中国物理B ›› 2026, Vol. 35 ›› Issue (2): 24301-024301.doi: 10.1088/1674-1056/adee01

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Single broadband source depth estimation using Stokes parameters in shallow water

Yizheng Wei(韦宜政)1,2, Chao Sun(孙超)1,2, Lei Xie(谢磊)1,2,†, and Mingyang Li(李明杨)1,2,‡   

  1. 1 School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China;
    2 Key Laboratory of Ocean Acoustic and Sensing, Ministry of Industry and Information Technology, Northwestern Polytechnical University, Xi'an 710072, China
  • 收稿日期:2025-03-17 修回日期:2025-07-07 接受日期:2025-07-10 发布日期:2026-01-31
  • 通讯作者: Lei Xie, Mingyang Li E-mail:xielei2014@mail.nwpu.edu.cn;mingyang.li@nwpu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12274348 and 12004335) and the National Key Research and Development Program of China (Grant No. 2024YFC2813800).

Single broadband source depth estimation using Stokes parameters in shallow water

Yizheng Wei(韦宜政)1,2, Chao Sun(孙超)1,2, Lei Xie(谢磊)1,2,†, and Mingyang Li(李明杨)1,2,‡   

  1. 1 School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China;
    2 Key Laboratory of Ocean Acoustic and Sensing, Ministry of Industry and Information Technology, Northwestern Polytechnical University, Xi'an 710072, China
  • Received:2025-03-17 Revised:2025-07-07 Accepted:2025-07-10 Published:2026-01-31
  • Contact: Lei Xie, Mingyang Li E-mail:xielei2014@mail.nwpu.edu.cn;mingyang.li@nwpu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12274348 and 12004335) and the National Key Research and Development Program of China (Grant No. 2024YFC2813800).

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摘要： Presented in this study is a novel method for estimating the depth of single underwater source in shallow water, utilizing vector sensors. The approach leverages the depth distribution of the broadband Stokes parameters to estimate source depth accurately. Unlike traditional matched field processing (MFP) and matched mode processing (MMP), the proposed approach can estimate source depth directly from the data received by sensors without requiring complete environmental information. Firstly, the broadband Stokes parameters (BSP) are established using the normal mode theory. Then the nonstationary phase approximation is used to simplify the theoretical derivation, which is necessary when dealing with broadband integrals. Additionally, range terms of the BSP are eliminated by normalization. By analyzing the depth distribution of the normalized broadband Stokes parameters (NBSP), it is found that the NBSP exhibit extreme values at the source depth, which can be used for source depth estimation. So the proposed depth estimation method is based on searching the peaks of the NBSP. Simulations show that this method is effective in relatively simple shallow water environments. Finally, the effect of source range, frequency bandwidth, sound speed profile (SSP), water depth, and signal-to-noise ratio (SNR) are studied. The findings indicate that the proposed method can accurately estimate the source depth when the SNR is greater than $-5$ dB and does not need to consider model mismatch issues. Additionally, variations in environmental parameters have minimal impact on estimation accuracy. Compared to MFP, the proposed method requires a higher SNR, but demonstrates superior robustness against fluctuations in environmental parameters.

关键词: broadband source depth estimation, shallow water, polarization, Stokes parameters

Abstract: Presented in this study is a novel method for estimating the depth of single underwater source in shallow water, utilizing vector sensors. The approach leverages the depth distribution of the broadband Stokes parameters to estimate source depth accurately. Unlike traditional matched field processing (MFP) and matched mode processing (MMP), the proposed approach can estimate source depth directly from the data received by sensors without requiring complete environmental information. Firstly, the broadband Stokes parameters (BSP) are established using the normal mode theory. Then the nonstationary phase approximation is used to simplify the theoretical derivation, which is necessary when dealing with broadband integrals. Additionally, range terms of the BSP are eliminated by normalization. By analyzing the depth distribution of the normalized broadband Stokes parameters (NBSP), it is found that the NBSP exhibit extreme values at the source depth, which can be used for source depth estimation. So the proposed depth estimation method is based on searching the peaks of the NBSP. Simulations show that this method is effective in relatively simple shallow water environments. Finally, the effect of source range, frequency bandwidth, sound speed profile (SSP), water depth, and signal-to-noise ratio (SNR) are studied. The findings indicate that the proposed method can accurately estimate the source depth when the SNR is greater than $-5$ dB and does not need to consider model mismatch issues. Additionally, variations in environmental parameters have minimal impact on estimation accuracy. Compared to MFP, the proposed method requires a higher SNR, but demonstrates superior robustness against fluctuations in environmental parameters.

Key words: broadband source depth estimation, shallow water, polarization, Stokes parameters

中图分类号:  (Underwater sound)

  • 43.30.+m
43.60.Jn (Source localization and parameter estimation) 43.60.-c (Acoustic signal processing) 43.30.Bp (Normal mode propagation of sound in water)