水下基准定位时变声速误差修正方法

doi:10.11947/j.AGCS.2025.20240459

测绘学报 ›› 2025, Vol. 54 ›› Issue (8): 1452-1463.doi: 10.11947/j.AGCS.2025.20240459

水下基准定位时变声速误差修正方法

赵一杰(), 王君婷(), 徐天河, 舒建旭, 刘杨范

山东大学空间科学与技术学院，山东　威海　264209

收稿日期:2024-11-18 修回日期:2025-07-07 出版日期:2025-09-16 发布日期:2025-09-16
通讯作者: 王君婷 E-mail:zhaoyjnice@163.com;wjtsci2015@163.com
作者简介:赵一杰（2001—），男，硕士生，研究方向为水下声学定位和多传感器组合导航。E-mail：zhaoyjnice@163.com
基金资助:
国家重点研发计划(2024YFB3909701);国家自然科学基金(42304011);山东省自然科学基金(ZR2023QD163);青岛市自然科学基金(23-2-1-65-zyyd-jch);空间基准全国重点实验室开放基金(SKLSD2025-KF-05);自然资源部海洋测绘重点实验室(2024B08);山东省博士后创新项目(SDCX-ZG-202501009);“国家资助博士后研究人员计划”和“中国博士后科学基金”资助(GZC20250169)

Correction method for time-varying sound speed errors in underwater geodetic datum positioning

Yijie ZHAO(), Junting WANG(), Tianhe XU, Jianxu SHU, Yangfan LIU

School of Space Science and Technology, Shandong University, Weihai 264209, China

Received:2024-11-18 Revised:2025-07-07 Online:2025-09-16 Published:2025-09-16
Contact: Junting WANG E-mail:zhaoyjnice@163.com;wjtsci2015@163.com
About author:ZHAO Yijie (2001—), male, postgraduate, majors in underwater acoustic positioning and multi-sensor integrated navigation. E-mail: zhaoyjnice@163.com

摘要/Abstract

摘要：

海洋声速时空变化是水下声学导航定位中重要的误差来源。针对水下声速时变误差会严重影响水下基准定位精度的问题，本文提出了基于时变声速误差修正的水下基准标定方法，该方法首先利用基于经验正交函数的部分声速剖面匹配扩展方法将实测声速剖面延拓至海底基准布设深度；然后利用实测声速剖面数据构建基于最小二乘支持向量机的水下时分辨率声速预报模型，并根据试验的基准点标定数据时段预测声速剖面，最终基于预报声速剖面构建水下基准点定位时变声速误差实时修正模型。本文通过中国南海3000 m实测基准标定数据对提出算法进行验证分析，结果表明，以声线跟踪方法的标定结果为真值，相较于单声速剖面的加权平均声速法，本文方法对于测站1，标定的3D精度从0.839 m提高到了0.424 m，提高了49.5%；对于测站2，标定的3D精度从0.928 m提高到了0.19 m，提高了79.5%。因此本文方法能够较好地改正声速时变误差的影响，从而提高海底基准标定精度。

关键词: 海底基准点标定, 声速时变误差, 最小二乘支持向量机

Abstract:

The spatio-temporal variability of oceanic sound speed is a significant source of error in underwater acoustic navigation and positioning. Addressing the issue that temporal variations in sound speed can severely impact the accuracy of underwater geodetic datum positioning, this paper proposes a method for real-time forecasting of local sound speed fields based on the least squares support vector machine (LSSVM) algorithm, and applies it to oceanic geodetic datum positioning. The method first extrapolates the measured sound speed profiles to the depth of the seabed geodetic datum layout; then, using the measured sound speed profile data, it constructs a sound speed forecasting model based on the LSSVM algorithm, and predicts the sound speed profile based on the positioning data of the experimental geodetic datum points, ultimately applying it to the underwater geodetic datum point positioning model for real-time correction of sound speed representative errors. Through validation analysis using the actual measured geodetic datum positioning data from the South China Sea at 3000 m, the results indicate that, taking the positioning results of the ray tracing method as the true value, compared to the weighted average sound speed method of a single sound speed profile, the underwater geodetic datum positioning method proposed in this paper has achieved a significant enhancement in 3D positioning accuracy for both survey stations. Specifically, for marine geodetic datum 1, the positioning accuracy has been improved from 0.839 m to 0.424 m, representing a 49.5% increase. For marine geodetic datum 2, the positioning accuracy has been elevated from 0.928 m to 0.190 m, which corresponds to a substantial improvement of 79.5%. Therefore, the proposed algorithm can effectively correct the impact of sound speed representative errors, thereby enhancing the accuracy of seabed geodetic datum positioning.

Key words: marinegeodetic datum positioning, sound speed error, least squares support vector machine

中图分类号:

P229.2

赵一杰, 王君婷, 徐天河, 舒建旭, 刘杨范. 水下基准定位时变声速误差修正方法[J]. 测绘学报, 2025, 54(8): 1452-1463.

Yijie ZHAO, Junting WANG, Tianhe XU, Jianxu SHU, Yangfan LIU. Correction method for time-varying sound speed errors in underwater geodetic datum positioning[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(8): 1452-1463.

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声速剖面	测量开始时间	最大深度/m
SSP1	08-30 15:57	2921
SSP2	23:58 09-02	3408
SSP3	09-05 05:04	2983
SSP4	09-06 13:32	2803
SSP5	09-07 06:20	2787
SSP6	09-10 07:58	2615
SSP7	09-11 06:41	2504
SSP8	09-12 01:29	3387
SSP9	09-12 09:28	2978
SSP10	09-14 10:16	2586
SSP11	09-16 06:29	2811
SSP12	09-17 23:59	3107
SSP13	09-18 04:34	3086

声速剖面	EOF-PSSP-ME	EOF
SSP1	0.375 5	0.810 1
SSP3	0.761 6	0.920 8
SSP4	0.583 2	0.562 8
SSP5	0.591 0	0.655 8
SSP6	0.431 8	0.813 1
SSP7	0.390 8	0.962 8
SSP9	0.662 5	1.305 2
SSP10	0.834 1	1.183 7
SSP11	0.483 4	1.360 9
SSP12	0.696 2	1.133 5
SSP13	0.733 7	1.629 3
平均RMS	0.594 6	1.031 7

声速剖面	RMS
SSP1	0.959 8
SSP2	0.551 2
SSP3	0.052 4
SSP4	0.631 5
SSP5	0.775 1
SSP6	0.260 1
SSP7	0.324 7
SSP8	0.745 8
SSP9	0.228 2
SSP10	1.176 9
SSP11	0.482 6
SSP12	0.717 8
SSP13	0.395 1
平均RMS	0.561 6

试验	样本和测量时间
4条样本	SSP13(04:34)、SSP10(10:16)、SSP1(15:57)、SSP12(23:59)
7条样本	SSP8(01:29)、SSP3(05:04)、SSP6(07:58)、SSP10(10:16)、SSP4(13:32)、SSP1(15:57)、SSP2(23:58)

验证样本	RMS
SSP2	0.229 1
SSP3	0.853 9
SSP4	1.031 6
SSP5	0.874 8
SSP6	0.888 4
SSP7	0.882 1
SSP8	0.845 5
SSP9	0.985 0
SSP11	0.877 7
平均RMS	0.829 8

水下基准定位时变声速误差修正方法

Correction method for time-varying sound speed errors in underwater geodetic datum positioning

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参考文献 33

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Metrics

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验证样本	RMS
SSP5	0.546 8
SSP7	0.594 2
SSP9	0.776 4
SSP11	0.558 3
SSP12	1.165 3
SSP13	0.411 6
平均RMS	0.675 4

声速剖面	RMS
SSP1	0.351 0
SSP2	1.061 1
SSP3	0.921 2
SSP4	0.285 1
SSP5	0.526 4
SSP6	1.110 9
SSP7	0.785 9
SSP8	0.358 8
SSP9	0.338 3
SSP10	0.083
SSP11	0.063 2
SSP12	1.095 7
SSP13	0.989 3
平均RMS	0.613 1

声速剖面	RMS
SSP1	0.742 0
SSP2	1.077 4
SSP3	0.924 3
SSP4	0.370 2
SSP5	0.491 3
SSP6	1.089 9
SSP7	0.765 7
SSP8	1.979 8
SSP9	0.265 7
SSP10	0.290 4
SSP11	0.100 8
SSP12	1.074 5
SSP13	1.306 7
平均RMS	0.805 4

测段		SSP预测时间
基准点1	15:30-18:40 18:50-19:50 20:40-21:50	15:45、16:15、17:15、17:45、18:15、18:45、19:00、19:30、21:00、21:30
基准点2	9:20-13:45 14:35-15:40	9:30、10:00、10:30、11:00、11:30、12:00、12:30、13:00、13:30、15:00、15:30

测站	方法	X/m	Y/m	Z/m	ΔX/m	ΔY/m	ΔZ/m	Sigma-X	Sigma-Y	Sigma-Z
测站1	声线跟踪	-2 674 347.480	5 417 451.158	2 026 714.051	—		—	0.017	0.017	0.009
	加权平均声速A	-2 674 346.939	5 417 449.993	2 026 713.370	-0.541	1.165	0.681	0.015	0.017	0.007
	加权平均声速B	-2 674 347.607	5 417 450.634	2 026 713.551	0.127	0.524	0.499	0.015	0.017	0.007
测站2	声线跟踪	-2 675 608.492	5 414 476.353	2 033 908.222	—		—	0.023	0.023	0.013
	加权平均声速A	-2 675 607.774	5 414 475.005	2 033 907.718	-0.718	1.348	0.504	0.024	0.023	0.011
	加权平均声速B	-2 675 608.668	5 414 476.631	2 033 908.203	0.176	-0.277	0.019	0.040	0.038	0.019

测站	方法	2D坐标差	提升/(%)	3D坐标差	提升/(%)	2D-Sigma	3D-Sigma
测站1	加权平均声速A	0.908	—	0.839	—	0.017	0.015
测站1	加权平均声速B	0.381	58	0.424	49.5	0.016	0.014
测站2	加权平均声速A	1.080	—	0.928	—	0.024	0.020
测站2	加权平均声速B	0.232	78.5	0.190	79.5	0.039	0.034

测站	方法	2D标定互差	提升/(%)	3D标定互差	提升/(%)
测站1	加权平均声速A	0.629	—	0.839	—
测站1	加权平均声速B	0.363	42.2	0.364	56.6
测站2	加权平均声速A	0.804	—	0.847	—
测站2	加权平均声速B	0.658	18.1	0.667	21.3