﻿ 一种基于同心双曲线相交的多波束测深归位算法
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 哈尔滨工程大学学报  2020, Vol. 41 Issue (6): 922-928  DOI: 10.11990/jheu.201903020 0

### 引用本文

WU Dongqiang, BU Xianhai, XU Fangzheng, et al. Multi-beam footprint reduction algorithm in an echo sounder system based on the intersection of co-concentric hyperbolas[J]. Journal of Harbin Engineering University, 2020, 41(6): 922-928. DOI: 10.11990/jheu.201903020.

### 文章历史

1. 山东科技大学 测绘科学与工程学院, 山东 青岛 266590;
2. 自然资源部海岛(礁)测绘技术重点实验室, 山东 青岛 266590

Multi-beam footprint reduction algorithm in an echo sounder system based on the intersection of co-concentric hyperbolas
WU Dongqiang 1, BU Xianhai 1, XU Fangzheng 1, FENG Chengkai 1, YANG Fanlin 1,2
1. College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China;
2. Key Laboratory of Surveying and Mapping Technology on Island and Reef, Ministry of Natural Resources, Qingdao 266590, China
Abstract: Existing multi-beam footprint reduction algorithms mostly ignore the changes in attitude and heading during the round trip of a beam, and some models are relatively complex, which bring errors into the final results. To solve these problems, in this paper, a new algorithm based on the intersection of co-concentric hyperbolas, in which the transmitted beam energy and received beam energy are abstracted as two regular cones that share the same vertex, is proposed. Thus, the footprints of wave beams are products of the intersecting hyperbolas, which are formed by the projection of two cones on the seabed. Finally, by solving the equations of the intersecting hyperbolas, the coordinates of the footprints are acquired. To verify the effectiveness of the proposed method, data from shallow water and mid-deep water are processed by the conventional algorithm, virtual concentric array algorithm, and proposed algorithm. Moreover, by comparing the results and depth discrepancy of overlapping regions, the proposed algorithm was found to be consistent with the results of the virtual concentric array algorithm, and they have the same level of accuracy. The proposed algorithm is also more accurate than the conventional algorithm and has a significant effect on improving the accuracy of multi-beam data processing.
Keywords: multi-beam echo sounder system    footprint reduction    footprints    transducer orientation    cones    co-concentric    hyperbolas    virtual intersection

1 同心双曲线相交模型构建 1.1 相关坐标系定义

1.2 双曲线相交归位原理

 Download: 图 1 平面与圆锥面相交得到不同的圆曲线 Fig. 1 Different curves formed with different planes intersecting the cone
2 同心双曲线相交模型的波束向量计算

 Download: 图 2 本文算法中波束脚印表示方式 Fig. 2 Description of footprints formed by the intersection of two hyperbolas in this paper

 ${\left\{ {\begin{array}{*{20}{l}} {{x_t} = {a_t}\cosh {t_1}}\\ {{y_t} = {b_t}\sinh {t_1}} \end{array}} \right.}$ (1)
 ${\left\{ {\begin{array}{*{20}{l}} {{x_r} = {a_r}\cosh {t_2}}\\ {{y_r} = {b_r}\sinh {t_2}} \end{array}} \right.}$ (2)

 $\left\{\begin{array}{l} a_{t}=\tan T_{\text {steer }} \\ b_{t}=1 \\ a_{r}=\tan R_{\text {steer }} \\ b_{r}=1 \end{array}\right.$ (3)

 $\delta=\arccos \left(\boldsymbol{T}_{x} \cdot \boldsymbol{R}_{x}\right)-\frac{\pi}{2}$ (4)

 $\left\{\begin{array}{l} x_{t}=a_{t} \cosh t_{1} \\ y_{t}=b_{t} \sinh t_{1} \\ x_{r}=b_{r} \cos \delta \sinh t_{2}-a_{r} \sin \delta \cosh t_{2} \\ y_{r}=b_{r} \sin \delta \sinh t_{2}+a_{r} \cos \delta \cosh t_{2} \end{array}\right.$ (5)

 $\left\{\begin{array}{l} \theta_{1}=\arctan \left(\sqrt{\left(x_{L}^{2}+y_{L}^{2}\right)} / z_{L}\right) \\ \theta_{2}=\arctan \left(x_{L} / y_{L}\right) \end{array}\right.$ (6)

3 实验与分析

3.1 浅水数据实验分析

 Download: 图 4 MB-system处理后得到的浅水区光照地形图 Fig. 4 Sun illuminate, depth colored grid of the shallow water data processed by MB-system

 Download: 图 5 浅水数据水深偏差统计 Fig. 5 Statistics of the depth deviations with shallow water data

3.2 深水数据实验分析

 Download: 图 6 MB-system处理后得到的深水区光照地形图 Fig. 6 Sun illuminate, depth colored grid of the deep water data processed by MB-system

 Download: 图 7 深水数据水深偏差统计 Fig. 7 Statistics of the depth deviations with deep water data

4 结论

1) 多波束测深波束往返期间发射换能器的姿态变化产生的影响在浅水区相对较小，因此，常规模型只适用于浅水区；当测区水深增加时，该影响产生的误差逐渐增大，使用常规模型易导致测深点位置整体出现偏差且水深误差易超出1%的测深精度要求。

2) 本文基于VCCA算法，提出一种同心双曲线相交的波束归位算法，将波束脚印作为发射圆锥面和接收圆锥面与交点平面投影形成的两双曲线交点，并推导了双曲线参数定义与解算方法，从而将VCCA算法中复杂的波束向量推导过程转化为求解相交双曲线方程的形式，模型更加直观且易于理解。

3) 使用实测数据对本文算法进行验证，结果表明，常规波束归位算法由于忽略波束往返期间换能器的姿态变化，使得数据处理结果存在误差，且随着水深的逐渐增加误差也逐渐增大，因此常规算法仅适用于处理浅水多波束测量数据；本文算法对浅水与深水多波束数据的计算结果与VCCA算法数据处理结果基本一致，计算结果满足1%的水深测量精度要求，因此本文算法具有有效性，对后续多波束数据处理研究具有很好的参考性。

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