectively, and A is the Jacobian (or sensitivity) matrix containing the physics of the forward problem given by However, for the observed (fixed) data, P (d|m) can be interpreted as a function of m, which defines the likelihood function.…”