Propagation-Time-Consistent Ray-Path Correction for Long-Baseline Underwater Acoustic Localization

Non-uniform sound velocity profiles (SVPs) cause sound-ray refraction and propagation-path bending. The straight-line mapping among propagation time, propagation distance, and target position is, therefore, disrupted, leading to systematic errors in constant-sound-speed localization. To improve the consistency between propagation correction and geometric localization, an iterative ray-path correction method based on propagation-time consistency is proposed. The method contains three coupled steps. First, a path-dependent local layered SVP model is constructed for each target-to-base-station path, rather than using a global or fixed sound-speed model. Second, the ray parameter is inverted under the constraint of measured time-of-arrival (TOA), so that the corrected ray path remains consistent with the observed propagation time. Third, the corrected slant range obtained by layered ray tracing is fed back into a known-depth weighted least squares (WLS) localization model, forming a closed-loop position update. The method is evaluated through long-baseline (LBL) simulations with multiple SVPs and propagation geometries and is validated using measured TOA data and an observation-derived SVP. The simulation results show that sub-meter accuracy can be achieved under the tested TOA-noise conditions. In measured-data validation, the planar localization error is reduced from 4.6866 m to 0.1923 m. No divergence is observed in the tested small SVP-perturbation cases.