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.

图/表 11

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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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