Equivalent-Gradient Sound-Speed Correction and Joint Time-Bias Estimation for Stratified-Ocean Acoustic Ranging in Seafloor Geodesy

High-precision seafloor geodesy such as GNSS-A positioning or seabed transponder networks is critically dependent on acoustic travel time measurements to recover seafloor benchmarks; however, in stratified ocean acoustic ranging, sound-speed-profile variations invalidate the approximately linear travel-time-to-range mapping that commonly holds for the terrestrial case. Simplified sound-speed models therefore yield biases that could be aliased into deformation time series, leading to errors in inference of plate motions and lithospheric deformation. Furthermore, underwater transponders deployed within the geodetic network are unable to maintain strict time synchronization in cold, high-pressure deep-ocean environments, imposing an added challenge on the usage of travel-time ranging.

To overcome these limitations, we develop an equivalent-gradient framework with a closed-form delay–range relationship and represent synchronization imperfections by a lumped time-bias term, enabling joint recovery of seafloor transponder position(s) and the bias. Specifically, let k = 1,...,K index the reception epochs along a moving surface vessel trajectory; s_k denotes the GNSS-referenced vessel position and t_k the recorded one-way arrival timestamp from a fixed seafloor transponder. We then form inter-epoch TDOA measurements that eliminate the unknown transmit epoch and reduce the problem to estimating a reference one-way delay τ₀ together with the transponder location u. Under the equivalent-gradient framework, travel time is efficiently mapped to an slant range dk = Req (τ; ξ_k),  , where ξ_k collects the equivalent-gradient parameters derived from the layered SSP, yielding the range–geometry constraints dk^2 = u − s^2. A squared-difference with respect to a reference epoch leads to a stable pseudo-linear regression:

This yields a WLS closed-form initializer followed by weighted Gauss–Newton refinement. An SDR-based global initializer is also developed, offering complementary insight into the problem’s geometry. The approach accommodates different acoustic link geometries (e.g., ship-to-seafloor and AUV-to-seafloor) and can exploit identifiable multipath (e.g., surface-reflected arrivals) for additional constraints. Monte-Carlo simulations under realistic stratified SSPs provide a controlled assessment of performance and robustness, showing that the proposed method substantially reduces range bias and improves seafloor position recovery relative to constant-sound-speed and single-gradient baselines, while remaining stable under SSP mismatch.

We further present an underwater acoustic transponder prototype integrating a chip-scale atomic clock (CSAC) and an FPGA-based multi-channel parallel clock disciplining subsystem.Sea trials in the South China Sea validate the end-to-end design and demonstrate representative ranging results, confirming kilometer-scale capability and stable real-time performance under in situ conditions. Overall, the proposed approach improves the fidelity of seafloor positioning time series and strengthens geodetic constraints on ilithospheric deformation and related earthquake hazard assessment.