## 5 Conclusions  
The sound speed profile stratification method proposed in this paper improves the accuracy and robustness of underwater positioning, especially in scenarios with a tilted transducer at 30\({}^{\circ}\). The improved k-means clustering-based sound speed profile stratification method allows for the autonomous selection of a reasonable number of layers. Combined with the quadratic curve fitting method, it ensures relatively high positioning accuracy at different incident angles. From the positioning results, it can be seen that the k-means clustering stratification method based on maximum density and maximum distance has better positioning accuracy under clustering stratification, outperforming traditional k-means clustering and hierarchical clustering methods. This indicates that the proposed stratification method in this paper has practical engineering application value.  
However, there is still room for improvement in this method, especially in how to rationally select the number of layers to achieve more precise positioning. Further research and exploration are needed in this regard to enhance the method's applicability to different real-world scenarios.  
Due to the heterogeneity of the datasets, the optimal number of layers chosen may vary in different scenarios. Certain geological features might require more or fewer layers for accurate representation. To overcome this limitation, the introduction of an adaptive algorithm could be considered, automatically determining the optimal number of layers based on statistical features or specific patterns within the data. Additionally, considering the uncertainties in complex underwater environments influenced by factors such as ocean currents and temperature gradients, it might be beneficial to explore methods for dynamically adjusting the number of layers. This would enable the system to adaptively tune the stratification based on real-time environmental conditions.  
Different experimental designs and data collection methods may result in varying demands for the optimal number of layers. To enhance the method's versatility, experiments can be conducted at multiple locations, using different devices, and incorporating diverse geological scenarios to ensure robustness across various conditions. Research into introducing machine learning algorithms or expert systems, capable of providing automatic layering recommendations for specific scenarios based on learning from historical data and user feedback, is also recommended. Moreover, multimodal data fusion methods could be explored, involving the integration of different sensor data, such as sonar and magnetometer readings, to enhance the understanding of underground structures and reduce reliance on the number of layers.  
However, these methods and ideas are preliminary suggestions, and their effectiveness may need validation through further theoretical research and empirical experiments. Continuous improvement and optimization are crucial for enhancing the robustness and applicability of the method, better meeting the requirements of practical engineering applications.  
[PERSON] initiated the idea; [PERSON] contributed to the experiment; [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] contributed to the statical analysis of data. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National key R&D Program (2022 YFB4703403), the NSF of China (Grant No. 12274113), and in part by the Research Fund from Science and Technology on Underwater Vehicle Technology Laboratory (No. 6142215200102).  
Not applicable.  
Data Availability StatementData are presented in the article.  
The authors would like to express their gratitude for the support provided by the University of HoHai.  
The authors declare no conflicts of interest.