﻿ 一种线面组合的水下地形匹配算法
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A Line-surface Integrated Algorithm for Underwater Terrain Matching
ZHANG Lihua , LIU Xianpeng , JIA Shuaidong , SHI Yan
Department of Military Oceanography and Hydrography, Dalian Naval Academy, Dalian 116018, China
Foundation support: The National Natural Science Foundation of China (Nos. 41471380; 41601498; 41774014)
First author: ZHANG Lihua(1973—), male, PhD, professor, majors in marine GIS. E-mail:zlhua@163.com
Corresponding author: LIU Xianpeng, E-mail: ouc_lxp@163.com
Abstract: The current underwater terrain surface matching algorithm, which uses Hu moment as similarity index, cannot gain fairly precious location due to its disadvantage in detecting slight difference.To solve this problem, a line-surface integrated terrain matching algorithm is presented.Firstly, the similarity evaluation method of traditional terrain contour matching (TERCOM) algorithm is improved, and strategy used to select the matching regions is developed.Then, a surface matching algorithm based on geometric similarity is established to find the optimum matching of real terrain.Finally, an integration means of the "line matching algorithm" and "surface matching algorithm" based on fixed threshold is proposed.Experimental results show that the proposed algorithm can obtain much higher location precision and better robustness than the surface underwater matching algorithm based on Hu moment.
Key words: terrain matching     integrated matching     surface matching algorithm     multi-beam bathymetric system

1 线面组合水下地形匹配算法 1.1 算法的基本思路

 图 1 算法的基本思路示意 Fig. 1 Schematic diagram of the algorithm

1.2 线匹配算法

1.2.1 相似性度量方法

(1)

(2)

(3)
(4)

1.2.2 匹配区的搜索策略

 图 2 匹配搜索区示意图 Fig. 2 Schematic diagram of the searching area

(1) 在搜索过程中，对P1P2的每个平移变换位置进行旋转变换。

(2) 在第i次平移变换中，选取与实测水深相似性最高的待匹配水深序列，将该水深序列对应的水平位置线段Pi, 1Pi, 2与线段P1P2的夹角作为航向修正角ωi

(3) 计算前n次平移变换中，各航向修正角的均值为ωn，若第n+1次航向修正角ωn+1满足|ωn+1ωn| < (1－k)ωn，且线段Pi, 1Pi, 2重心与线段P1P2重心的水平距离σn+1小于INS误差限σ，则认为匹配成功，停止搜索；若不满足，则继续搜索直至满足，或者完成对整个匹配区的搜索。其中，k表示匹配搜索的置信度阈值，为了提高定位精度本文取k为99%。

1.2.3 匹配结果的检验

1.3 面匹配算法

1.3.1 待匹配地形的选取

 图 3 待匹配地形面的选取示意图 Fig. 3 Schematic diagram of the selection of terrain

1.3.2 面匹配算子

 图 4 WSS算子的原理示意图 Fig. 4 Schematic diagram of the principle of the algorithm WSS

(5)

(6)

1.4 线面匹配算法的组合策略

(7)
(8)

2 试验与分析

 图 5 试验区海底三维示意图 Fig. 5 3D chart of the experimental sea bed

2.1 定位精度分析

 图 6 一号海区中两种算法的定位精度对比 Fig. 6 Precision comparison of two algorithm in experimental area 1

 图 7 二号海区中两种算法的精度对比 Fig. 7 Precision comparison of two algorithms in experimental area 2

 图 8 具有代表性的10组试验平均定位精度 Fig. 8 Mean location precision of 10 typical experiments

 图 9 两种算法定位精度的核密度分布对比 Fig. 9 Mean location precision of 10 typical experiments

 m 统计参数 匹配算法 Hu距算法 本文算法 中位数 31.93 18.06 平均值 89.03 24.45 标准差 122.97 40.88 上四分位数 16.36 9.48 下四分位数 79.01 28.29

2.2 稳健性分析

2.2.1 地形稳健性分析

 m 试验区编号 一号海区 二号海区 地形标准差 Hu矩 本文算法 地形标准差 Hu矩 本文算法 1 2.22 84.13 13.51 0.6 168.83 11.83 2 1.19 17.27 8.85 0.89 45.86 16.09 3 0.68 46.57 9.54 1.04 29.23 16.05 4 1.38 77.77 7.91 1.08 159.01 6.81 5 2.81 30.52 29.67 1.21 37.68 26.99 6 2.54 104.89 38.11 1.27 174.63 11.09 7 2.55 16.95 10.26 1.38 119.99 9.44 8 1.86 64.93 17.33 1.66 14.03 12.71 9 1.99 151.71 11.3 1.72 183.72 19.49 10 2.52 130.38 98.0 2.94 51.96 14.25

2.2.2 抗旋转稳健性分析

 图 10 定位精度随航向误差变化的箱形图 Fig. 10 Box chart of location precision along with INS course error

3 结论

(1) 在相同的INS和水深测量误差条件下，相比基于Hu矩的水下地形匹配定位算法，本文所提线面组合的匹配定位算法具有更高的定位精度和可靠性。

(2) 本文所提组合算法首先以线匹配算法对航向误差进行初步校正，然后以面匹配算法对UV进行精确定位，使组合算法具有更好的地形稳健性和抗旋转稳健性。

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http://dx.doi.org/10.11947/j.AGCS.2018.20170673

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#### 文章信息

ZHANG Lihua, LIU Xianpeng, JIA Shuaidong, SHI Yan

A Line-surface Integrated Algorithm for Underwater Terrain Matching

Acta Geodaetica et Cartographica Sinica, 2018, 47(10): 1406-1414
http://dx.doi.org/10.11947/j.AGCS.2018.20170673