## 1 Introduction  
The complexity of the marine environment results in the curved propagation of sound waves in the ocean rather than straight lines. In ultra-short baseline acoustic positioning systems, the curved propagation of sound waves leads to propagation delays from the transmitting source to the receiving source greater than those in linear propagation. Consequently, curved sound wave propagation induces shifts in underwater positioning results, diminishing positioning accuracy. Estimating distance using average sound velocity further reduces accuracy. To address these issues, researchers have proposed various underwater acoustic positioning methods. Ref. [1] enhances water depth measurement accuracy by autonomously detecting different water mass boundaries, enabling independent adjustment of Sound Velocity Profiles (SVP) for each beam. Ref. [2] introduces a hierarchical linear SVP simplification method utilizing a distance-minimizing equally spaced control point search algorithm, achieving improved SVP approximation accuracy. Ref. [3] proposes an effective sound velocity computation method, enhancing real-time measurements for small underwater vehicles and facilitating low-complexity underwater acoustic ranging in deep-sea IoT. Ref. [4] explores the correlation between propagation time and SVP in underwater reference point positioning. Ref. [5] presents a clustering method based on Sound Speed Profile (SSP), which is divided into two stages: linearization and clustering. In the linearization stage, the SSP is represented as a set of line segments and inflection points through piecewise linear fitting. In the clustering stage, SSP grouping is performed using parameters derived from the SSP. Ref. [6] presents a localization algorithm based on improved particle swarm optimization, demonstrating effective compensation for layering effects and improved positioning accuracy. Ref. [7] tackles the difficulty of obtaining continuous temporal SVP in deep-sea operations by proposing an SVP temporal prediction method based on the EMD-NARX model. Ref. [8] corrects deviations caused by acoustic ray bending effects by fixing SVP and adaptively adjusts fixed SVP with in-situ sound velocity measurements. Ref. [9] introduces a self-constrained underwater positioning method to address the unreliability of solutions due to the lack of SVP data. Ref. [10] offers a novel method using Stimulated Brillouin Scattering LiDAR for detecting the sound velocity profile of the upper mixed layer in the ocean. Ref. [11] proposes an algorithm for calculating ocean water sound velocity profiles using flight time measurements, enhancing accuracy through the discrete cosine transform domain and well-known metaheuristic algorithms. Ref. [12] swiftly converts actual sound velocity profiles into constant gradient profiles, proposing a fast and accurate underwater acoustic horizontal ranging method. Ref. [13] contributes to sonar detection support by studying the classification and distribution characteristics of sound velocity profiles. Ref. [14] classifies and studies deep-sea sound velocity profiles in the Northwest Pacific using layered clustering and fuzzy C-means clustering methods. Finally, Ref. [15] addresses biases in traditional sound signal distance estimation methods with a depth-based sound velocity vertical layer compensation method. Ref. [16] proposes a sound velocity profile layering method based on minimum variance, utilizing global search and maximum difference, with the threshold directly influencing layering results. Ref. [17] conducts a comprehensive analysis and comparison of underwater positioning and navigation systems. It initially introduces various types of underwater positioning and navigation systems, including acoustic, multi-sensor, GPS buoys, vision-based, SLAM, and cooperative systems. Subsequently, a detailed analysis of the advantages and disadvantages of these systems is provided, along with recommendations for their optimal deployment in different environments.