Inversion for sound speed profile in shallow water based on long short-term memory networks and ray theory
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摘要:
针对水声多途信道环境下的水下声速剖面反演问题, 将深度学习与射线声学理论结合, 提出了一种基于长短期记忆网络(LSTM)的反演方法。该方法根据有序线阵等距的特点, 将到达时间差、到达角度等多模态数据融合组成的感知矩阵作为输入, 利用LSTM网络处理时序数据的能力挖掘空间上有序分布的接收阵元之间的关联信息, 从而实现声速剖面反演。在此基础上, 还提出了基于互相关函数的硬阈值估计方法, 通过降低感知矩阵的测量误差提高模型的抗多途性能。通过数值仿真验证了该反演方法的可行性和准确性, 与传统优化算法相比, 所提算法能够更好地捕捉声速剖面的非线性特征, 具有更高的反演精度和较强的抗噪能力。
Abstract:To address the problem of underwater sound speed profile (SSP) inversion in underwater acoustic multipath channels, this paper combines deep learning and ray theory to propose an inversion method using a long short-term memory network (LSTM). Based on the equidistant characteristics of the horizontal line array, the proposed method takes the perceptual matrix composed of multi-modal data, such as time difference of arrival and angle of arrival, as input, and utilizes the ability of LSTM network to process time-series data to mine the correlations between spatially ordered receiving array elements for sound speed profile inversion. On this basis, a time delay estimation method based on hard threshold estimation method and cross-correlation function is proposed to reduce the measurement errors of the perceptual matrix and improve the anti-multipath performance. The feasibility and accuracy of the proposed method are verified through numerical simulations. Compared with the traditional optimization algorithm, the proposed algorithm better captures the nonlinear characteristics of SSP, with higher inversion accuracy and stronger noise resistance.
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表 1 CCF-HTP算法流程
01 输入:iter, l,u, err, u′ // iter: 最大迭代次数l: 稀疏度// u: 发送信号err: 最小误差 // u′: 接收信号 02 {\boldsymbol{S}} = \dfrac{1}{M}{\boldsymbol{S}}_{_u}^{\text{H}} \cdot {{\boldsymbol{S}}_{{u^{'}}}} // 计算互功率谱 03 {\boldsymbol{\varPhi }} = \left[ {\boldsymbol{a}\left( {{\tau_0}} \right), \boldsymbol{a}\left( {{\tau_1}} \right), \cdots , \boldsymbol{a}\left( {{\tau_{N - 1}}} \right)} \right] // 计算观测矩阵 04 {{\boldsymbol{r}}^0} = {\boldsymbol{S}}, \, {{\boldsymbol{\xi }}^0} = 0, \, {\mu ^0} = 1 // 初始化参数 05 {\text{while}}(i < {\text{iter}})\,{\text{and}}\,\left( {\left\| {{{\boldsymbol{r}}^n} - {{\boldsymbol{r}}^{n - 1}}} \right\|_{\text{2}}^{\text{2}} > {\text{err}}} \right) 06 \begin{gathered} {{\varGamma }^n} = {\text{\{ indices of }}k{\text{ largest entries of }} \\\qquad {\text{ }}{{\boldsymbol{x}}^n} + {\mu ^n}{{\boldsymbol{\varPhi }}^T}{{\boldsymbol{r}}^{n - 1}}{\text{\} }} \\ \end{gathered} // 取备选更新信号的l个
最大值索引构建索引
集合07 {\boldsymbol{v}} = \arg \min \{ ||{\boldsymbol{S}} - {\boldsymbol{\varPhi v}}||,{\text{supp}} ({\boldsymbol{v}}) \subseteq {{\varGamma }^n}\} // 选择支撑集包含于索引集合的有效信号 08 {{\boldsymbol{\xi }}^n} = {\boldsymbol{v}} // 更新信号 09 {\mu ^n} = \dfrac{{{\text{||(}}{{\boldsymbol{\varPhi }}^{\text{*}}}{\text{(}}{\boldsymbol{S}} - {\boldsymbol{\varPhi }}{{\boldsymbol{x}}^n}{\text{)}}{{\text{)}}_{{{\varGamma }^n}}}{\text{||}}_{\text{2}}^{\text{2}}}}{{{\text{||}}{\boldsymbol{\varPhi }}{{{\text{(}}{{\boldsymbol{\varPhi }}^{\text{*}}}{\text{(}}{\boldsymbol{S}} - {\boldsymbol{\varPhi }}{{\boldsymbol{x}}^n}{\text{))}}}_{{{\varGamma }^n}}}{\text{||}}_{\text{2}}^{\text{2}}}} // 更新步长 10 {{\mathrm{end}}} 11 输出: \; {\boldsymbol\xi }^{n} 
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表 2 参数设置
参数 仿真取值 采样率 (kHz) 100 Chirp信号频率范围 (kHz) 20~30 Chirp信号周期 (ms) 40 水声信道多途数量 10 最大时延拓展 (ms) 30 输入层神经元个数 4 输出层神经元个数 25 接收浮标个数 20 PSO粒子数 50 PSO迭代次数 50 学习率 0.0001 声速剖面训练集数量 8800 声速剖面测试集数量 2200 声速剖面深度采样间隔 (m) 8 训练迭代次数 10000
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