Inversion of Sound Speed Profile Using GNSS‑A Observations with Prior Sound Speed Structure Constraint

LI Baojin; XUE Shuqiang; XIAO Zhen; ZHU Jixing

doi:10.13203/j.whugis20240005

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Inversion of Sound Speed Profile Using GNSS‑A Observations with Prior Sound Speed Structure Constraint

Geodesy and Survey Engineering | 更新时间：2026-11-05

- Inversion of Sound Speed Profile Using GNSS‑A Observations with Prior Sound Speed Structure Constraint
- Geomatics and Information Science of Wuhan University Vol. 51, Issue 3, Pages: 618-628(2026)
- 作者机构：
  
  1.空间基准全国重点实验室，北京，100830
  2.中国测绘科学研究院，北京，100830
- 作者简介：
- 基金信息：
- DOI：10.13203/j.whugis20240005
  CLC： P229
- Received：19 June 2024，
  
  Published：05 March 2026
- 稿件说明：
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李保金,薛树强,肖圳，等.附加先验声速结构约束的GNSS‑A观测反演声速剖面[J].武汉大学学报（信息科学版）,2026,51(3):618-628.

LI Baojin,XUE Shuqiang,XIAO Zhen,et al.Inversion of Sound Speed Profile Using GNSS‑A Observations with Prior Sound Speed Structure Constraint[J].Geomatics and Information Science of Wuhan University,2026,51(3):618-628.
李保金,薛树强,肖圳，等.附加先验声速结构约束的GNSS‑A观测反演声速剖面[J].武汉大学学报（信息科学版）,2026,51(3):618-628. DOI：10.13203/j.whugis20240005

LI Baojin,XUE Shuqiang,XIAO Zhen,et al.Inversion of Sound Speed Profile Using GNSS‑A Observations with Prior Sound Speed Structure Constraint[J].Geomatics and Information Science of Wuhan University,2026,51(3):618-628. DOI：10.13203/j.whugis20240005

摘要

实施现场声速剖面（sound speed profile

SSP）测量不仅会增加海底大地测量观测的成本，也会制约各类海底大地测量监测的时效性，而基于观测信息反演SSP是替代现场SSP测量的有效途径。利用日本公开的全球导航卫星系统‑声学（global navigation satellite system-acoustic

GNSS‑A）观测数据集，比较分析了不同约束方案对Munk模型、双线性模型和自构经验模型反演SSP精度及实施海底大地测量定位精度的影响。结果表明，反演SSP若要实现高精度定位，必须在定位模型中考虑声速时空变化的影响。海面适当约束且海底梯度松约束条件下的自构经验模型通常具有相对更高的反演SSP精度与定位精度，与现场实测SSP互差的均方根（root mean square，RMS）在[10

1 000) m的浅海约5 m/s，在[1 000

1 727.8] m的深海约1 m/s，在东、北和天方向分别为0.002 m、0.002 m和0.022 m。建议采用海面适当约束且海底梯度松约束条件下的自构经验模型及两级优化方法实现替代现场SSP测量的海底大地测量定位。

Abstract

Objectives

The global navigation satellite system‑acoustic (GNSS‑A) ranging combined technology extends the geodetic observation network to the ocean

becoming an important technical means for monitoring submarine geophysical phenomena. Currently

high-precision seafloor geodetic positioning typically relies on a reference sound speed profile (SSP)

combined with acoustic ray-tracing methods to correct refraction errors

and direct inversion or parameterized compensation to mitigate the effects of spatiotemporal variations of sound speed. However

in-field SSP measurements not only increases the cost of seafloor geodetic observations

but also limits the timeliness of various seafloor geodetic monitoring efforts. Inverting the SSP based on GNSS‑A observation data is an effective approach to replace in-field SSP measurements.

Methods

Based on the long-term GNSS‑A observation data from the MYGI station publicly released by Japan

we systematically compare the performance of the Munk model

bilinear model

and self-constructed empirical model in inverting SSP under different constraint conditions. The positioning solutions are then calculated using the ray-tracing model

which considers only the vertical variation of sound speed

and the sonar zenith delay model

which further incorporates parameters to compensate for the spatiotemporal variations of sound speed

based on the inverted SSP. Finally

using the in-field SSP and its corresponding positioning results as references

a comprehensive evaluation is conducted to assess the impact of different SSP models and constraint schemes on the accuracy of seafloor geodetic positioning.

Results

The experimental results show that inverted SSP can effectively represent the overall variation trend of SSP

with more accurate characterization in deeper layers and relatively poorer characterization in shallower layers. The self-constructed empirical model under appropriate sea surface constraints and relaxed seafloor gradient constraints generally exhibits relatively higher inversion accuracy

with the root mean square (RMS) of differences compared to in-field measured SSP being approximately 5 m/s in shallow waters (in the depth range of 10-1 000 m) and about 1 m/s in deep waters (in the depth range of 1 000-1 727.8 m). When the positioning model only considers the vertical variation of sound speed

the self-constructed empirical model under different constraint conditions achieves the highest or comparable positioning accuracy compared to other SSP models

but high-precision positioning cannot yet be achieved. When the positioning model further accounts for the spatiotemporal variation of sound speed

the three-dimensional positioning accuracy is significantly improved. Except for the bilinear model under tight seafloor gradient constraints

the three SSP models under the remaining constraints achieve high-precision positioning. The self-constructed empirical model under appropriate sea surface constraints and relaxed seafloor gradient constraints achieves the relatively highest positioning accuracy

with RMS of differences compared to in-field SSP positioning results of 0.002 m

0.002 m

and 0.022 m in the east

north

and up directions

respectively.

Conclusions

Experimental results demonstrate that

to achieve high-precision positioning with inverted SSP

the influence of spatiotemporal variation of sound speed must be considered in the positioning model. It is recommended to adopt the self-constructed empirical model under appropriate sea surface constraints and relaxed seafloor gradient constraints

along with a two-level optimization method

to achieve seafloor geodetic positioning as an alternative to in-field SSP measurements. It should be noted that the proposed method still has certain limitations. On the one hand

the difficulty in obtaining prior information under special conditions

such as in shallow seas or polar regions

constrains inversion accuracy. On the other hand

the current algorithm relies on relatively accurate historical SSP initial values to ensure iterative convergence. Future research should explore how to integrate multi‑source ocean data to establish a more robust prior constraint system.

关键词

Keywords

references

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