GNSS-声呐观测反演双指数温度剖面

doi:10.11947/j.AGCS.2025.20240065

测绘学报 ›› 2025, Vol. 54 ›› Issue (2): 286-296.doi: 10.11947/j.AGCS.2025.20240065

• 海洋测量 • 上一篇

GNSS-声呐观测反演双指数温度剖面

朱冀星¹(), 薛树强¹^,²(), 李保金¹^,³, 肖圳¹^,⁴, 王凯明¹

^1.中国测绘科学研究院北京房山人卫激光国家野外科学观测研究站，北京　100830
^2.地理信息工程国家重点实验室，陕西　西安　710054
^3.中国石油大学（华东），山东　青岛　257061
^4.山东大学空间科学与技术学院，山东　威海　264200

收稿日期:2024-02-12 发布日期:2025-03-11
通讯作者: 薛树强 E-mail:2211286162@qq.com;xuesq@casm.ac.cn
作者简介:朱冀星（2001—），男，硕士生，研究方向为海洋大地测量。　E-mail：2211286162@qq.com
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);地理信息工程国家重点实验室自主研发课题项目(SKLGIE2023-ZZ-8)

GNSS-acoustic inversion of double-exponential temperature profile

Jixing ZHU¹(), Shuqiang XUE¹^,²(), Baojin LI¹^,³, Zhen XIAO¹^,⁴, Kaiming WANG¹

^1.Beijing Fangshan Satellite Laser Ranging National Observation and Research Station, Chinese Academy of Surveying and Mapping, Beijing 100830, China
^2.State Key Laboratory of Geographic Information Engineering, Xi'an 710054, China
^3.China University of Petroleum (East China), Qingdao 257061, China
^4.School of Space Science and Technology, Shandong University, Weihai 264200, China

Received:2024-02-12 Published:2025-03-11
Contact: Shuqiang XUE E-mail:2211286162@qq.com;xuesq@casm.ac.cn
About author:ZHU Jixing (2001—), male, postgraduate, majors in marine geodesy.　E-mail: 2211286162@qq.com
Supported by:
The National Natural Science Foundation of China(41931076);The Scientific and Technology Innovation Program of Laoshan Laboratory(LSKJ202205100);Independent Research Project of State Key Laboratory of Geo-information Engineering(SKLGIE2023-ZZ-8)

摘要/Abstract

摘要：

GNSS-声呐定位技术需要现场声速剖面测量，观测成本高且在一定程度上限制了应用服务的实时性。为解决这一问题，本文提出了一种双指数温度剖面模型，构建了附加海洋环境先验信息约束的声速剖面反演模型。利用日本长期的GNSS-声呐观测数据集，验证了双指数温度剖面反演的优越性。结果表明，基于双指数模型反演声速的均方根误差（RMSE）为5.54 m/s，优于基于单指数模型反演声速的RMSE为6.92 m/s。且在浅层，基于双指数模型反演声速精度优势更为明显，10～300 m的浅层平均偏差、标准差（STD）和RMSE分别为1.76、6.36和6.59 m/s，而基于单指数模型的相关统计指标分别为2.03、7.94、8.19 m/s；在300～500 m的中间层，基于双指数模型反演声速的平均偏差、STD和RMSE分别为0.07、3.18和3.18 m/s，而基于单指数模型的相关统计指标分别为-2.76、3.75、4.65 m/s。此外，当采用本文反演的双指数剖面代替现场实测剖面进行海底基准定位时，水平方向上的误差均值和标准差分别优于0.2 mm和2 mm，垂向误差均值和标准差分别优于3 mm和2 cm。这表明所提出的双指数模型可以实现厘米级精度的定位精度，并显著提高声速剖面的反演精度。

关键词: GNSS-声呐, 声速剖面反演, 海底大地测量定位, 双指数模型

Abstract:

GNSS-acoustic (GNSS-A) positioning technique needs to conduct in-suit sound speed profile (SSP) measurements, leading to a high cost and limiting to real-time applicability of this technique. To tackle this issue, a SSP inversion model based on a single-exponential empirical temperature profile (SETP) has been developed just recently. This contribution was to propose a novel SSP inversion model based on a double-exponential temperature profile (DETP) to improve the inversion precision. In addition, the proposed inversion model was appended with a prior constraints constructed by the marine environment product. Using the Japanese long-term seafloor geodetic observations, the superior of the proposed inversion model was validated sufficiently. The SSP inversion precision was evaluated by the in-suit SSP. It showed that the root mean square error (RMSE) of the DETP-based SSP inversion result of the whole water layer was 5.54 m/s, better than 6.92 m/s of the SETP-based SSP model, particularly in shallow and middle water layers. For water columns not exceeding 300 m depth, the mean bias, standard deviation (STD), and RMSE of DETP-based SSP inversion were 1.76, 6.36, and 6.59 m/s, respectively; while those of SETP-based SSP inversion were 2.03, 7.94, and 8.19 m/s, respectively. For the water columns from 300 m to 500 m, the mean bias, STD, and RMSE of DETP-based SSP inversion were 0.07, 3.18, and 3.18 m/s, respectively; while those of SETP-based SSP inversion were -2.76, 3.75, and 4.65 m/s, respectively. Moreover, the seafloor geodetic positioning based on the proposed DETP was more accurate than that based on SETP. Specifically, the positioning mean bias and STD in the horizontal direction are better than 0.2 mm and 2 mm, respectively, while those in the vertical direction are better than 3 mm and 2 cm, respectively. These indicate that the proposed DETP-based SSP can achieve a centimeter-precision-level positioning precision and improves the SSP inversion precision, significantly.

Key words: GNSS-A, sound speed profile inversion, seafloor geodetic positioning, double-exponential model

中图分类号:

P229.2

朱冀星, 薛树强, 李保金, 肖圳, 王凯明. GNSS-声呐观测反演双指数温度剖面[J]. 测绘学报, 2025, 54(2): 286-296.

Jixing ZHU, Shuqiang XUE, Baojin LI, Zhen XIAO, Kaiming WANG. GNSS-acoustic inversion of double-exponential temperature profile[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(2): 286-296.

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参考文献 34

[1]	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.
[2]	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
[3]	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.
[4]	陈冠旭, 高柯夫, 赵建虎, 等. GNSS-声学位置服务中声速误差修正方法[J]. 测绘学报, 2023, 52(4): 536-549. DOI:. doi: 10.11947/j.AGCS.2023.20220097
	CHEN Guanxu, GAO Kefu, ZHAO Jianhu, et al. The method of sound speed errors correction in GNSS-acoustic location service[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(4): 536-549. DOI:. doi: 10.11947/j.AGCS.2023.20220097
[5]	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.
[6]	孙大军, 郑翠娥, 张居成, 等. 水声定位导航技术的发展与展望[J]. 中国科学院院刊, 2019, 34(3): 331-338.
	SUN Dajun, ZHENG Cuie, ZHANG Jucheng, et al. Development and prospect for underwater acoustic positioning and navigation technology[J]. Bulletin of Chinese Academy of Sciences, 2019, 34(3): 331-338.
[7]	齐珂, 曲国庆, 苏晓庆, 等. 水下声纳定位浮标阵列解析优化[J]. 武汉大学学报(信息科学版), 2019, 44(9): 1312-1319.
	QI Ke, QU Guoqing, SU Xiaoqing, et al. Analytical optimization on GNSS/sonar buoy array deployment for underwater positioning[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1312-1319.
[8]	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
[9]	王凯明, 薛树强, 李景森. 有效声速泰勒级数逼近的适用条件[J]. 海洋测绘, 2023, 43(5): 31-34.
	WANG Kaiming, XUE Shuqiang, LI Jingsen. Applicable conditions of Taylor series approximation formulae of effective sound velocity[J]. Hydrographic Surveying and Charting, 2023, 43(5): 31-34.
[10]	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
[11]	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
[12]	李伟嘉, 王振杰, 孙振, 等. 基于深度约束的超短基线声速改正方法[J]. 导航定位学报, 2022, 10(5): 40-45.
	LI Weijia, WANG Zhenjie, SUN Zhen, et al. An USBL sound velocity correction method based on depth constraint[J]. Journal of Navigation and Positioning, 2022, 10(5): 40-45.
[13]	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
[14]	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 Jingsen, 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.
[15]	薛树强, 杨诚, 赵爽, 等. 海底大地控制网无人观测系统研究进展[J/OL]. 导航定位学报. [2025-01-06]. http://dhdwxb.chinajournal.net.cn/WKC/WebPublication/paperDigest.aspx?paperID=4d65ba60-5961-4f8f-b596-4cb9350a02e3.
	XUE Shuqiang, YANG Cheng, ZHAO Shuang, et al. Review of unmanned observation systems for seafloor geodetic network[J/OL]. Journal of Navigation and Positioning. [2025-01-06]. http://dhdwxb.chinajournal.net.cn/WKC/WebPublication/paperDigest.aspx?paperID=4d65ba60-5961-4f8f-b596-4cb9350a02e3.
[16]	胡军. 基于RBF神经网络的声速剖面反演及软件实现[D]. 湘潭: 湘潭大学, 2018.
	HU Jun. Inversion of sound velocity profile based on RBF neural network and its software implementation[D]. Xiangtan: Xiangtan University, 2018.
[17]	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): 1197-1203.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): 1197-1203. DOI:. doi: 10.11947/j.AGCS.2019.20190157
[18]	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.
[19]	HAN Fuxing, SUN Jianguo, WANG Kun. The influence of sea water velocity variation on seismic traveltimes, ray paths, and amplitude[J]. Applied Geophysics, 2012, 9(3): 319-325.
[20]	黄威, 高凡, 王君婷, 等. 水下声速场构建方法综述[J]. 哈尔滨工程大学学报, 2023, 44(11): 2005-2017.
	HUANG Wei, GAO Fan, WANG Junting, et al. A review on the construction of underwater sound speed fields[J]. Journal of Harbin Engineering University, 2023, 44(11): 2005-2017.
[21]	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.
[22]	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.
[23]	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
[24]	MUNK W H. Sound channel in an exponentially stratified ocean, with application to SOFAR[J]. The Journal of the Acoustical Society of America, 1974, 55(2): 220-226.
[25]	DAVIS T M, COUNTRYMAN K A, CARRON M J. Tailored acoustic products utilizing the NAVOCEANO GDEM (a generalized digital environmental model)[C]//Proceedings of the 36th Naval Symposium on Underwater Acoustics. San Diego: Naval Ocean Systems Center, 1986.
[26]	TEAGUE W J, CARRON M J, HOGAN P J. A comparison between the generalized digital environmental model and levitus climatologies[J]. Journal of Geophysical Research: Oceans, 1990, 95(C5): 7167-7183.
[27]	张旭, 张永刚, 张健雪, 等. 一种新的声速剖面结构参数化方法[J]. 海洋学报, 2011, 33(5): 54-60.
	ZHANG Xu, ZHANG Yonggang, ZHANG Jianxue, et al. A new model for calculating sound speed profile structure[J]. Acta Oceanologica Sinica, 2011, 33(5): 54-60.
[28]	CHEN H H. Travel-time approximation of acoustic ranging in GPS/acoustic seafloor geodesy[J]. Ocean Engineering, 2014, 84: 133-144.
[29]	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.
[30]	DEL GROSSO V A. New equation for the speed of sound in natural waters (with comparisons to other equations)[J]. The Journal of the Acoustical Society of America, 1974, 56(4): 1084-1091.
[31]	吴碧, 陈长安, 林龙. 声速经验公式的适用范围分析[J]. 声学技术, 2014, 33(6): 504-507.
	WU Bi, CHEN Chang'an, LIN Long. Analysis of applicable scope of empirical equation for sound velocity[J]. Technical Acoustics, 2014, 33(6): 504-507.
[32]	LEROY C C, PARTHIOT F. Depth-pressure relationships in the oceans and seas[J]. The Journal of the Acoustical Society of America, 1998, 103(3): 1346-1352.
[33]	YOKOTA Y, ISHIKAWA T, WATANABE S I. Seafloor crustal deformation data along the subduction zones around Japan obtained by GNSS-A observations[J]. Scientific Data, 2018, 5: 180182.
[34]	李景森, 薛树强, 肖圳, 等. GNSS/声呐组合观测臂长改正不确定度评估[J/OL]. 武汉大学学报(信息科学版). [2025-01-06]. http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20220673.
	LI Jingsen, XUE Shuqiang, XIAO Zhen, et al. Uncertainty evaluation on the arm length correction of GNSS-A observation[J/OL]. Geomatics and Information Science of Wuhan Universiny.[2025-01-06]. http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20220673.

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参数	温度/（℃）	温度斜率
平均值	2.15	-8.09×10^-4
标准差	0.087 4	1.924 9×10^-4

MYGI站复测日期	平均值/（℃）	标准差/（℃）
2011-03-28	3.87	1.69
2011-04-11	8.35	1.16
2011-04-29	11.66	1.06
2011-08-29	24.70	0.22
2011-11-18	17.60	0.75
2012-01-12	8.60	0.45
2012-04-22	12.69	0.53
2012-09-03	25.30	1.20
2012-11-14	19.28	0.21
2012-12-12	15.90	0.36
2013-01-29	8.53	1.46
2013-06-30	17.55	0.90
2013-09-05	22.16	0.76
2013-11-08	17.73	0.80
2014-01-15	11.22	1.14
2014-08-07	24.37	0.31
2015-01-15	8.55	0.75
2015-04-22	14.56	0.86
2015-08-12	24.85	0.13
2015-10-18	19.40	0.86
2016-03-09	11.90	0.21
2016-06-05	19.42	0.27
2016-07-23	24.67	0.34
2016-10-17	20.07	0.41
2017-03-10	6.28	1.70
2017-04-22	11.06	0.65
2017-08-19	23.44	0.31
2018-01-11	11.21	2.11
2018-02-07	11.44	1.22
2018-08-21	24.69	0.70
2019-03-10	16.48	1.85
2019-06-01	12.47	1.64
2019-10-20	18.32	0.38
2020-02-05	11.11	1.15
2020-06-15	15.47	0.90

单指数模型参数	约束值	约束标准差
中间过渡量T_m/（℃）	2	100
温度差ΔT/（℃）	10	100
温跃层深度u₀/m	300	20
换能器深度温度	*	**
1 727.8 m处温度/（℃）	2.15	0.01
1 727.8 m处斜率	-8.09×10^-4	0.000 01

双指数模型参数	约束值	约束标准差
h₁	4.093 7	100
h₂	-0.000 4	100
h₃	13.649 8	100
h₄	-0.004 0	100
换能器深度温度	*	**
1 727.8 m处温度/（℃）	2.15	0.01
1 727.8 m处斜率	-8.09×10^-4	0.000 01

深度分层/m	单指数模型			双指数模型
深度分层/m	偏差均值/（m/s）	STD/（m/s）	RMSE/（m/s）	偏差均值/（m/s）	STD/（m/s）	RMSE/（m/s）
10~300	2.03	7.94	8.19	1.76	6.36	6.59
300~500	-2.76	3.75	4.65	0.07	3.18	3.18
500~1 727.8	-4.4×10^-3	2.39	2.39	0.08	1.83	1.83
10~1 727.8	1.11	6.83	6.92	1.21	5.40	5.54

GNSS-声呐观测反演双指数温度剖面

GNSS-acoustic inversion of double-exponential temperature profile

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指标	单指数模型			双指数模型
指标	E	N	U	E	N	U
偏差均值	-0.000 3	-1.2×10^-5	0.015	-0.000 1	-2.6×10^-6	0.002
标准差	0.002	0.002	0.014	0.001	0.001	0.017

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