GNSS-acoustic inversion of double-exponential temperature profile

doi:10.11947/j.AGCS.2025.20240065

Abstract

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

CLC Number:

P229.2

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.

Figures/Tables 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