Ultra-fast calculation method of incident angle based on underwater acoustic round-trip positioning

In underwater acoustic round-trip positioning, the incident angle calculation in constant gradient acoustic ray tracing significantly hinders the efficiency of positioning calculation. To address this issue, we proposed an ultrafast calculation method for determining incident angle based on underwater acoustic round-trip positioning. Specifically, the method employs the k -mean++ clustering algorithm to streamline the sound velocity profile. Additionally, a function formula for the incident angle is constructed, and its partial derivative with respect to Snell's constant is derived. Finally, Newton's method is applied to iteratively calculate the incident angles of the signal emission and reception, respectively. The simulation test results demonstrate that the proposed method reduces the positioning calculation time by 80.123%, 80.105%, 80.136%, and 80.104% on four transponders compared to the traditional method. In the field experiment, the proposed method is superior to the traditional method by 81.693% in positioning calculation time. These findings indicate the significant superiority of the proposed method in positioning calculation efficiency compared to the traditional method.