A target depth estimation method in shallow water based on matched normal mode intensity

YIN Jingwei; YIN Jiarui; CAO Ran; HUANG Chunlong; LI Li

doi:10.7498/aps.74.20250419

Abstract

A novel target depth estimation method based on normal mode intensity match is proposed for shallow water environment by using horizontal array to overcome the performance degradation observed in traditional approaches under the condition that seabed parameters are not matched. Firstly, horizontal wavenumbers and normal mode intensities are estimated through wavenumber domain beamforming. Secondly, modal function of normal mode inversion is performed by solving the modal function characteristic equation by using the finite difference method. Thirdly, the match degree between inverted and estimated normal mode intensities is evaluated to estimate target depth. The numerical simulation results show that the proposed method can accurately estimate the target depth in shallow water scenarios without knowing the seabed parameters. Furthermore, the performance of the method is analyzed under different conditions including different seabed parameters, array apertures and source frequencies. The results reveal three conclusions: 1) the mismatch of seabed parameters has no influence on the method; 2) the effective performance of full depth source estimation requires no less than 128 array elements, a frequency band range of 50–150 Hz, and the signal-to-noise radio of the element on a horizontal line array exceeding –10 dB; 3) the method has robust performance against sound speed profile mismatch. Finally, the feasibility of the proposed method is validated by the experimental data received by a horizontally towing 77-element array during the shallow-water sea trial in the South China Sea.

Keywords:

Authors and contacts

1.
National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
2.
Key Laboratory for Polar Acoustics and Application of Ministry of Education (Harbin Engineering University), Harbin 150001, China
3.
College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Corresponding author: CAO Ran, cran@hrbeu.edu.cn

Funds: Project supported by the Natural Science Foundation of Heilongjiang Province of China for the Excellent Youth Scholars (Grant No. YQ2023A008) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 12204127, 12304498).

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References

[1]	Bucker H P 1976 J. Acoust. Soc. Am. 59 368 Google Scholar
[2]	Baggeroer A B, Kuperman W A, Mikhalevsky P N 1993 IEEE J. Oceanic Eng. 18 401 Google Scholar
[3]	Krolik J L 1992 J. Acoust. Soc. Am. 92 1408 Google Scholar
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[11]	Li X L, Xu Y J, Gao W, Wang H Z, Wang L 2024 Remote Sens. 16 2227 Google Scholar
[12]	Akins F H, Kuperman W A 2022 JASA Express Lett. 2 074802 Google Scholar
[13]	Yang T C 2014 J. Acoust. Soc. Am. 135 1218 Google Scholar
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[17]	王宣, 孙超, 李明杨, 张少东 2022 物理学报 71 084304 Google Scholar Wang X, Sun C, Li M Y, Zhang S D 2022 Acta Phys. Sin. 71 084304 Google Scholar
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[24]	李鹏, 章新华, 付留芳, 曾祥旭 2017 物理学报 66 084301 Google Scholar Li P, Zhang X H, Fu L F, Zeng X X 2017 Acta Phys. Sin. 66 084301 Google Scholar
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[31]	国家标准化管理委员会 2024 GB/T 44042-2024(北京: 国家标准化管理委员会)第三部分 Standardization Administration of the People’s Republic of China 2024 GB/T 44042-2024 (Beijing: Standardization Administration of the People’s Republic of China) Part3

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图 1 浅海水平分层波导模型

Figure 1. Model of shallow water horizontal layered waveguide.

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图 2 有限差分网格

Figure 2. Finite difference grids.

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图 3 仿真使用的浅海波导模型

Figure 3. Model of shallow water waveguide used in simulation.

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图 4 20 m声源深度下简正波水平波数与强度仿真结果　(a) 理论与估计水平波数; (b) 低阶简正波理论与估计水平波数; (c) 理论与估计简正波强度

Figure 4. Simulation results of normal mode wavenumbers and intensities at 20 m source depth: (a) Theoretical and estimated horizontal wavenumbers; (b) theoretical and estimated horizontal wavenumbers of low order normal modes; (c) theoretical and estimated normal mode intensities.

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图 5 70 Hz处反演简正波模态函数

Figure 5. Modal functions of normal mode in 70 Hz by inverting.

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图 6 目标深度估计结果　(a) 目标深度$1 — 99{\text{ m}}$; (b) 目标深度$52{\text{ m}}$

Figure 6. Results of depth estimation: (a) Source depth of $1 - 99{\text{ m}}$; (b) source depth of $52{\text{ m}}$.

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图 7 不同阵列孔径下深度估计结果　(a) 水平阵阵元数64; (b) 水平阵阵元数128; (c) 声源深度$52$ m与$69{\text{ m}}$

Figure 7. Results of depth estimation in different array aperture: (a) Number of horizontal array sensors is 64; (b) number of horizontal array sensors is 128; (c) source depth of $52$m and $69{\text{ m}}$.

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图 8 不同波导深度下$\delta $与$N$的关系

Figure 8. Relationship between number of sensor and $\delta $in different waveguide depth.

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图 9 $\delta $与$\Delta B$的关系

Figure 9. Relationship between $\delta $and bandwidth $\Delta B$.

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图 10 不同频率下深度估计结果　(a) 频率30 Hz; (b) 频率100 Hz; (c) 频率 200 Hz

Figure 10. Results of depth estimation in different frequency: (a) Frequency is 30 Hz; (b) frequency is 100 Hz; (c) frequency is 200 Hz.

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图 11 30 m声源深度下简正波水平波数与强度仿真结果　(a) 理论与估计水平波数; (b) 低阶简正波理论与估计水平波数; (c) 理论与估计简正波强度

Figure 11. Simulation results of normal mode wavenumbers and intensities at 30 m source depth: (a) Theoretical and estimated horizontal wavenumbers; (b) theoretical and estimated horizontal wavenumbers of low order normal modes; (c) theoretical and estimated normal mode intensities.

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图 12 不同底质参数下深度估计结果　(a) MFP (无失配); (b) 波数域匹配方法(无失配); (c) 本文所提方法(无失配); (d) MFP(失配); (e) 波数域匹配方法(失配); (f) 本文所提方法(失配)

Figure 12. Results of depth estimation in different seabed parameters: (a) MFP (without mismatch); (b) wavenumber domain match method (without mismatch); (c) proposed method (without mismatch); (d) MFP (mismatch); (e) wavenumber domain match method (mismatch); (f) proposed method (mismatch).

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图 13 不同信噪比下深度估计结果　(a) MFP (${\text{SNR}} = - 15{\text{ dB}}$); (b) 波数域匹配 (${\text{SNR}} = - 15{\text{ dB}}$); (c) 本文方法 (${\text{SNR}} = $$ - 15{\text{ dB}}$); (d) MFP (${\text{SNR}} = - 10{\text{ dB}}$); (e) 波数域匹配 (${\text{SNR}} = - 10{\text{ dB}}$); (f) 本文方法 (${\text{SNR}} = - 10{\text{ dB}}$); (g) MFP (${\text{SNR}} = $$ - 5{\text{ dB}}$); (h) 波数域匹配; (${\text{SNR}} = - 5{\text{ dB}}$); (i) 本文方法 (${\text{SNR}} = - 5{\text{ dB}}$)

Figure 13. Results of depth estimation in different SNR: (a) MFP (${\text{SNR}} = - 15{\text{ dB}}$); (b) wavenumber domain match method (${\text{SNR}} = - 15{\text{ dB}}$); (c) proposed method (${\text{SNR}} = - 15{\text{ dB}}$); (d) MFP (${\text{SNR}} = - 10{\text{ dB}}$); (e) wavenumber domain match method (${\text{SNR}} = - 10{\text{ dB}}$); (f) proposed method (${\text{SNR}} = - 10{\text{ dB}}$); (g) MFP (${\text{SNR}} = - 5{\text{ dB}}$); (h) wavenumber domain match method (${\text{SNR}} = - 5{\text{ dB}}$); (i) proposed method (${\text{SNR}} = - 5{\text{ dB}}$).

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图 14 不同$\delta $下深度估计结果　(a) MFP ($\delta = 5{\text{ m/s}}$); (b) 波数域匹配 ($\delta = 5{\text{ m/s}}$); (c) 本文方法 ($\delta = 5{\text{ m/s}}$); (d) MFP ($\delta = $$ 10{\text{ m/s}}$); (e) 波数域匹配 ($\delta = 10{\text{ m/s}}$); (f) 本文方法 ($\delta = 10{\text{ m/s}}$); (g) MFP ($\delta = 15{\text{ m/s}}$); (h) 波数域匹配; ($\delta = 15{\text{ m/s}}$); (i) 本文方法 ($\delta = 15{\text{ m/s}}$)

Figure 14. Results of depth estimation in different $\delta $: (a) MFP ($\delta = 5{\text{ m/s}}$); (b) wavenumber domain match method ($\delta = 5{\text{ m/s}}$); (c) proposed method ($\delta = 5{\text{ m/s}}$); (d) MFP ($\delta = 10{\text{ m/s}}$); (e) wavenumber domain match method ($\delta = 10{\text{ m/s}}$); (f) proposed method ($\delta = 10{\text{ m/s}}$); (g) MFP ($\delta = 15{\text{ m/s}}$); (h) wavenumber domain match method ($\delta = 15{\text{ m/s}}$); (i) proposed method ($\delta = 15{\text{ m/s}}$).

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图 15 试验态势

Figure 15. Experimental situation.

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图 16 海试数据处理结果　(a) 估计水平波数; (b) 波数域波束形成; (c) 160 Hz处反演简正波模态函数; (d) 估计目标深度; (e) 1—5 m内估计目标深度

Figure 16. Results of experiment data processing: (a) Estimated horizontal wavenumbers; (b) wavenumber domain beamforming; (c) modal functions of normal mode at 160 Hz by inverting; (d) estimated target depth; (e) estimated target depth between 1 and 5 m.

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[1]	Bucker H P 1976 J. Acoust. Soc. Am. 59 368 Google Scholar
[2]	Baggeroer A B, Kuperman W A, Mikhalevsky P N 1993 IEEE J. Oceanic Eng. 18 401 Google Scholar
[3]	Krolik J L 1992 J. Acoust. Soc. Am. 92 1408 Google Scholar
[4]	Schmidt H, Kuperman W A, Scheer E K 1990 J. Acoust. Soc. Am. 88 1851 Google Scholar
[5]	李建龙, 潘翔 2008 声学学报 33 205 Google Scholar Li J L, Pan X 2008 Acta Acustica 33 205 Google Scholar
[6]	杨坤德, 马远良, 邹士新, 雷波 2006 声学学报 31 496 Google Scholar Yang K D, Ma Y L, Zou S X, Lei B 2006 Acta Acustica 31 496 Google Scholar
[7]	王奇, 王英民, 魏志强 2020 声学学报 45 475 Google Scholar Wang Q, Wang Y M, Wei Z Q 2020 Acta Acustica 45 475 Google Scholar
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[10]	Dosso S E, Wilmut M J 2013 JASA Express Lett. 133 274 Google Scholar
[11]	Li X L, Xu Y J, Gao W, Wang H Z, Wang L 2024 Remote Sens. 16 2227 Google Scholar
[12]	Akins F H, Kuperman W A 2022 JASA Express Lett. 2 074802 Google Scholar
[13]	Yang T C 2014 J. Acoust. Soc. Am. 135 1218 Google Scholar
[14]	Yang T C 2019 J. Acoust. Soc. Am. 146 4740 Google Scholar
[15]	周玉媛, 孙超, 谢磊, 刘宗伟 2023 物理学报 72 084302 Google Scholar Zhou Y Y, Sun C, Xie L, Liu Z W 2023 Acta Phys. Sin. 72 084302 Google Scholar
[16]	孟瑞洁, 周士弘, 李风华, 戚聿波 2019 物理学报 68 134304 Google Scholar Meng R J, Zhou S H, Li F H, Qi Y B 2019 Acta Phys. Sin. 68 134304 Google Scholar
[17]	王宣, 孙超, 李明杨, 张少东 2022 物理学报 71 084304 Google Scholar Wang X, Sun C, Li M Y, Zhang S D 2022 Acta Phys. Sin. 71 084304 Google Scholar
[18]	Bogart C W, Yang T C 1994 J. Acoust. Soc. Am. 96 1677 Google Scholar
[19]	Nicolas B, Mars J, Lacoume J 2006 EURASIP J. Adv. Signal Process 65901 1 Google Scholar
[20]	Zhang Y K, Yang Q L, Yang K D 2023 Ocean Eng. 286 115502 Google Scholar
[21]	Liang G L, Zhang Y F, Zou N, Wang J J 2018 Math. Prob. Eng. 7824671 7824671 Google Scholar
[22]	Premus V E, Helfrick M N 2013 J. Acoust. Soc. Am. 133 4019 Google Scholar
[23]	李天宇, 李宇, 黄海宁, 杨习山 2021 声学学报 46 497 Google Scholar Li T Y, Li Y, Huang H N, Yang X S 2021 Acta Acustica 46 497 Google Scholar
[24]	李鹏, 章新华, 付留芳, 曾祥旭 2017 物理学报 66 084301 Google Scholar Li P, Zhang X H, Fu L F, Zeng X X 2017 Acta Phys. Sin. 66 084301 Google Scholar
[25]	Zhang H C, Zhou S H, Liu C P, Qi Y B 2024 J. Acoust. Soc. Am. 156 1148 Google Scholar
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[28]	芬恩 B 延森, 威廉 A 库珀曼, 亨利克施米特著 (周利生, 王鲁军, 杜栓平译) 2017 计算海洋声学(北京: 国防工业出版社)第286—287页 Jensen F B, Kuperman W A, Porter M B, Schimit H(translated by Zhou L S, Wang L J, Du S P)2017 Computational Ocean Acoustics (Beijing: National Defense Industry Press) pp286–287
[29]	Li X L, Wang P Y 2021 JASA Express Lett. 1 126002 Google Scholar
[30]	Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) p1
[31]	国家标准化管理委员会 2024 GB/T 44042-2024(北京: 国家标准化管理委员会)第三部分 Standardization Administration of the People’s Republic of China 2024 GB/T 44042-2024 (Beijing: Standardization Administration of the People’s Republic of China) Part3

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