引用本文: 孙文舟, 殷晓冬, 曾安敏, 刘强. 海底控制点定位初始入射角迭代计算方法的比较研究[J]. 武汉大学学报 ( 信息科学版), 2020, 45(10): 1588-1593.
SUN Wenzhou, YIN Xiaodong, ZENG Anmin, LIU Qiang. Calculating the Starting Incidence Angle by Iterative Method for Positioning Seafloor Control Points[J]. Geomatics and Information Science of Wuhan University, 2020, 45(10): 1588-1593.
 Citation: SUN Wenzhou, YIN Xiaodong, ZENG Anmin, LIU Qiang. Calculating the Starting Incidence Angle by Iterative Method for Positioning Seafloor Control Points[J]. Geomatics and Information Science of Wuhan University, 2020, 45(10): 1588-1593.

## Calculating the Starting Incidence Angle by Iterative Method for Positioning Seafloor Control Points

• 摘要: 针对传统方法迭代计算初始入射角存在测距误差随入射角增加而发散和大入射角条件下迭代不收敛的问题, 提出了一种利用牛顿法迭代计算初始入射角的方法。首先介绍了传统算法的原理和步骤; 其次根据传播时间和初始入射角的函数关系建立了迭代方程; 最后通过深海和浅海两组仿真实验对两种方法的优劣进行了对比分析。结果表明, 当初始入射角小于78°时, 传统方法的计算效率高于所提方法; 除此之外, 当初始入射角大于60°时, 传统方法计算的测距误差开始发散, 而且在浅海仿真实验中, 当初始入射角大于85°时, 传统方法还出现了迭代不收敛的问题, 而所提方法在任何角度下均可收敛于真值。

Abstract: Focuses on the problem of ranging error diverges with the increase of the starting incidence angle and non-convergence of iteration process at the large incidence angle by using the traditional method to calculate the starting incidence angle, this paper proposes a new method of calculating the starting incidenceangle by Newton method. Firstly, the principle and steps of traditional method are introduced. Secondly, the iteration equation is established according to the relationship between the propagation time and the starting incidence angle. Finally, the two methods are compared by two simulation experiments in deepsea and shallow sea. The results show that the computational efficiency of the traditional method is higher than our proposed method when the starting incidence angle is less than 78°. In addition, it is found out that when the starting incidence angle is greater than 60°, the ranging error calculated by the traditional method begins to diverge. In the shallow water simulation experiment, the traditional method also has the problem of non-convergence in the iteration process when the starting incidence angle is greater than 85°. In contrast, our proposed method can converge to the real value at any starting incidence angle.

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