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Article(id=1241060180096504490, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1241060178263601474, articleNumber=null, orderNo=null, doi=10.12347/j.ycyk.20231225001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1703433600000, receivedDateStr=2023-12-25, revisedDate=1704211200000, revisedDateStr=2024-01-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1773821404713, onlineDateStr=2026-03-18, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773821404713, onlineIssueDateStr=2026-03-18, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773821404713, creator=13701087609, updateTime=1773821404713, updator=13701087609, issue=Issue{id=1241060178263601474, tenantId=1146029695717560320, journalId=1238841944844054536, year='2024', volume='45', issue='2', pageStart='1', pageEnd='123', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773821404281, creator=13701087609, updateTime=1773821891324, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241062221128724613, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1241060178263601474, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241062221128724614, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1241060178263601474, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=29, endPage=36, ext={EN=ArticleExt(id=1241060182575338173, articleId=1241060180096504490, tenantId=1146029695717560320, journalId=1238841944844054536, language=EN, title=Forward-looking Imaging Algorithm Based on CNN-LSTM Neural Network, columnId=1241060179823882575, journalTitle=Journal of Telemetry, Tracking and Command, columnName=Artificial Intelligence Technology, runingTitle=null, highlight=null, articleAbstract=

As a difficulty and focus in the field of radar imaging, radar forward-looking imaging has broad application prospects in automatic driving, navigation, precision guidance and so on. The traditional forward-looking imaging algorithm is limited by the width of the antenna aperture and cannot achieve high-resolution imaging. In this paper, CNN ( Convolutional Neural Networks )neural network and LSTM ( Long Short-Term Memory ) neural network are combined to realize the prediction of azimuth in forward-looking imaging. Firstly, the convolution-like model of the scanning forward-looking imaging signal and its ill-posedness are introduced. The echo signal is preprocessed by pulse compression and range migration correction, and input into the CNN-LSTM neural network to perform azimuth estimation by range unit. The simulation results show that the algorithm can effectively improve the azimuth resolution of forward-looking imaging and realize the super-resolution of forward-looking imaging.

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雷达前视成像作为雷达成像领域的难点与重点，在自动驾驶、导航、精确制导等方面具有广阔的应用前景。传统的前视成像算法受限于天线孔径的宽度，无法实现高分辨率的成像，本文使用卷积神经网络（Convolutional Neural Networks， CNN）与长短期记忆（Long Short-Term Memory，LSTM）网络相结合实现前视成像中方位向的预测，首先介绍了扫描前视成像信号的类卷积模型及其病态性，利用脉冲压缩以及距离徙动校正对回波信号预处理，输入CNN-LSTM神经网络逐距离单元进行方位向估计。仿真结果表明：算法能有效提高前视成像的方位分辨率，实现前视成像的超分辨。

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孙晓翰 1998年生，硕士研究生。

李凉海 1965年生，硕士，研究员。

张彬 1981年生，硕士，研究员。

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孙晓翰 1998年生，硕士研究生。

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孙晓翰 1998年生，硕士研究生。

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李凉海 1965年生，硕士，研究员。

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李凉海 1965年生，硕士，研究员。

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张彬 1981年生，硕士，研究员。

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张彬 1981年生，硕士，研究员。

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Radar parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名参数值参数名参数值
载频Fc10 GHz波束扫描速度40 （°）/s
带宽B100 M波束主瓣宽度5.37°
时宽Tp1.5 μs距离分辨率0.5 m
采样频率Fs200 M距离范围4 000 m ~ 5 000 m
脉冲重复频率PRF4 000扫描角范围-5°~5°
信噪比0~10 dB扫描积累脉冲数100
), ArticleFig(id=1241060196773056727, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1241060180096504490, language=CN, label=表1, caption=

雷达参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名参数值参数名参数值
载频Fc10 GHz波束扫描速度40 （°）/s
带宽B100 M波束主瓣宽度5.37°
时宽Tp1.5 μs距离分辨率0.5 m
采样频率Fs200 M距离范围4 000 m ~ 5 000 m
脉冲重复频率PRF4 000扫描角范围-5°~5°
信噪比0~10 dB扫描积累脉冲数100
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基于CNN-LSTM神经网络的前视成像算法
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孙晓翰 1 , 李凉海 2 , 张彬 1
遥测遥控 | 人工智能技术 2024,45(2): 29-36
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遥测遥控 | 人工智能技术 2024, 45(2): 29-36
基于CNN-LSTM神经网络的前视成像算法
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孙晓翰1, 李凉海2, 张彬1
作者信息
  • 1北京遥测技术研究所　北京　100076
  • 2中国航天电子技术研究院　北京　100094

    • 孙晓翰 1998年生，硕士研究生。

    李凉海 1965年生，硕士，研究员。

    张彬 1981年生，硕士，研究员。

Forward-looking Imaging Algorithm Based on CNN-LSTM Neural Network
Xiaohan SUN1, Lianghai LI2, Bin ZHANG1
Affiliations
  • 1.Beijing Research Institute of Telemetry, Beijing 100076, China
  • 2.China Academy of Aerospace Electronics Technology, Beijing 100080, China
doi: 10.12347/j.ycyk.20231225001
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摘要
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雷达前视成像作为雷达成像领域的难点与重点，在自动驾驶、导航、精确制导等方面具有广阔的应用前景。传统的前视成像算法受限于天线孔径的宽度，无法实现高分辨率的成像，本文使用卷积神经网络（Convolutional Neural Networks， CNN）与长短期记忆（Long Short-Term Memory，LSTM）网络相结合实现前视成像中方位向的预测，首先介绍了扫描前视成像信号的类卷积模型及其病态性，利用脉冲压缩以及距离徙动校正对回波信号预处理，输入CNN-LSTM神经网络逐距离单元进行方位向估计。仿真结果表明：算法能有效提高前视成像的方位分辨率，实现前视成像的超分辨。

前视成像  /  深度学习  /  卷积神经网络  /  病态性逆问题

As a difficulty and focus in the field of radar imaging, radar forward-looking imaging has broad application prospects in automatic driving, navigation, precision guidance and so on. The traditional forward-looking imaging algorithm is limited by the width of the antenna aperture and cannot achieve high-resolution imaging. In this paper, CNN ( Convolutional Neural Networks )neural network and LSTM ( Long Short-Term Memory ) neural network are combined to realize the prediction of azimuth in forward-looking imaging. Firstly, the convolution-like model of the scanning forward-looking imaging signal and its ill-posedness are introduced. The echo signal is preprocessed by pulse compression and range migration correction, and input into the CNN-LSTM neural network to perform azimuth estimation by range unit. The simulation results show that the algorithm can effectively improve the azimuth resolution of forward-looking imaging and realize the super-resolution of forward-looking imaging.

Forward-looking imaging  /  Deep learning  /  Convolutional neural network  /  Ill-posed inverse problem
孙晓翰, 李凉海, 张彬. 基于CNN-LSTM神经网络的前视成像算法. 遥测遥控, 2024 , 45 (2) : 29 -36 . DOI: 10.12347/j.ycyk.20231225001
Xiaohan SUN, Lianghai LI, Bin ZHANG. Forward-looking Imaging Algorithm Based on CNN-LSTM Neural Network[J]. Journal of Telemetry, Tracking and Command, 2024 , 45 (2) : 29 -36 . DOI: 10.12347/j.ycyk.20231225001
正文
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0　引言
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雷达成像技术是一种利用雷达系统生成目标图像的技术。它通过发射无线电波，接收目标表面反射回来的信号，然后通过分析这些信号生成目标的空间位置、形状和运动信息。雷达成像的工作原理包括发射脉冲或连续波，通过调整雷达波束的方向和形状来扫描感兴趣区域[1]。多普勒锐化技术(Doppler Beam Sharpening, DBS)[2,3]与合成孔径雷达(Synthetic Aperture Radar, SAR)[4-6]是常见的雷达成像技术，前者通过观测平台与目标之间的运动产生的多普勒频移来分辨目标的方位信息，后者通过在雷达平台运动中合成长孔径来提高成像分辨率。雷达成像技术因其在各种天气条件下的全天候性和在复杂环境中的高效性而受到青睐，广泛应用于军事、气象、地质勘探、自动驾驶等领域。
当雷达处在前视位置时，平台的运动方向与波束指向一致，等距离线与等多普勒线平行，DBS与SAR技术同时失效[7]，而一般的实波束前视成像技术受限于雷达的天线孔径宽度，无法实现高分辨成像。各国学者在此领域展开了诸多的探索和研究，提出了多种解决方案。文献[8-12]利用和差测角原理，将单脉冲技术与前视成像结合，提高了方位向的分辨率，但无法精确分辨同一波束内的多个目标，存在一定的缺陷；双基地SAR技术[13-15]，由于其复杂的时空同步、几何构型等问题，使得其在实际应用中存在一定的难度；解卷积成像技术[16-22]的本质是信号还原技术，其将同距离单元回波信号建模为目标散射系数与天线方向图的类卷积模型，通过解卷积运算反演方位向的目标分布函数。
近几年来，随着深度学习的迅速兴起，深度学习网络在逆问题求解中得到广泛应用，如图像超分辨、图像去噪、图像复原等光学图像逆问题，在图像重构质量和工作效率方面均表现优异，成为解决逆问题的主流方法。深度神经网络(Deep Neural Networks, DNN)基于数据驱动通过监督学习的方式自动从数据中学习先验知识，以获得更加适用于观测场景的先验信息。通过网络训练去探索观测数据与重构图像之间复杂的非线性映射关系，自行建立隐式成像模型，以最大限度拟合输入与输出的精确映射关系，具有较强的适应能力。同时，DNN将优化过程和计算压力集中在网络训练阶段，训练完成后，基于DNN的测试过程具有较高的工作效率。因此，深度学习理论为突破当前雷达成像技术的瓶颈提供了全新思路[23,24]。
传统的雷达前视成像算法在收敛速度、计算复杂度和成像分辨率等方面存在一些局限性。本论文致力于探讨一种基于CNN-LSTM神经网络的新型雷达前视成像算法，旨在提高前视成像的分辨率和系统的稳健性。深度学习的引入使得我们能够从大规模数据中学习复杂的目标特征，从而更好地适应不同的场景和目标类型。
1　扫描前视成像模型
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1.1　静止的几何模型
扫描前视成像的静止几何模型如图1所示，图1(a)为雷达扫描过程图，图1(b)给出了静止雷达与点目标的几何关系图。如图1(a)所示，雷达平台与目标保持相对静止。
如图1(a)，假设机载雷达平台处于O'位置，目标在XOY平面，平台垂直高度为H，天线波束以角速度ϖ沿逆时针方向对目标进行扫描。雷达天线波束初始方位角为θ0，俯仰角为φ0。如图1(b)，以点P为例，t=0时刻，机载平台与目标之间的方位夹角为θ0，距离为R0；在t 时刻，机载平台与目标之间的方位向夹角变为θt，但由于目标始终在天线波束扫描范围内，瞬时斜距Rt仍为R0，表示为Rt=R0。
1.2　回波模型
对于前视成像，一般采用线性调频信号：
其中，τ为发射信号的快时间，Tr为脉宽，γ为调频率，rect(u)为矩形信号。
以点P为例进行回波分析，初始作用距离为R0，目标反射系数为σ0，可得回波为：
随着波束的扫描，发射信号经过点P的反射接收得到的回波可以表示为：
其中，t为慢时间，t0为波束中心扫过P点的时间，可以看出，方位向回波的强度受到天线方向图的调制，对回波进行下变频后可得：
1.3　方位向类卷积模型
由式(5)可知，一次前视扫描的回波经过下变频，并进行脉冲压缩后距离向固定，同距离单元的方位向回波可建模为目标散射系数与天线方向图的卷积，方位向回波为：
其中，θ为扫描波束的方位角，扫描中雷达按照一定的脉冲重复频率发射脉冲信号，故收到的方位向回波为离散信号，同时将天线方向图和目标散射系数离散化可得：
式中，M，L，N分别为回波、天线方向图和目标散射系数的采样点数，实际的物理过程中存在噪声，所以方位向回波的类卷积模型可以写为：
将其改写为矩阵离散化形式为：
根据公式(9)，前视扫描回波可以视为目标散射系数和天线方向图的卷积并叠加接收机噪声的结果，对目标散射系数的求解是一个求逆过程，在时域上分析，雷达天线方向图所确定的卷积矩阵本身就是一个病态矩阵，直接利用最小二乘法求解得到的值与真实值的差距很大，该方程是一个病态方程。从频域上分析，首先对公式(8)进行傅里叶变换可得：
对公式(10)直接进行频域反卷积运算可得：
可以直接求得结果，然而实际上，一般的天线方向图为sinc函数，其傅里叶变换为带限信号，截止频率以外的幅度趋于零，会导致高频区域的噪声被无限放大，使得反卷积结果不准确，并不能直接求解。该问题是一个病态问题。
2　基于CNN-LSTM神经网络的前视成像算法
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2.1　雷达成像与神经网络
在雷达前视领域，传统算法存在一定的局限性，而以数据驱动为核心的深度学习算法为雷达前视成像处理提供了新的思路。在上节所述问题中，在脉压处理后，回波信号的距离向固定，方位向视为天线方向图与目标散射系数的卷积，一般的天线方向图为辛格函数，其构成的卷积矩阵为奇异矩阵，所以方位向回波与目标散射系数存在一定的非线性关系，利用CNN-LSTM神经网络去估计和预测，探索方位向序列中包含的复杂的非线性关系，从而得到方位向目标散射系数。
2.2　神经网络结构
在图2所示模型中，将采集的回波数据经过脉冲压缩处理后，逐距离单元输入CNN-LSTM神经网络，利用CNN层与LSTM层提取隐含在方位向回波中的目标散射系数信息，经过全连接层变换到图像域，通过反向传播算法进行权值更新，最终完成该距离单元的方位向目标散射系数识别。
本文所用的神经网络共两个部分，特征提取部分和序列回归部分，输入数据规模为100*1*1，由两个卷积层，两个池化层，一个LSTM层组成，利用卷积层提取高维特征，LSTM层提取时域特征。
一维的卷积层的输入输出关系为：
其中，y为输出矢量，x，w分别为输入矢量和卷积核，b表示为偏置矢量，σ(·)为线性整流函数(Linear Rectification Function, ReLU)。
利用最大池化层压缩数据信息，降低维度，计算公式为：
经过特征提取后，通过全连接的方式连接到回归层，全连接层的公式为：
图2所示为神经网络的结构，其中卷积层的时间复杂度为O(M2·K2·Cin·Cout)，其中M为特征图边长，K为卷积核的边长，C为输入输出的通道数。LSTM层的时间复杂度为O(4·T·h2+4·T·n·h)，其中，T为输入序列长度，n为特征维度，h为隐含状态维度。如图，神经网络有两个卷积层，一个LSTM层，故该算法的时间复杂度为：
2.3　网络训练方法
在给定场景中生成多个目标点，其位置和目标散射系数均服从高斯分布，仿真生成目标在前视区域下的回波数据，对回波数据进行脉冲压缩处理使其距离向固定，得到前视实波束成像，逐距离单元输入神经网络，输出预测方位向目标散射系数，仿真点位置与仿真的目标散射系数为真实值。
网络训练模式为监督训练，使用均方根误差函数(Root Mean Squared Error, RMSE)作为损失函数，表达式为：
其中yi是预测值，是真实值，N为序列元素个数。
训练中采用SGDM梯度下降算法更新权值，更新公式为：
其中，V为动量因子，W为网络权值，ΔT为梯度，η为动量系数，α为学习率。本文网络的学习率为1E-5，每800次迭代下降一次，学习率下降因子为0.1。
2.4　算法流程
综上所述，本文提出了基于CNN-LSTM神经网络的前视成像算法，该算法对接收后的信号进行距离向处理，逐距离单元输入神经网络，实现方位向的精准估计。
雷达前视成像的CNN-LSTM算法流程图如图3所示，算法训练主要步骤如下：
① 对训练集数据进行脉冲压缩处理，实现距离向上的超分辨；
② 逐距离门输入神经网络，输出方位向预测结果；
③ 计算损失函数，利用反向传播机制与SGDM梯度下降算法更新神经网络权值；
④ 经过一定次数的迭代，使损失函数最小；
⑤ 利用测试集对算法功能性进行验证；
⑥ 训练完成。
2.5　仿真结果及分析
为了验证本文所提基于CNN-LSTM神经网络的前视成像算法的有效性，本节分别进行了点目标以及场景的前视成像仿真实验。为了衡量算法对实孔径成像的分辨率改善程度，本文定义超分辨系数为：
其中，ΔL为实孔径雷达的前视成像分辨率，ΔLreal为超分辨算法的分辨率。
在表1给定的雷达参数下，在成像区域中放置了10个点目标，距离和方位分别为：
图4给出了仿真的实波束成像图，可以看出，同一距离单元内的多个点目标的回波发生了混叠现象，无法进行高分辨成像，这是因为点目标之间的角度差小于波束宽度，实波束成像算法失效，此时成像分辨率约为θ×R=421.76 m。
图5给出了在不同信噪比下的基于CNN-LSTM神经网络算法处理后的成像结果图。可以看出：在0~10 dB的信噪比区间下，图像均有明显目标亮点，可以清晰地分辨；其中，在0 dB条件下存在幅度较小的噪点。在10 dB的信噪比条件下时，目标点清晰可见且没有明显噪点，有较好的噪声抑制能力。
为了进一步定量分析不同信噪比条件下算法的成像效果，进行了100次蒙特卡洛实验，统计得在不同信噪比下的均方根误差(Root Mean Square Error, RMSE)，其定义为：
其中，K为蒙特卡洛实验次数，图6给出了该算法在不同SNR条件下的均方根误差的变化曲线。从图中可以看出，随着SNR的提升，RMSE大幅度降低，在SNR>9 dB时趋于平稳，得到最佳成像效果。
进一步分析算法的方位向分辨率，图7给出了在10 dB条件下某一距离单元的两种成像结果对比图。可以看出：图7(a)实波束成像对同个波束内多个点成像失效，四个目标的方位向信息混叠，无法分辨其位置与幅度。图7(b)中可以看出：基于CNN-LSTM算法的扫描方位向分辨结果出现四个峰值，并与实际波达方向一致，其中，中间两点的角度为-0.1与0.1，证明该算法可以对目标角度大于0.1°的目标点进行分辨，分辨率约为θ×R=15.7 m。
为进一步验证CNN-LSTM网络模型的成像适用性，选用一幅高分辨SAR图像作为仿真场景，生成雷达回波信号，并进行成像处理，如图8所示。图8(a)为实波束成像，图8(b)为本文所提算法的成像结果，图8(c)为仿真所用的高清图像。本文所提算法的成像结果中海岸分辨明显，强散射目标清晰可见，前视成像效果较好。
为进一步验证CNN-LSTM网络模型的成像适用性，选用一副高分辨SAR图像作为仿真场景，生成雷达回波信号，并用多种算法进行成像处理，如图8所示，图8(a)为经过脉压处理的实波束成像，图8(b)为仿真所用的高清图像，图8(c)、图8(d)、图8(e)分别为SNR=10 dB情况下三种不同的前视成像算法，可以看出，基于Tikhonov正则化的传统解卷积算法对噪声敏感，极易受到噪声干扰，且图像存在混叠现象；单脉冲前视成像算法在面对非稀疏场景时存在散焦现象，边界轮廓不清晰；而本文所提算法的成像结果中海岸分辨明显，强散射目标清晰可见，同时对噪声有着一定的抑制能力，前视成像效果较好。
成像距离为4 500 m，波束宽度为5.37°，根据公式：
可得实波束分辨率约为421.76 m。
扫描解卷积成像模型中，扫描角范围为[-5°，5°]，计算可得方位向扫描宽度为1 570.8 m，匀速扫描100个脉冲，理论分辨率为15.7 m，可得该模型下的超分辨系数为：
该成像算法的超分辨系数为26.85。该结果与点目标仿真所得超分辨系数一致。
通过上述仿真实验，分析了静止平台前视成像模式下各种基于CNN-LSTM的超分辨成像方法的成像效果和分辨率改善情况，对不同信噪比情况下的成像效果进行了对比，验证了基于CNN-LSTM的前视成像方法能够在远距低信噪比环境下进一步提高方位向分辨率。
3　结束语
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前视成像的传统算法中，实波束成像受限于孔径宽度回波易发生混叠现象，分辨率较低，而解卷积前视成像在面对简单场景时可以成像，但面对复杂场景时成像效果不佳，本文针对解卷积前视成像的病态性进行了分析，提出了一种基于CNN-LSTM神经网络的前视成像算法。该算法通过学习仿真方位向回波与目标散射系数的非线性关系来预测场景的方位向目标分布函数，仿真结果表明：该算法可以有效提高前视成像的方位分辨率。
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doi: 10.12347/j.ycyk.20231225001
  • 接收时间：2023-12-25
  • 首发时间：2026-03-18
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  • 收稿日期：2023-12-25
  • 修回日期：2024-01-03
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    1北京遥测技术研究所　北京　100076
    2中国航天电子技术研究院　北京　100094
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