Objectives Acoustic ray-tracing method is an important means to solve the problem of acoustic ray bending in the process of propagation. This method calculates the slant range in deep-water positioning and can effectively minimize errors from the acoustic ranging system. However, the accompanying problem causes the reduction of computational efficiency. To solve this problem, this paper proposes a self-adaptive layering method based on the area difference of sound velocity profile (SVP), which reduces the computational cost by optimizing the layering strategy of SVP.

Methods First, the relationship between the SVP area difference and ranging error is established according to the corresponding research. Based on this relationship, the constant-gradient and the zero-gradient ray-tracing method are analyzed, which is more suitable for slant range calculation. And the maximum tolerance of SVP area difference is obtained by setting the maximum tolerance of ranging error. Then, the structural layering is carried out according to the change law of sound velocity gradient, and the refined layering is carried out on constraint of the maximum tolerance of SVP area difference.

Results The results show that the measured SVP in the same sea area and during a similar time can be considered as the same cluster SVP, which satisfies the inear relationship between SVP area and propagation time. The average value of multiple measured SVPs can be approximately considered as the background SVP to estimate the linear coefficient. The adaptive layering method can optimize the layering scheme according to the changing law of SVP curve. The layering interval increases when the gradient change rate is small, and reduces when the gradient change rate is large, so as to reduce the number of layers as much as possible under the condition of meeting the maximum tolerance ranging error. Compared with equally spaced layering of 10 m, when the number of layering is reduced by 86%, the ranging error caused by layering reduces from centimeter level to millimeter level, which proves the effectiveness of the proposed method.

Conclusions The adaptive method has strong robustness and practicability. It can adjust the layering strategy according to the structural characteristics of SVP and the usage scenarios of offshore operation. Since the number of SVP layers is greatly reduced, the calculation speed is greatly improved. It will be helpful for large amount of data process or real-time underwater acoustic navigation.