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 哈尔滨工程大学学报  2019, Vol. 40 Issue (5): 899-905  DOI: 10.11990/jheu.201801075 0

引用本文

TANG Hao, XU Feng, YANG Juan. Small target localization in shallow water based on the sound pressure sensitivity kernel for perturbed eigenrays[J]. Journal of Harbin Engineering University, 2019, 40(5), 899-905. DOI: 10.11990/jheu.201801075.

文章历史

1. 中国科学院声学研究所 海洋声学技术中心, 北京 100190;
2. 中国科学院大学, 北京 100049

Small target localization in shallow water based on the sound pressure sensitivity kernel for perturbed eigenrays
TANG Hao 1,2, XU Feng 1, YANG Juan 1
1. Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China
Abstract: The monostatic sonar's ability to locate small targets declines significantly owing to the strong reverberation in shallow water waveguides. An experimental study on an acoustic barrier was conducted through the forward scattering of targets. Small target positioning was achieved by utilizing the sound pressure sensitivity kernel for perturbed eigenrays, which was previously used in large target localization. Further, performance simulations were performed under different precision conditions of the bottom model. The simulation results indicate the superiority of this method in two aspects. First, it exhibits robustness to bottom measurement error. Second, for the bottom part that fluctuates within a proper range, the targets can also be located approximately by directly assuming the bottom to be flat, particularly when the targets are located in the upper-middle part of the water column. Additionally, experiments were made in the lake. The lake test results suggest that the localization method based on the sound pressure sensitivity kernel for perturbed eigenrays is applicable for assessing real environments. Finally, the localization performance is found to be consistent with simulation results.
Keywords: forward scattering    small target localization    sensitivity kernel    perturbed eigenray    shallow water waveguide    acoustic barrier    bistatic sonar    sound field perturbation

1 基于扰动声线声压敏感核的定位方法 1.1 目标引起声压相对变化的原理

 $\begin{array}{*{20}{c}} {\Delta G\left( {\omega ;{\mathit{\boldsymbol{r}}_{\rm{r}}}, {\mathit{\boldsymbol{r}}^\prime }, {\mathit{\boldsymbol{r}}_{\rm{s}}}} \right) = - 4\pi {f_\infty }\left( {\omega , {\varphi _{\rm{s}}} + {\varphi _{\rm{r}}}} \right) \cdot }\\ {G\left( {\omega ;{\mathit{\boldsymbol{r}}_{\rm{r}}}, {\mathit{\boldsymbol{r}}^\prime }} \right)G\left( {\omega ;{\mathit{\boldsymbol{r}}^\prime }, {\mathit{\boldsymbol{r}}_{\rm{s}}}} \right)} \end{array}$ (1)

 $\Delta P\left(t ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}^{\prime}, \boldsymbol{r}_{\mathrm{s}}\right)=\frac{1}{2 \pi} \int \Delta G\left(\omega ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}^{\prime}, \boldsymbol{r}_{\mathrm{s}}\right) P_{\mathrm{s}}(\boldsymbol{\omega}) \mathrm{e}^{\mathrm{i} \omega t} \mathrm{d} \omega$ (2)

 $P\left(t ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}_{\mathrm{s}}\right)=\frac{1}{2 \pi} \int G\left(\boldsymbol{\omega} ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}_{\mathrm{s}}\right) P_{\mathrm{s}}(\boldsymbol{\omega}) \mathrm{e}^{i \omega t} \mathrm{d} \omega$ (3)

 $\begin{array}{c}{\Delta P\left(t ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}^{\prime}, \boldsymbol{r}_{\mathrm{s}}\right) / P\left(t ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}_{\mathrm{s}}\right)=-4 \pi \int f_{\infty}\left(\omega, \varphi_{\mathrm{s}}+\right.} \\ {\varphi_{\mathrm{r}} ) G\left(\omega ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}^{\prime}\right) G\left(\omega ; \boldsymbol{r}^{\prime}, \boldsymbol{r}_{\mathrm{s}}\right) P_{\mathrm{s}}(\omega) \mathrm{e}^{\mathrm{i} \omega t} \mathrm{d} \omega /} \\ {\int G\left(\omega ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}_{\mathrm{s}}\right) P_{\mathrm{s}}(\omega) \mathrm{e}^{\mathrm{i} \omega t} \mathrm{d} \omega}\end{array}$ (4)

 \begin{aligned} f_{\infty}\left(\omega, \varphi_{{\rm s}}+\varphi_{\mathrm{r}}\right)=& 2 / 3 k^{2} a^{3}\left[\Delta c\left(\boldsymbol{r}^{\prime}\right) / c\left(\boldsymbol{r}^{\prime}\right)+\right.\\ & \Delta \boldsymbol{\rho}\left(\boldsymbol{r}^{\prime}\right) / \boldsymbol{\rho}\left(\boldsymbol{r}^{\prime}\right)\left(1+\cos \left(\varphi_{\mathrm{s}}+\right.\right.\\ & \varphi_{\mathrm{r}} ) ) / 2 ] \end{aligned} (5)

 $\begin{array}{c}{\Delta P\left(t ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}^{\prime}, \boldsymbol{r}_{\mathrm{s}}\right) / P\left(t ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}_{\mathrm{s}}\right)=\int\left[\Delta c\left(\boldsymbol{r}^{\prime}\right) / c\left(\boldsymbol{r}^{\prime}\right)+\right.} \\ {\Delta \boldsymbol{\rho}\left(\boldsymbol{r}^{\prime}\right) / \boldsymbol{\rho}\left(\boldsymbol{r}^{\prime}\right)\left(1+\cos \left(\varphi_{\mathrm{s}}+\varphi_{\mathrm{r}}\right)\right) / 2 ]}\cdot \\ {Q\left(\omega ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}^{\prime}, \boldsymbol{r}_{\mathrm{s}}\right) V P_{\mathrm{s}}(\boldsymbol{\omega}) \mathrm{e}^{i \omega t} \mathrm{d} \omega}/ \\ {\int G\left(\omega ; \boldsymbol{r}_{\mathrm{r}}, \boldsymbol{r}_{\mathrm{s}}\right) P_{\mathrm{s}}(\omega) \mathrm{e}^{i \omega t} \mathrm{d} \omega}\end{array}$ (6)

 \begin{aligned} f_{\infty}\left(\omega, \varphi_{\mathrm{s}}+\varphi_{\mathrm{r}}\right)=& \frac{1}{k} \sum\limits_{n=0}^{\infty}(2 n+1) \sin \eta_{n} ·\\ & \exp \left(\mathrm{i} \eta_{n}\right) \mathrm{P}_{n}\left(\cos \left(\varphi_{\mathrm{s}}+\varphi_{\mathrm{r}}\right)\right) \end{aligned} (7)

1.2 基于声压敏感核的目标定位方法

 Download: 图 1 某条扰动声线的声压相对变化 Fig. 1 Relative pressure changes of a perturbed eigenray

Marandet[6]统计了一次实验室等比缩放实验中7 000条本征声线的声压相对变化，发现多数扰动声线的声压是减弱的。所以本文利用声压相对变化为负的扰动声线进行目标定位，该集合用M表示。目标处于不同位置所引起的声压相对变化ΔP/P有正有负，那么一条声压相对变化为负的扰动声线所提供的目标位置信息是目标应该在ΔP/P < 0的区域。因此只保留ΔP/P < 0的区域的计算结果，用Ψm(r′)表示，其中下角标表示第m条扰动声线的结果。将所有声压相对变化为负的扰动声线的计算结果相加，并求得绝对值最大的位置rt

 $\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}\left( {{\mathit{\boldsymbol{r}}^\prime }} \right) = \sum\limits_{m \in M} {{\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}_{\rm{m}}}} \left( {{\mathit{\boldsymbol{r}}^\prime }} \right)$ (8)
 ${\mathit{\boldsymbol{r}}_{\rm{t}}} = \max \left( {\left| {\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}\left( {{\mathit{\boldsymbol{r}}^\prime }} \right)} \right|} \right)$ (9)

1.3 定位方法的信号处理流程

2 仿真实验及性能分析

 Download: 图 2 定位区域及目标位置示意图 Fig. 2 Schematic diagram of location area and target locations
 Download: 图 3 精确已知水底地形的定位结果 Fig. 3 Location results under accurate bottom model
2.1 精确已知水底地形时的定位结果

2.2 水底地形存在0.1%和0.3%测量误差时的定位结果

 Download: 图 4 2种测量精度下的测量值与实际深度的相对误差的仿真结果 Fig. 4 Simulation results of depth relative error between true value and measurement value under two measurement precisions
 Download: 图 5 存在地形测量误差时不同区域的平均定位误差 Fig. 5 Average location error of different areas under bottom models with measurement error
2.3 起伏水底近似为平底时的定位结果

 Download: 图 6 10种随机起伏的水底地形 Fig. 6 10 different bottoms of random fluctuation

3 湖试实验 3.1 实验简介

3.2 实验结果