## 9 Conclusions  
The development of ocean needs the cooperation of many kinds of ocean equipment, various sensors are especially needed. The sensors work either independently or form an underwater sensor network [31; 32; 33; 34; 35] to accomplish the preset mission. Sufficient accurate position information is the primary prerequisite for achieving the goal. To improve the accuracy of slant distance in the USBL positioning system, the ray tracing method is introduced in the underwater acoustic positioning system to eliminate the influence of the ray bending on the calculation of the slant distance for the positioning accuracy. This paper presents a combined ray tracing method that combines the constant sound speed ray tracing method with the equal gradient ray tracing method. The proposed method can adaptively determine which ray tracing method should be employed; namely, the constant sound speed ray tracing method is used in the regions where the sound velocity is stable, and the equal gradient ray tracing method is used in regions where the sound velocity changes significantly. In the simulation experiments, the EOF was used to invert the real-time sound speed profile, which mitigated the errors in the measured sound velocity profile caused by the environmental and some other factors. After the sound speed profile was obtained, the combined ray tracing method autonomously judged which ray tracing method to use based on the gradient change in the sound speed profile. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Azimuth Angle** & \multicolumn{1}{c}{**Error Comparison (\(\epsilon\))**} & **Depth (m)** & **10** & **50** & **100** & **150** & **200** \\ \hline \multirow{3}{*}{\(30^{\circ}\)} & Traditional method & 10.6\% & 2.3\% & 2.0\% & 1.9\% & 1.1\% \\  & M1 & 10.6\% & 2.3\% & 1.9\% & 1.6\% & 0.9\% \\  & M2 & 3.8\% & 0.5\% & 1.4\% & 1.1\% & 0.4\% \\ \hline \multirow{3}{*}{\(40^{\circ}\)} & Traditional method & 21.3\% & 4.0\% & 4.4\% & 1.9\% & 2.0\% \\  & M1 & 21.3\% & 3.8\% & 4.0\% & 1.4\% & 1.4\% \\  & M2 & 7.4\% & 2.7\% & 2.7\% & 0.5\% & 0.6\% \\ \hline \multirow{3}{*}{\(45^{\circ}\)} & Traditional method & 20.5\% & 7.3\% & 3.1\% & 3.4\% & 2.5\% \\  & M1 & 20.5\% & 7.1\% & 2.6\% & 2.7\% & 1.7\% \\ \cline{1-1}  & M2 & 4.3\% & 1.7\% & 1.6\% & 1.6\% & 0.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Error of various ray tracing methods. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ratio Error(M2)/Error(M1)** & **10 m** & **50 m** & **100 m** & **150 m** & **200 m** \\ \hline \(30^{\circ}\) & 36.4\% & 23.1\% & 76.2\% & 67.9\% & 45.0\% \\ \(40^{\circ}\) & 34.8\% & 70.8\% & 68.0\% & 37.0\% & 42.9\% \\ \(45^{\circ}\) & 20.8\% & 23.4\% & 62.9\% & 58.2\% & 42.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ratio error(M2)/error(M1). The operational time of the proposed method is very short, so the sound source of the USBL remains relatively stationary with the transponder on the underwater target. To improve the positioning accuracy of the USBL positioning system further, it is also possible to optimize the sound ray correction and continuous positioning between the ultra-short baselines and moving sound sources, which is not presented in this work due to the limited space. Besides, we will conduct more in-depth studies on that subject in the future. Methodology, G.S. ; Project administration, Y.C. ; Writing--original draft, Q.G. ; Writing--review & editing, J.L. and H.H. This research was funded by National Key R&D Program of China (2017 YFC0306100), Natural Science Foundation of Jiangsu Province of China (No. BK20161195), the Fundamental Research Funds for the Central Universities (2018B791X14), Open fund of State Key Laboratory of acoustics (No. SKLA201703), the Postgraduate Research & Practice Innovation Program of Jiangsu Province, under the Grant: SJCX18_0196, the National Natural Science Foundation of China under Grant No. 61572172 and No.