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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, $50 - 150{\text{ Hz}}$ 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 $ - 10{\text{ 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.
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Keywords:
- seabed parameters /
- shallow water /
- horizontal array /
- depth estimation
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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.
图 2 有限差分网格
Figure 2. Finite difference grids.
图 3 仿真使用的浅海波导模型
Figure 3. Model of shallow water waveguide used in simulation.
图 4 $20{\text{ m}}$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 $20{\text{ m}}$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.
图 5 70 Hz处反演简正波模态函数
Figure 5. Modal functions of normal mode in $70{\text{ Hz}}$by inverting.
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 $52{\text{ m}}$.
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 $69{\text{ m}}$.
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.
图 9 $\delta $与$\Delta B$的关系
Figure 9. Relationship between $\delta $and bandwidth $\Delta B$.
图 10 不同频率下深度估计结果 (a) 频率$30{\text{ Hz}}$; (b) 频率$100{\text{ Hz}}$; (c) 频率$200{\text{ Hz}}$
Figure 10. Results of depth estimation in different frequency: (a) Frequency is $30{\text{ Hz}}$; (b) frequency is $100{\text{ Hz}}$; (c) frequency is $200{\text{ Hz}}$.
图 11 $30{\text{ m}}$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 $30{\text{ m}}$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.
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).
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}}$).
图 14 不同$\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 = $$ 10{\text{ m/s}}$); (e) 波数域匹配 ($\delta = 10{\text{ m/s}}$); (f) 本文方法 ($\delta = 10{\text{ m/s}}$); (g) MFP ($\delta = 15{\text{ m/s}}$); (h) 波数域匹配; ($\delta = 15{\text{ m/s}}$); (i) 本文方法 ($\delta = 15{\text{ m/s}}$)
Figure 14. Results of depth estimation in different $\delta $: (a) MFP ($\delta = 5{\text{ m/s}}$); (b) wavenumber domain match method ($\delta = 5{\text{ m/s}}$); (c) proposed method ($\delta = 5{\text{ m/s}}$); (d) MFP ($\delta = 10{\text{ m/s}}$); (e) wavenumber domain match method ($\delta = 10{\text{ m/s}}$); (f) proposed method ($\delta = 10{\text{ m/s}}$); (g) MFP ($\delta = 15{\text{ m/s}}$); (h) wavenumber domain match method ($\delta = 15{\text{ m/s}}$); (i) proposed method ($\delta = 15{\text{ m/s}}$).
图 15 试验态势
Figure 15. Experimental situation.
图 16 海试数据处理结果 (a) 估计水平波数; (b) 波数域波束形成; (c) $160{\text{ Hz}}$处反演简正波模态函数; (d) 估计目标深度; (e) $1 — $$ 5{\text{ 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 $160{\text{ Hz}}$by inverting; (d) estimated target depth; (e) estimated target depth between $1$ and $5{\text{ m}}$.
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