海洋声速场水平梯度对海底大地测量定位的影响

doi:10.11947/j.AGCS.2024.20230551

测绘学报 ›› 2024, Vol. 53 ›› Issue (12): 2328-2337.doi: 10.11947/j.AGCS.2024.20230551

海洋声速场水平梯度对海底大地测量定位的影响

周杰¹^,²(), 薛树强¹^,³(), 肖圳⁴, 徐莹², 王凯明¹, 李景森¹

^1.中国测绘科学研究院，北京　100036
^2.山东科技大学测绘与空间信息学院，山东　青岛　266100
^3.地理信息工程国家重点实验室，陕西　西安　710054
^4.山东大学空间科学与物理学院，山东　威海　264200

收稿日期:2023-11-27 出版日期:2025-01-06 发布日期:2025-11-06
通讯作者: 薛树强 E-mail:202282020044@sdust.edu.cn;xuesq@casm.ac.cn
作者简介:第一周杰(2000—)，男，硕士，研究方向为海洋大地测量。E-mail：202282020044@sdust.edu.cn
基金资助:
国家自然科学基金(41931076);崂山实验室科技创新项目(LSKJ202205100);国家重点研发计划(2020YFB0505802);中国测绘科学研究院基本科研业务费项目(AR2313)

Impact of the horizontal gradient of sound speed on seafloor geodetic positioning

Jie ZHOU¹^,²(), Shuqiang XUE¹^,³(), Zhen XIAO⁴, Ying XU², Kaiming WANG¹, Jingsen LI¹

^1.Chinese Academy of Surveying and Mapping, Beijing 100036, China
^2.College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266100, China
^3.State Key Laboratory of Geographic Information Engineering, Xi'an 710054, China
^4.School of Space Science and Physics, Shandong University (Weihai), Weihai 264200, China

Received:2023-11-27 Online:2025-01-06 Published:2025-11-06
Contact: Shuqiang XUE E-mail:202282020044@sdust.edu.cn;xuesq@casm.ac.cn
About author:ZHOU Jie (2000—), male, master, majors in marine geodesy. E-mail: 202282020044@sdust.edu.cn
Supported by:
The National Natural Science Foundation of China(41931076);The Scientific and Technology Innovation Program of Laoshan Laboratory(LSKJ202205100);The National Key Research and Development Program of China(2020YFB0505802);The Basic Scientific Research Foundation of the Chinese Academy of Surveying and Mapping(AR2313)

摘要/Abstract

摘要：

复杂多变的海洋环境导致声速结构不仅存在明显的垂向分层特征，同时，受海洋暖流、内波等海洋物理过程影响使声速场存在显著的水平梯度。声速场水平梯度是影响水下高精度定位的重要因素。本文从三维声线跟踪定位模型出发探讨声速场水平梯度对水下定位的影响，给出了声速场平均梯度的定义及其反演模型，分析了声速场水平梯度反演精度的主要影响因素。研究结果表明，定位误差与水平梯度方向、海底应答器位置、海面控制网尺寸密切相关，当水平梯度的数量级达10^-5（m/s/m）时，可导致3000 m深海超过分米级定位误差；附加声速场水平梯度参数的海底定位模型可显著提高定位精度，其在平均意义下的水平梯度参数估计能够实现厘米级精度定位。

关键词: 水平梯度, 水下定位, 三维声线跟踪, 平均梯度, 定位误差, 参数反演

Abstract:

The complex and dynamic marine environment results in a sound speed structure characterized by distinct vertical stratification. Additionally, influenced by oceanographic processes such as warm currents and internal waves, the sound speed field exhibits significant horizontal gradients, which are critical factors affecting high-precision underwater positioning. In this paper, the impact of horizontal gradients in the sound speed field on underwater positioning is investigated based on a three-dimensional ray-tracing positioning model, and the definition of the average gradient of the sound speed field and its inversion model are presented. Then the main factors influencing the accuracy of horizontal gradient inversion are further analyzed. The results indicate that positioning errors are closely related to the direction of the horizontal gradient, the location of seafloor transponders, and the size of the surface trajectory network. When the magnitude of the horizontal gradient reaches 10^-5 (m/s/m), it can lead to positioning errors exceeding decimeter level in deep sea environments at depths of 3000 m. The seafloor positioning model considering the horizontal gradient parameters of the sound speed field can significantly enhance positioning accuracy. Moreover, the estimation of the horizontal gradient parameter in the average sense can achieve centimeter-level precision positioning.

Key words: horizontal gradient, underwater positioning, 3D acoustic ray tracing, average gradient, positioning error, parameter inversion

中图分类号:

P258

周杰, 薛树强, 肖圳, 徐莹, 王凯明, 李景森. 海洋声速场水平梯度对海底大地测量定位的影响[J]. 测绘学报, 2024, 53(12): 2328-2337.

Jie ZHOU, Shuqiang XUE, Zhen XIAO, Ying XU, Kaiming WANG, Jingsen LI. Impact of the horizontal gradient of sound speed on seafloor geodetic positioning[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(12): 2328-2337.

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参考文献 40

[1]	SPIESS F N, CHADWELL C D, HILDEBRAND J A, et al. Precise GPS/acoustic positioning of seafloor reference points for tectonic studies[J]. Physics of the Earth and Planetary Interiors, 1998, 108(2): 101-112.
[2]	YANG Yuanxi, QIN Xianping. Resilient observation models for seafloor geodetic positioning[J]. Journal of Geodesy, 2021, 95(7): 79.
[3]	杨元喜. 弹性PNT基本框架[J]. 测绘学报, 2018, 47(7): 893-898. DOI:. doi: 10.11947/j.AGCS.2018.20180149
	YANG Yuanxi. Resilient PNT concept frame[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(7): 893-898. DOI:. doi: 10.11947/j.AGCS.2018.20180149
[4]	陈冠旭, 刘杨, 李梦昊, 等. GNSS-声学海底定位的声速误差处理方法综述[J]. 武汉大学学报(信息科学版), 2022, 47(9): 1349-1363.
	CHEN Guanxu, LIU Yang, LI Menghao, et al. Review on the processing methods of sound speed errors in GNSS-acoustic seafloor positioning[J]. Geomatics and Information Science of Wuhan University, 2022, 47(9): 1349-1363.
[5]	党亚民, 蒋涛, 杨元喜, 等. 中国大地测量研究进展(2019—2023)[J]. 测绘学报, 2023, 52(9): 1419-1436. DOI:. doi: 10.11947/j.AGCS.2023.20230343
	DANG Yamin, JIANG Tao, YANG Yuanxi, et al. Research progress of geodesy in China(2019—2023)[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(9): 1419-1436. DOI:. doi: 10.11947/j.AGCS.2023.20230343
[6]	刘经南, 赵建虎, 马金叶. 通导遥一体化深远海PNT基准及服务网络构想[J]. 武汉大学学报(信息科学版), 2022, 47(10): 1523-1534.
	LIU Jingnan, ZHAO Jianhu, MA Jinye. Concept of constructing the underwater PNT network with the abilities of communication, navigation and remote sensing in the deep sea[J]. Geomatics and Information Science of Wuhan University, 2022, 47(10): 1523-1534.
[7]	杨元喜, 徐天河, 薛树强. 我国海洋大地测量基准与海洋导航技术研究进展与展望[J]. 测绘学报, 2017, 46(1): 1-8. DOI:. doi: 10.11947/j.AGCS.2017.20160519
	YANG Yuanxi, XU Tianhe, XUE Shuqiang. Progresses and prospects in developing marine geodetic datum and marine navigation of China[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(1): 1-8. DOI:. doi: 10.11947/j.AGCS.2017.20160519
[8]	杨元喜, 刘焱雄, 孙大军, 等. 海底大地基准网建设及其关键技术[J]. 中国科学：地球科学, 2020, 50(7): 936-945.
	YANG Yuanxi, LIU Yanxiong, SUN Dajun, et al. Seafloor geodetic network establishment and key technologies[J]. Scientia Sinica (Terrae), 2020, 50(7): 936-945.
[9]	刘焱雄, 李梦昊, 刘杨, 等. 海底大地基准建设技术及其研究进展[J]. 海洋科学进展, 2022, 40(4): 684-700.
	LIU Yanxiong, LI Menghao, LIU Yang, et al. Research progress of seafloor geodetic datum construction technology[J]. Advances in Marine Science, 2022, 40(4): 684-700.
[10]	赵建虎, 梁文彪. 海底控制网测量和解算中的几个关键问题[J]. 测绘学报, 2019, 48(9): 1197-1202. DOI:. doi: 10.11947/j.AGCS.2019.20190157
	ZHAO Jianhu, LIANG Wenbiao. Some key points of submarine control network measurement and calculation[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(9): 1197-1202. DOI:. doi: 10.11947/j.AGCS.2019.20190157
[11]	XUE Shuqiang, YANG Yuanxi, YANG Wenlong. Single-differenced models for GNSS-acoustic seafloor point positioning[J]. Journal of Geodesy, 2022, 96(5): 38.
[12]	赵爽, 王振杰, 聂志喜, 等. 顾及声速结构时域变化的海底基准站高精度定位方法[J]. 测绘学报, 2023, 52(1): 41-50. DOI:. doi: 10.11947/j.AGCS.2023.20210326
	ZHAO Shuang, WANG Zhenjie, NIE Zhixi, et al. Precise positioning method for seafloor geodetic stations based on the temporal variation of sound speed structure[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(1): 41-50. DOI:. doi: 10.11947/j.AGCS.2023.20210326
[13]	张盛秋, 杨元喜, 徐天河. 基于GNSS-A的海洋声速变化估计及其对定位的影响[J]. 地球物理学报, 2023, 66(3): 961-972.
	ZHANG Shengqiu, YANG Yuanxi, XU Tianhe. Estimation of ocean sound velocity variation based on GNSS-A and its influence on positioning[J]. Chinese Journal of Geophysics, 2023, 66(3): 961-972.
[14]	CHADWELL C D, SWEENEY A D. Acoustic ray-trace equations for seafloor geodesy[J]. Marine Geodesy, 2010, 33(2/3): 164-186.
[15]	辛明真, 阳凡林, 薛树强, 等. 顾及波束入射角的常梯度声线跟踪水下定位算法[J]. 测绘学报, 2020, 49(12): 1535-1542. DOI:. doi: 10.11947/j.AGCS.2020.20190518
	XIN Mingzhen, YANG Fanlin, XUE Shuqiang, et al. A constant gradient sound ray tracing underwater positioning algorithm considering incident beam angle[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(12): 1535-1542. DOI:. doi: 10.11947/j.AGCS.2020.20190518
[16]	YANG Wenlong, XUE Shuqiang, LIU Yixu. P-order secant method for rapidly solving the ray inverse problem of underwater acoustic positioning[J]. Marine Geodesy, 2023, 46(1): 3-15.
[17]	赵爽, 王振杰, 刘慧敏. 顾及声线入射角的水下定位随机模型[J]. 测绘学报, 2018, 47(9): 1280-1289. DOI:. doi: 10.11947/j.AGCS.2018.20170026
	ZHAO Shuang, WANG Zhenjie, LIU Huimin. Investigation on underwater positioning stochastic model based on sound ray incidence angle[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(9): 1280-1289. DOI:. doi: 10.11947/j.AGCS.2018.20170026
[18]	LIU Yixu, XUE Shuqiang, QU Guoqing, et al. Influence of the ray elevation angle on seafloor positioning precision in the context of acoustic ray tracing algorithm[J]. Applied Ocean Research, 2020, 105: 102403.
[19]	王薪普, 薛树强, 曲国庆, 等. 水下定位声线扰动分析与分段指数权函数设计[J]. 测绘学报, 2021, 50(7): 982-989. DOI:. doi: 10.11947/j.AGCS.2021.20200424
	WANG Xinpu, XUE Shuqiang, QU Guoqing, et al. Disturbance analysis of underwater positioning acoustic ray and design of piecewise exponential weight function[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(7): 982-989. DOI:. doi: 10.11947/j.AGCS.2021.20200424
[20]	闫凤池, 王振杰, 赵爽, 等. 顾及双程声径的常梯度声线跟踪水下定位算法[J]. 测绘学报, 2022, 51(1): 31-40. DOI:. doi: 10.11947/j.AGCS.2022.20210234
	YAN Fengchi, WANG Zhenjie, ZHAO Shuang, et al. A layered constant gradient acoustic ray tracing underwater positioning algorithm considering round-trip acoustic path[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(1): 31-40. DOI:. doi: 10.11947/j.AGCS.2022.20210234
[21]	LIU Yang, LIU Yanxiong, CHEN Guanxu, et al. Seafloor single point positioning using GNSS-acoustic technique with horizontal sound speed gradient estimation[C]//Proceedings of 2021 Scientific Assembly of the International Association of Geodesy. Beijing: [s.n.], 2021.
[22]	王凯明, 薛树强, 韩保民, 等. 海洋内波对海底精密定位的影响[J]. 哈尔滨工程大学学报, 2023, 44(11): 2054-2061.
	WANG Kaiming, XUE Shuqiang, HAN Baomin, et al. Effect of ocean internal waves on high-precision seafloor geodetic positioning[J]. Journal of Harbin Engineering University, 2023, 44(11): 2054-2061.
[23]	TOMITA F, KIDO M. An approximate travel time calculation and a robust GNSS-acoustic positioning method using an MCMC technique[J]. Earth, Planets and Space, 2022, 74(1): 176.
[24]	SAKIC P, BALLU V, CRAWFORD W C, et al. Acoustic ray tracing comparisons in the context of geodetic precise off-shore positioning experiments[J]. Marine Geodesy, 2018, 41(4): 315-330.
[25]	李林洋, 徐天河, 王君婷, 等. 联合匹配场和神经网络的声速时间场构建方法[J]. 哈尔滨工程大学学报, 2023, 44(11): 2044-2053.
	LI Linyang, XU Tianhe, WANG Junting, et al. A method for constructing a sound velocity time field by combining a matched field and neural network[J]. Journal of Harbin Engineering University, 2023, 44(11): 2044-2053.
[26]	曾安敏, 杨元喜, 明锋, 等. 海底大地基准点圆走航模式定位模型及分析[J]. 测绘学报, 2021, 50(7): 939-952. DOI:. doi: 10.11947/j.AGCS.2021.20200529
	ZENG Anmin, YANG Yuanxi, MING Feng, et al. Positioning model and analysis of the sailing circle mode of seafloor geodetic datum points[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(7): 939-952. DOI:. doi: 10.11947/j.AGCS.2021.20200529
[27]	李景森, 薛树强, 徐莹, 等. 声速剖面测量误差对水下定位的影响[J]. 哈尔滨工程大学学报, 2023, 44(11): 2062-2070.
	LI Jingshen, XUE Shuqiang, XU Ying, et al. Effects of sound speed profile measurement error on underwater positioning[J]. Journal of Harbin Engineering University, 2023, 44(11): 2062-2070.
[28]	薛树强, 杨元喜, 肖圳, 等. 全球导航卫星系统-声呐组合观测模型分类体系[J]. 哈尔滨工程大学学报, 2023, 44(11): 1857-1868.
	XUE Shuqiang, YANG Yuanxi, XIAO Zhen, et al. Global navigation satellite system-acoustic combined observation model classification system[J]. Journal of Harbin Engineering University, 2023, 44(11): 1857-1868.
[29]	KIDO M. Detecting horizontal gradient of sound speed in ocean[J]. Earth, Planets and Space, 2007, 59(8): e33-e36.
[30]	YASUDA K, TADOKORO K, TANIGUCHI S, et al. Interplate locking condition derived from seafloor geodetic observation in the shallowest subduction segment at the Central Nankai Trough, Japan[J]. Geophysical Research Lellers, 2017, 44(8): 3572-3579.
[31]	HONSHO C, KIDO M. Comprehensive analysis of travel time data collected through GPS-acoustic observation of seafloor crustal movements[J]. Journal of Geophysical Research: Solid Earth, 2017, 122(10): 8583-8599.
[32]	YOKOTA Y, ISHIKAWA T, WATANABE S I. Gradient field of undersea sound speed structure extracted from the GNSS-a oceanography[J]. Marine Geophysical Research, 2019, 40(4): 493-504.
[33]	YOKOTA Y, ISHIKAWA T, WATANABE S I, et al. Kilometer-scale sound speed structure that affects GNSS-a observation: case study off the kii channel[J]. Frontiers in Earth Science, 2020, 8: 331.
[34]	WATANABE S I, ISHIKAWA T, YOKOTA Y, et al. GARPOS: analysis software for the GNSS-a seafloor positioning with simultaneous estimation of sound speed structure[J]. Frontiers in Earth Science, 2020, 8: 508.
[35]	WATANABE S I, ISHIKAWA T, NAKAMURA Y, et al. Full-bayes GNSS-A solutions for precise seafloor positioning with single uniform sound speed gradient layer assumption[J]. Journal of Geodesy, 2023, 97(10): 89.
[36]	TOMITA F, KIDO M, HONSHO C, et al. Development of a kinematic GNSS-Acoustic positioning method based on a state-space model[J]. Earth, Planets and Space, 2019, 71: 102.
[37]	明锋, 杨元喜, 曾安敏. 基于贝叶斯估计的深海GNSS-A定位精度[J]. 地球物理学报, 2023, 66(3): 951-960.
	MING Feng, YANG Yuanxi, ZENG Anmin. Positioning accuracy of GNSS-A in deep sea based on Bayesian estimation[J]. Chinese Journal of Geophysics, 2023, 66(3): 951-960.
[38]	XUE Shuqiang, YANG Yuanxi, YANG Wenlong, et al. GNSS-A network solution with zenith acoustic delay estimation[J]. Marine Geodesy, 2021, 47(3): 237-268.
[39]	XUE Shuqiang, LI Baojin, XIAO Zhen, et al. Centimeter-level-precision seafloor geodetic positioning model with self-structured empirical sound speed profile[J]. Satellite Navigation, 2023, 4(1): 30.
[40]	肖圳, 薛树强, 韩保民, 等. 参考声速剖面误差对主动式声呐定位影响仿真分析[J]. 地球物理学报, 2023, 66(12): 4889-4899.
	XIAO Zhen, XUE Shuqiang, HAN Baomin, et al. Simulation analysis on reference sound velocity profile error influence on active acoustic positioning[J]. Chinese Journal of Geophysics, 2023, 66(12): 4889-4899.

参数种类	参数配置
海面网半径/m
海底控制网半径/m	1500
海底点深度/m	3000
观测时长/min	80
观测历元	1200
水平格网间隔/m	200
垂直格网间隔/m	100
参考声速剖面间隔/m	100
水平梯度方向	N方向
其他误差	无

海底点	坐标真值			解算策略	定位误差
海底点	E	N	U	解算策略	ΔE	ΔN	ΔU
M01	0	0	-3000	Model1	-0.001 0	0.217 5	-0.000 5
				Model2	-0.001 6	-0.001 1	0.003 3
				Model3	0.000 5	0.008 6	-0.000 2
M02	1 060.660 2	1 060.660 2	-3000	Model1	-0.012 7	0.210 2	0.063 5
				Model2	-0.005 1	-0.002 7	0.001 6
				Model3	0.012 1	0.022 7	-0.037 3
M03	-1 060.660 2	-1 060.660 2	-3000	Model1	-0.012 8	0.211 2	-0.064 0
				Model2	0.000 2	0.001 9	0.004 9
				Model3	0.012 1	0.022 7	0.037 0
M04	1 060.660 2	-1 060.660 2	-3000	Model1	0.011 0	0.210 0	-0.064 3
				Model2	-0.005 1	0.001 1	0.003 7
				Model3	-0.011 1	0.022 9	0.038 2
M05	-1 060.660 2	1 060.660 2	-3000	Model1	0.010 4	0.211 0	0.064 2
				Model2	-0.000 1	0.006 0	0.002 6
				Model3	-0.011 6	0.022 6	-0.038 5

方向	仿真平均梯度	模型3估计
E方向	0	-2.481 1×10^-7
N方向	2.15×10^-5	3.230 2×10^-5

海底点	Model1定位误差			Model3定位误差
海底点	ΔE	ΔN	ΔU	ΔE	ΔN	ΔU
M01	-0.034 4	0.089 1	0.267 2	0.001 7	0.007 5	-0.004 4
M02	-0.131 5	-0.004 5	0.256 3	0.002 2	0.013 1	-0.010 8
M03	0.055 1	0.188 4	0.228 2	0.004 3	0.008 1	0.001 6
M04	-0.121 2	0.179 9	0.215 8	0.008 8	0.004 8	0.003 1
M05	0.061 0	-0.003 2	0.274 3	-0.006 5	0.013 6	-0.007 0

参数名称	参数设置
B样条阶数	3
B样条节点间隔	k_t：15 min
B样条节点间隔	k_e、k_n：15、15 min
B样条平滑因子	k_t：1
B样条平滑因子	k_e、k_n：1、1

海洋声速场水平梯度对海底大地测量定位的影响

Impact of the horizontal gradient of sound speed on seafloor geodetic positioning

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模型		STD		最大偏差
模型	ΔE	ΔN	ΔU	ΔE	ΔN	ΔU
Model1	0.129 8	0.186 8	0.251 3	0.162 5	0.611 1	0.622 5
Model3-1	0.060 6	0.084 5	0.137 7	0.067 1	0.285 6	0.343 2
Model3-2	0.058 4	0.039 4	0.012 7	0.128 8	0.112 8	0.023 0
GARPOS	0.019 1	0.023 5	0.014 8	0.053 2	0.045 5	0.028 1

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[3]	张继贤, 顾海燕, 杨懿, 张鹤, 李海涛, 韩文立, 沈晶. 自然资源要素智能解译研究进展与方向[J]. 测绘学报, 2022, 51(7): 1606-1617.
[4]	王薪普, 薛树强, 曲国庆, 刘以旭, 杨文龙. 水下定位声线扰动分析与分段指数权函数设计[J]. 测绘学报, 2021, 50(7): 982-989.
[5]	王乐洋, 高华, 冯光财. 利用InSAR和GPS数据分析台湾西南两次M_w>6地震的触发关系及应力影响[J]. 测绘学报, 2019, 48(10): 1244-1253.
[6]	赵爽, 王振杰, 刘慧敏. 顾及声线入射角的水下定位随机模型[J]. 测绘学报, 2018, 47(9): 1280-1289.
[7]	王虎彪,王勇,许大欣戴全发. 重力垂直梯度导航值特征分布与可导航性分析[J]. 测绘学报, 2010, 39(4): 0-440.