An improved method for computing acoustic ray incident angle based on secant method

Abstract

Constant gradient acoustic ray tracking is usually used in high-precision underwater acoustic positioning. However, it needs to calculate the incident angle of the acoustic ray, and the traditional incident angle computation method is very inefficient. To resolve this problem, we propose an improved acoustic ray incident angle iterative computation method. It firstly constructs the mathematical model for incident angle by using the function between horizontal propagation distance and incident angle based on secant method. The initial value of the incident angle is then determined by the incident angle calculated from the previous epoch and the last iteration. Meanwhile, the root-containing interval of the incident angle is reduced according to experimental parameters and coordinate correction values. Finally, the incident angle calculated in the last iteration is directly used for acoustic ray tracking and positioning solution until the end, when the coordinate correction values reach a threshold. Experiment conducted on the simulation cases demonstrates that the positioning calculation time of the proposed method is 77.7%, 77.1% and 88.1% lower than traditional methods in order of the dichotomy, secant method, and Newton method, respectively. As for the real experiment of the South China Sea, the computation efficiency improvement of the proposed method is about 62.9%, 67.6% and 66.1% compared with the dichotomy, secant method, and Newton method respectively. These results suggest that the proposed method can significantly improve the positioning calculation efficiency without loss of positioning accuracy compared with conventional methods.