SVP-Free USBL Positioning with Theoretical Ray-Bending Compensation via Joint Effective Sound Velocity Estimation

Abstract This paper presents a novel Sound Velocity Profile (SVP)-free positioning algorithm for Ultra-Short Baseline (USBL) systems, addressing the critical challenge of accurate underwater localization in scenarios where real-time SVP measurements are impractical or unavailable. The proposed method formulates positioning as a joint estimation problem, simultaneously recovering the target's three-dimensional coordinates and a path-averaged effective sound velocity parameter. This unified framework theoretically compensates for first-order ray-bending effects without requiring explicit ray tracing or prior knowledge of the local sound speed field. To address the numerical ill-conditioning intrinsic to ultra-short baseline geometries, a stabilized Levenberg-Marquardt solver is adopted. Experimental validation conducted in a controlled anechoic water tank demonstrates that the algorithm achieves sub-decimeter positioning precision, with mean three-dimensional deviations from the epoch‑averaged position ranging from 2.08 cm to 5.34 cm and standard deviations up to 2.84 cm. The effective sound velocity is estimated with a standard deviation within 2.60 m/s, and the relative positioning repeatability error (defined as RMSE divided by slant range) remains below 0.5\% across all tested configurations. The algorithm exhibits computational efficiency suitable for real-time implementation. From an engineering perspective, this SVP-free approach offers significant potential operational advantages: it eliminates the logistical burden and inaccuracies associated with continuous sound velocity profiling, and maintains computational efficiency suitable for real-time AUV navigation.