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针对浅海波导中存在的底质参数失配造成水平阵难以正确获取目标深度的问题, 在未知底质参数条件下, 提出了一种基于简正波强度匹配的目标深度估计方法. 通过波数域波束形成技术估计波导中各阶简正波的水平波数和强度, 在简正波模态函数特征方程的基础上利用有限差分法对简正波模态函数进行反演, 计算估计和反演简正波强度之间的匹配度, 最终实现目标深度估计. 基于水平均匀线列阵的仿真结果表明, 所提的算法无需底质参数即可实现对浅海目标深度较为准确的估计. 同时分析了算法在不同的底质参数、阵列孔径、声源频率、信噪比和声速失配条件下的深度估计性能. 结果表明, 所提方法不受底质参数失配的影响, 同时对声速失配较为稳健, 在阵元数不少于128, 频带范围为$50— 150{\text{ Hz}}$, 阵元信噪比大于$ - 10{\text{ dB}}$的条件下可对全海深目标深度进行有效估计. 最终利用南海浅海的海试数据对所提方法的可行性进行了验证.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 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
Fig. 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
Fig. 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$52{\text{ m}}$
Fig. 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$69{\text{ m}}$
Fig. 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
Fig. 8. Relationship between number of sensor and $\delta $in different waveguide depth.
图 9 $\delta $与$\Delta B$的关系
Fig. 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$200{\text{ Hz}}$
Fig. 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
Fig. 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)
Fig. 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}}$)
Fig. 13. Results of depth estimation in different SNR: (a) MFP (${\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 = $$ 10{\text{ m/s}}$); (e) 波数域匹配 ($\delta = 10{\text{ m/s}}$); (f) 本文方法 ($\delta = 10{\text{ m/s}}$); (g) MFP ($\delta = 15{\text{ m/s}}$); (h) 波数域匹配; ($\delta = 15{\text{ m/s}}$); (i) 本文方法 ($\delta = 15{\text{ m/s}}$)
Fig. 14. Results of depth estimation in different $\delta $: (a) MFP ($\delta = 5{\text{ m/s}}$); (b) wavenumber domain match method ($\delta = 5{\text{ m/s}}$); (c) proposed method ($\delta = 5{\text{ m/s}}$); (d) MFP ($\delta = 10{\text{ m/s}}$); (e) wavenumber domain match method ($\delta = 10{\text{ m/s}}$); (f) proposed method ($\delta = 10{\text{ m/s}}$); (g) MFP ($\delta = 15{\text{ m/s}}$); (h) wavenumber domain match method ($\delta = 15{\text{ m/s}}$); (i) proposed method ($\delta = 15{\text{ m/s}}$).
图 16 海试数据处理结果 (a) 估计水平波数; (b) 波数域波束形成; (c) $160{\text{ Hz}}$处反演简正波模态函数; (d) 估计目标深度; (e) $1 — $$ 5{\text{ m}}$内估计目标深度
Fig. 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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