技术领域Technical Field
本发明涉及雷达技术领域，尤其涉及一种雷达干扰的抑制方法、装置及存储介质。The present invention relates to the field of radar technology, and in particular to a method, device and storage medium for suppressing radar interference.
背景技术Background Art
车载毫米波雷达(automotivemillimeterwaveradar)是一种专用于感知外界环境、辅助高级驾驶辅助系统根据道路环境实时产生必要的驾驶指令的传感器。和其它相似传感器如照相机、激光雷达相比，车载毫米波雷达具有其全天时、全天候的工作特性，可以获得目标的距离、速度和角度等有用信息，且造价低廉，是一类重要的民用雷达系统。同时，因为芯片产业的发展，多输入多输出(MIMO)雷达系统成本显著降低且因为其具有角度估计的能力，对于解速度模糊具有重大意义。然而，因为车载毫米波雷达所用带宽被限制在77-81GHz，所以车载毫米波雷达之间的相互干扰不可避免。因为干扰信号是直接到达雷达接受天线的，中间没有经过目标的反射，所以能量较有用信号往往高出20-30dB，它会显著降低回波的信干噪比，淹没有用回波信号，导致整个图像呈现压制式污染，使RD图像纹理完全不可见。Automotive millimeter wave radar is a sensor dedicated to sensing the external environment and assisting the advanced driver assistance system to generate necessary driving instructions in real time according to the road environment. Compared with other similar sensors such as cameras and laser radars, automotive millimeter wave radars have the characteristics of working all day and all weather, can obtain useful information such as the distance, speed and angle of the target, and are low-cost, making them an important type of civilian radar system. At the same time, due to the development of the chip industry, the cost of multiple-input multiple-output (MIMO) radar systems has been significantly reduced, and because of its ability to estimate angles, it is of great significance for resolving speed ambiguity. However, because the bandwidth used by automotive millimeter wave radars is limited to 77-81GHz, mutual interference between automotive millimeter wave radars is inevitable. Because the interference signal directly reaches the radar receiving antenna without being reflected by the target in the middle, the energy is often 20-30dB higher than the useful signal, which will significantly reduce the signal-to-noise ratio of the echo, drown out the useful echo signal, and cause the entire image to present a suppressed pollution, making the RD image texture completely invisible.
目前干扰检测的方法主要依靠能量的变化，一般射频干扰的能量会比有用信号的能量高20至40dB，所以可以用能量门限检测的方法对干扰的存在与否进行检测。这种方法虽然计算量小且实现方法简单，但并不适用于干扰能量非标准和干扰持续时间较长等特殊情况，尤其不适用于对目标估计精度要求较高的情况。At present, the interference detection method mainly relies on the change of energy. Generally, the energy of RF interference is 20 to 40 dB higher than that of useful signals, so the energy threshold detection method can be used to detect the presence of interference. Although this method has a small amount of calculation and a simple implementation method, it is not suitable for special cases such as non-standard interference energy and long duration of interference, especially for situations with high requirements for target estimation accuracy.
发明内容Summary of the invention
本发明提供了一种雷达干扰的抑制方法、装置及存储介质，旨在有效解决现有技术中对雷达干扰信号进行检测时，存在目标信号评估精度较低的技术问题，现有技术不适用于干扰能量非标准以及干扰持续时间较长的雷达信号。The present invention provides a radar interference suppression method, device and storage medium, aiming to effectively solve the technical problem of low target signal evaluation accuracy when detecting radar interference signals in the prior art. The prior art is not suitable for radar signals with non-standard interference energy and long interference duration.
根据本发明的一方面，本发明提供一种雷达干扰的抑制方法，所述抑制方法包括：According to one aspect of the present invention, the present invention provides a method for suppressing radar interference, the suppression method comprising:
通过短傅里叶变换将雷达回波信号由时域转换到时频域，根据所述雷达回波信号中的目标信号在时频域的低秩特性构建所述目标信号的秩函数，根据雷达回波信号中的干扰信号在时域的稀疏特性，用范数函数约束所述干扰信号；The radar echo signal is converted from the time domain to the time-frequency domain by short Fourier transform, a rank function of the target signal in the radar echo signal is constructed according to the low rank characteristic of the target signal in the time-frequency domain, and the interference signal in the radar echo signal is constrained by a norm function according to the sparse characteristic of the interference signal in the time domain;
基于所述秩函数和所述范数函数构建第一目标函数，并基于所述雷达回波信号构建第一约束函数，通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数，根据所述第二目标函数和所述第二约束函数构建干扰抑制模型；Constructing a first objective function based on the rank function and the norm function, and constructing a first constraint function based on the radar echo signal, converting the first objective function and the first constraint function into a second objective function and a second constraint function through a convex relaxation optimization method, and constructing an interference suppression model according to the second objective function and the second constraint function;
通过交替方向乘子法对所述干扰抑制模型进行求解，以得到干扰抑制后的真实目标信号。The interference suppression model is solved by an alternating direction multiplier method to obtain a real target signal after interference suppression.
进一步地，所述通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数包括：Further, converting the first objective function and the first constraint function into a second objective function and a second constraint function by using a convex relaxation optimization method comprises:
用虚拟目标信号和矩阵字典表示所述目标信号；Representing the target signal using a virtual target signal and a matrix dictionary;
将所述秩函数转换为基于所述虚拟目标信号生成的虚拟目标信号范数，将所述范数函数转换为干扰信号范数，根据所述虚拟目标信号范数和所述干扰信号范数生成所述第二目标函数；Converting the rank function into a virtual target signal norm generated based on the virtual target signal, converting the norm function into an interference signal norm, and generating the second target function according to the virtual target signal norm and the interference signal norm;
基于所述雷达回波信号、所述干扰信号、所述虚拟目标信号和所述矩阵字典生成所述第二约束函数。The second constraint function is generated based on the radar echo signal, the interference signal, the virtual target signal and the matrix dictionary.
进一步地，所述基于所述秩函数和所述范数函数构建第一目标函数包括：Further, constructing a first objective function based on the rank function and the norm function includes:
根据下式构建所述第一目标函数：The first objective function is constructed according to the following formula:
其中，S表示所述目标信号，M表示所述干扰信号，rank()表示求秩函数，λ表示第一超参数，||||0表示l0范数，min()表示取最小值。Wherein, S represents the target signal, M represents the interference signal, rank() represents the rank function, λ represents the first hyperparameter, ||||0 represents the l0 norm, and min() represents taking the minimum value.
所述基于所述雷达回波信号构建第一约束函数包括：The constructing a first constraint function based on the radar echo signal comprises:
根据下式构建所述约束函数：The constraint function is constructed according to the following formula:
其中，Y表示所述雷达回波信号，S表示所述目标信号，M表示所述干扰信号，δ表示噪声容限，||||F表示张量的Frobenius范数。Wherein, Y represents the radar echo signal, S represents the target signal, M represents the interference signal, δ represents the noise margin, and ||||F represents the Frobenius norm of the tensor.
进一步地，所述根据所述虚拟目标信号范数和所述干扰信号范数生成所述第二目标函数包括：Further, generating the second objective function according to the virtual target signal norm and the interference signal norm includes:
根据下式构建所述第二目标函数：The second objective function is constructed according to the following formula:
其中，S′表示所述虚拟目标信号，M表示所述干扰信号，λ表示第一超参数，||||l表示l2,1范数或l1范数，||||1表示l1范数，min()表示取最小值。Among them, S′ represents the virtual target signal, M represents the interference signal, λ represents the first hyperparameter, ||||l represents the l2,1 norm or the l1 norm, ||||1 represents the l1 norm, and min() represents taking the minimum value.
所述基于所述雷达回波信号、所述干扰信号、所述虚拟目标信号和所述矩阵字典生成所述第二约束函数包括：The generating the second constraint function based on the radar echo signal, the interference signal, the virtual target signal and the matrix dictionary comprises:
根据下式构建所述第二约束函数：The second constraint function is constructed according to the following formula:
其中，Y表示所述雷达回波信号，Dbeat表示所述矩阵字典，S′表示所述虚拟目标信号，M表示所述干扰信号，δ表示噪声容限，||||F表示张量的Frobenius范数。Wherein, Y represents the radar echo signal, Dbeat represents the matrix dictionary, S′ represents the virtual target signal, M represents the interference signal, δ represents the noise margin, and ||||F represents the Frobenius norm of the tensor.
进一步地，所述通过交替方向乘子法对所述干扰抑制模型进行求解包括：Further, solving the interference suppression model by an alternating direction multiplier method includes:
根据所述第二目标函数和所述第二约束函数构建增广拉格朗日函数；constructing an augmented Lagrangian function according to the second objective function and the second constraint function;
当所述虚拟目标信号范数为l2,1范数时，构建软阈值函数和范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解；When the norm of the virtual target signal is a l2,1 norm, constructing a soft threshold function and a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method;
当所述虚拟目标信号范数为l1范数时，构建范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解。When the norm of the virtual target signal is the l1 norm, a norm threshold function is constructed and the augmented Lagrangian function is solved by the alternating direction multiplier method.
进一步地，所述根据所述第二目标函数和所述第二约束函数构建增广拉格朗日函数包括：Further, constructing an augmented Lagrangian function according to the second objective function and the second constraint function includes:
以虚拟目标信号、干扰信号、拉格朗日变量和超参数为变量，根据所述第二目标函数和所述第二约束函数构建所述增广拉格朗日函数。The augmented Lagrangian function is constructed according to the second objective function and the second constraint function, with the virtual target signal, the interference signal, the Lagrangian variable and the hyperparameter as variables.
可选地，所述当所述虚拟目标信号范数为l2,1范数时，构建软阈值函数和范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解包括：Optionally, when the norm of the virtual target signal is a l2,1 norm, constructing a soft threshold function and a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method comprises:
针对所述虚拟目标信号范数进行多次迭代，其中，在每次迭代时执行如下操作：Perform multiple iterations on the virtual target signal norm, wherein the following operations are performed in each iteration:
基于所述软阈值函数得到更新的虚拟目标信号闭式解；Obtaining an updated closed-form solution of the virtual target signal based on the soft threshold function;
根据所述虚拟目标信号闭式解和所述范数阈值函数得到干扰信号闭式解；Obtaining a closed-form solution for an interference signal according to the closed-form solution for the virtual target signal and the norm threshold function;
根据所述虚拟目标信号闭式解和所述干扰信号闭式解得到拉格朗日变量闭式解；Obtaining a Lagrangian variable closed-form solution according to the virtual target signal closed-form solution and the interference signal closed-form solution;
基于所述虚拟目标信号闭式解和所述干扰信号闭式解计算终止条件函数；Calculate a termination condition function based on the virtual target signal closed-form solution and the interference signal closed-form solution;
当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。When the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, the iteration is stopped.
可选地，所述当所述虚拟目标信号范数为l1范数时，构建范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解包括：Optionally, when the norm of the virtual target signal is a l1 norm, constructing a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method comprises:
针对所述虚拟目标信号范数进行多次迭代，其中，在每次迭代时执行如下操作：Perform multiple iterations on the virtual target signal norm, wherein the following operations are performed in each iteration:
基于所述范数阈值函数得到更新的虚拟目标信号闭式解；Obtaining an updated closed-form solution of the virtual target signal based on the norm threshold function;
根据所述虚拟目标信号闭式解和所述范数阈值函数得到干扰信号闭式解；Obtaining a closed-form solution for an interference signal according to the closed-form solution for the virtual target signal and the norm threshold function;
根据所述虚拟目标信号闭式解和所述干扰信号闭式解得到拉格朗日变量闭式解；Obtaining a Lagrangian variable closed-form solution according to the virtual target signal closed-form solution and the interference signal closed-form solution;
基于所述虚拟目标信号闭式解和所述干扰信号闭式解计算终止条件函数；Calculate a termination condition function based on the virtual target signal closed-form solution and the interference signal closed-form solution;
当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。When the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, the iteration is stopped.
进一步地，所述方法还包括：Furthermore, the method further comprises:
在所述得到干扰抑制后的真实目标信号之后，通过逆短时傅里叶变换将所述真实目标信号转换为时域信号。After obtaining the interference-suppressed real target signal, the real target signal is converted into a time domain signal by inverse short-time Fourier transform.
根据本发明的另一方面，本发明还提供了一种雷达干扰的抑制装置，所述装置包括：According to another aspect of the present invention, the present invention also provides a radar interference suppression device, the device comprising:
函数构建模块，用于通过短傅里叶变换将雷达回波信号由时域转换到时频域，根据所述雷达回波信号中的目标信号在时频域的低秩特性构建所述目标信号的秩函数，根据雷达回波信号中的干扰信号在时域的稀疏特性，用范数函数约束所述干扰信号；A function construction module, used to convert the radar echo signal from the time domain to the time-frequency domain through short Fourier transform, construct a rank function of the target signal in the radar echo signal according to the low rank characteristics of the target signal in the time-frequency domain, and constrain the interference signal with a norm function according to the sparse characteristics of the interference signal in the radar echo signal in the time domain;
模型构建模块，用于基于所述秩函数和所述范数函数构建第一目标函数，并基于所述雷达回波信号构建第一约束函数，通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数，根据所述第二目标函数和所述第二约束函数构建干扰抑制模型；A model construction module, used to construct a first objective function based on the rank function and the norm function, and to construct a first constraint function based on the radar echo signal, convert the first objective function and the first constraint function into a second objective function and a second constraint function through a convex relaxation optimization method, and construct an interference suppression model according to the second objective function and the second constraint function;
计算模块，用于通过交替方向乘子法对所述干扰抑制模型进行求解，以得到干扰抑制后的真实目标信号。The calculation module is used to solve the interference suppression model by an alternating direction multiplier method to obtain a real target signal after interference suppression.
根据本发明的另一方面，本发明还提供了一种存储介质，所述存储介质中存储有多条指令，所述指令适于由处理器加载以执行如上所述的任一雷达干扰的抑制方法。According to another aspect of the present invention, the present invention further provides a storage medium, wherein a plurality of instructions are stored in the storage medium, and the instructions are suitable for being loaded by a processor to execute any radar interference suppression method as described above.
通过本发明中的上述实施例中的一个实施例或多个实施例，至少可以实现如下技术效果：Through one or more of the above embodiments of the present invention, at least the following technical effects can be achieved:
在本发明所公开的技术方案中，利用短时傅里叶变换将雷达回波信号转移到时频域，分析干扰信号和目标信号的不同性质，构造干扰抑制问题来分离具有稀疏特性的干扰信号和具有低秩特性的目标信号。引入矩阵字典作为具有低秩特性的目标信号的向量基，在优化问题中以正则项的形式约束有用目标信号，矩阵字典能够有效降低计算复杂度，简化算法，然后通过交替方向乘子法求解模型。该干扰抑制方法适用于干扰持续时间较长、干扰数目较多的多种应用场景，较传统方法能明显提高抑制干扰信号的精确度。In the technical solution disclosed in the present invention, the radar echo signal is transferred to the time-frequency domain by using short-time Fourier transform, the different properties of the interference signal and the target signal are analyzed, and the interference suppression problem is constructed to separate the interference signal with sparse characteristics and the target signal with low-rank characteristics. A matrix dictionary is introduced as the vector basis of the target signal with low-rank characteristics, and the useful target signal is constrained in the form of a regular term in the optimization problem. The matrix dictionary can effectively reduce the computational complexity, simplify the algorithm, and then solve the model by the alternating direction multiplication method. This interference suppression method is suitable for a variety of application scenarios with long interference duration and a large number of interferences, and can significantly improve the accuracy of suppressing interference signals compared with traditional methods.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
下面结合附图，通过对本发明的具体实施方式详细描述，将使本发明的技术方案及其它有益效果显而易见。The technical solutions and other beneficial effects of the present invention will be made apparent by describing in detail the specific embodiments of the present invention in conjunction with the accompanying drawings.
图1为本发明实施例提供的一种雷达干扰的抑制方法的步骤流程图；FIG1 is a flowchart of a method for suppressing radar interference provided by an embodiment of the present invention;
图2为信号在时频域具有不同特性的示意图；FIG2 is a schematic diagram showing that a signal has different characteristics in the time-frequency domain;
图3为干扰抑制后的真实目标信号示意图和距离多普勒图；FIG3 is a schematic diagram of a real target signal and a range Doppler diagram after interference suppression;
图4为本发明实施例提供的一种雷达干扰的抑制装置的结构示意图。FIG. 4 is a schematic diagram of the structure of a radar interference suppression device provided by an embodiment of the present invention.
具体实施方式DETAILED DESCRIPTION
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述。显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域技术人员在没有作出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。The technical scheme in the embodiment of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.
在本发明的描述中，需要说明的是，除非另有明确的规定和限定，本文中术语“和/或”，仅仅是一种描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。另外，本文中字符“/”，在不做特别说明的情况下，一般表示前后关联对象是一种“或”的关系。In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the term "and/or" herein is merely a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and/or B may represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character "/" herein, unless otherwise specified, generally indicates that the associated objects before and after are in an "or" relationship.
图1所示为本发明实施例所提供的雷达干扰的抑制方法的步骤流程图，根据本发明的一方面，本发明提供一种雷达干扰的抑制方法，所述抑制方法包括：FIG1 is a flowchart of a method for suppressing radar interference provided by an embodiment of the present invention. According to one aspect of the present invention, the present invention provides a method for suppressing radar interference, and the method for suppressing radar interference includes:
步骤101：通过短傅里叶变换将雷达回波信号由时域转换到时频域，根据所述雷达回波信号中的目标信号在时频域的低秩特性构建所述目标信号的秩函数，根据雷达回波信号中的干扰信号在时域的稀疏特性，用范数函数约束所述干扰信号；Step 101: converting the radar echo signal from the time domain to the time-frequency domain by short Fourier transform, constructing a rank function of the target signal in the radar echo signal according to the low rank characteristic of the target signal in the time-frequency domain, and constraining the interference signal with a norm function according to the sparse characteristic of the interference signal in the radar echo signal in the time domain;
步骤102：基于所述秩函数和所述范数函数构建第一目标函数，并基于所述雷达回波信号构建第一约束函数，通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数，根据所述第二目标函数和所述第二约束函数构建干扰抑制模型；Step 102: constructing a first objective function based on the rank function and the norm function, and constructing a first constraint function based on the radar echo signal, converting the first objective function and the first constraint function into a second objective function and a second constraint function through a convex relaxation optimization method, and constructing an interference suppression model according to the second objective function and the second constraint function;
步骤103：通过交替方向乘子法对所述干扰抑制模型进行求解，以得到干扰抑制后的真实目标信号。Step 103: Solve the interference suppression model by using an alternating direction multiplier method to obtain a real target signal after interference suppression.
为了抑制干扰，并保留更多有用信号，需要根据干扰与有用信号的特性寻找特定基来分离有用信号和干扰。本发明对于使用调频连续波(Frequency-ModulatedContinuousWave，简称为FMCW)的车载毫米波雷达之间的相互干扰进行联合稀疏低秩分析，提供一种雷达干扰的抑制方法。In order to suppress interference and retain more useful signals, it is necessary to find a specific basis to separate useful signals from interference according to the characteristics of interference and useful signals. The present invention performs joint sparse low-rank analysis on the mutual interference between vehicle-mounted millimeter-wave radars using frequency-modulated continuous wave (FMCW), and provides a method for suppressing radar interference.
利用短时傅里叶变换(Short Time Fourier Transform，简称为STFT)将单一chirp接收信号转移到时频域之后，分析干扰和有用信号在时频域的特殊低秩和稀疏性质，构造两个干扰抑制问题来分离具有稀疏特性的干扰信号和具有低秩特性的目标信号。After transferring the single chirp received signal to the time-frequency domain using Short Time Fourier Transform (STFT), the special low-rank and sparse properties of the interference and useful signals in the time-frequency domain are analyzed, and two interference suppression problems are constructed to separate the interference signal with sparse characteristics and the target signal with low-rank characteristics.
引入字典作为具有低秩特性的有用目标信号的向量基，在优化问题中以正则项的形式约束有用目标回波信号。通过交替方向乘子法(Alternating Direction Method ofMultipliers，简称为ADMM)解决上述优化问题，获得干扰抑制的结果。本发明创新地将车载雷达信号转移到时频域之后根据干扰和有用回波的特殊性质对二者进行分离，面对干扰持续时间较长、干扰数目较多的情况具有更大的潜力，且干扰抑制效果较传统方法更好。A dictionary is introduced as a vector basis of useful target signals with low-rank characteristics, and the useful target echo signals are constrained in the form of regular terms in the optimization problem. The above optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM) to obtain the result of interference suppression. The present invention innovatively transfers the vehicle-mounted radar signal to the time-frequency domain and then separates the interference and useful echo according to their special properties. It has greater potential in the case of long interference duration and large number of interferences, and the interference suppression effect is better than the traditional method.
以下对上述步骤101～103进行具体描述。The above steps 101 to 103 are described in detail below.
步骤101：通过短傅里叶变换将雷达回波信号由时域转换到时频域，根据所述雷达回波信号中的目标信号在时频域的低秩特性构建所述目标信号的秩函数，根据雷达回波信号中的干扰信号在时域的稀疏特性，用范数函数约束所述干扰信号。Step 101: convert the radar echo signal from the time domain to the time-frequency domain through short Fourier transform, construct a rank function of the target signal in the radar echo signal according to the low rank characteristics of the target signal in the time-frequency domain, and constrain the interference signal with a norm function according to the sparse characteristics of the interference signal in the radar echo signal in the time domain.
示例性地，使用短时傅里叶变换，将接收信号从时域转移到时频域。从时频域可以看出，图2为信号在时频域具有不同特性的示意图，图(a)代表雷达回波信号在时频域的图像，包括干扰信号和有用信号。图(b)代表目标信号在时频域的图像，目标信号在时频谱图中表现为水平线，目标信号经过下变频和去斜操作之后会保持一个较为恒定的频率。图(c)代表干扰信号在时频域的图像，在时频谱图中则表现为V形的图案，干扰的频率与时间呈现线性关系，并能量较强。因此，根据所述雷达回波信号中的目标信号在时频域的低秩特性构建所述目标信号的秩函数，根据雷达回波信号中的干扰信号在时域的稀疏特性，用范数函数约束所述干扰信号。Exemplarily, a short-time Fourier transform is used to transfer the received signal from the time domain to the time-frequency domain. As can be seen from the time-frequency domain, Figure 2 is a schematic diagram of a signal having different characteristics in the time-frequency domain, and Figure (a) represents the image of the radar echo signal in the time-frequency domain, including an interference signal and a useful signal. Figure (b) represents the image of the target signal in the time-frequency domain, and the target signal is shown as a horizontal line in the time-frequency spectrum diagram. After the target signal is down-converted and de-skewing, it will maintain a relatively constant frequency. Figure (c) represents the image of the interference signal in the time-frequency domain, which is shown as a V-shaped pattern in the time-frequency spectrum diagram. The frequency of the interference is linearly related to time, and the energy is strong. Therefore, the rank function of the target signal is constructed according to the low-rank characteristics of the target signal in the radar echo signal in the time-frequency domain, and the interference signal in the radar echo signal is constrained by a norm function according to the sparse characteristics of the interference signal in the time domain.
步骤102：基于所述秩函数和所述范数函数构建第一目标函数，并基于所述雷达回波信号构建第一约束函数，通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数，根据所述第二目标函数和所述第二约束函数构建干扰抑制模型。Step 102: construct a first objective function based on the rank function and the norm function, and construct a first constraint function based on the radar echo signal, convert the first objective function and the first constraint function into a second objective function and a second constraint function through a convex relaxation optimization method, and construct an interference suppression model according to the second objective function and the second constraint function.
示例性地，从时频谱图可知，目标信号在时频谱图中具有低秩特征，干扰信号在时频域则呈现稀疏性。基于这两条特征，提出一个干扰抑制模型来消除干扰对有用目标回波的影响。如果直接基于第一目标函数和第一约束函数建立模型，则为非凸问题，不能得出准确解，需要通过凸松弛优化方法将不可解的第一目标函数和第一约束函数进行数据处理，松弛为凸问题，转换为可解的第二目标函数和第二约束函数，进而建立干扰抑制模型。For example, it can be seen from the time-frequency spectrum that the target signal has a low-rank feature in the time-frequency spectrum, and the interference signal is sparse in the time-frequency domain. Based on these two characteristics, an interference suppression model is proposed to eliminate the influence of interference on useful target echoes. If the model is established directly based on the first objective function and the first constraint function, it is a non-convex problem and no accurate solution can be obtained. It is necessary to use the convex relaxation optimization method to process the unsolvable first objective function and the first constraint function, relax them into a convex problem, and convert them into a solvable second objective function and a second constraint function, and then establish an interference suppression model.
步骤103：通过交替方向乘子法对所述干扰抑制模型进行求解，以得到干扰抑制后的真实目标信号。Step 103: Solve the interference suppression model by using an alternating direction multiplier method to obtain a real target signal after interference suppression.
示例性地，示例性地，通过交替方向乘子法解决上述优化问题，获得干扰抑制的结果。其中，在求解时，可以选择不同的范数进行求解，具体根据实际应用的需求确定选择的范数类型。Exemplarily, the above optimization problem is solved by an alternating direction multiplier method to obtain the interference suppression result. When solving the problem, different norms can be selected for solving, and the selected norm type is determined according to the needs of the actual application.
进一步地，所述通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数包括：Further, converting the first objective function and the first constraint function into a second objective function and a second constraint function by using a convex relaxation optimization method comprises:
用虚拟目标信号和矩阵字典表示所述目标信号；Representing the target signal using a virtual target signal and a matrix dictionary;
将所述秩函数转换为基于所述虚拟目标信号生成的虚拟目标信号范数，将所述范数函数转换为干扰信号范数，根据所述虚拟目标信号范数和所述干扰信号范数生成所述第二目标函数；Converting the rank function into a virtual target signal norm generated based on the virtual target signal, converting the norm function into an interference signal norm, and generating the second target function according to the virtual target signal norm and the interference signal norm;
基于所述雷达回波信号、所述干扰信号、所述虚拟目标信号和所述矩阵字典生成所述第二约束函数。The second constraint function is generated based on the radar echo signal, the interference signal, the virtual target signal and the matrix dictionary.
示例性地，该步骤主要是基于凸松弛优化方法处理数据。其中，凸松弛算法是一种常用的优化算法，核心思想是将原问题转化为一个凸问题，然后通过松弛约束来逐步逼近原问题的最优解。在凸松弛算法中，凸问题是指目标函数为凸函数,约束条件为凸集合的优化问题。Exemplarily, this step mainly processes data based on the convex relaxation optimization method. Among them, the convex relaxation algorithm is a commonly used optimization algorithm. The core idea is to transform the original problem into a convex problem, and then gradually approach the optimal solution of the original problem by relaxing the constraints. In the convex relaxation algorithm, a convex problem refers to an optimization problem in which the objective function is a convex function and the constraint condition is a convex set.
进一步地，所述基于所述秩函数和所述范数函数构建第一目标函数包括：Further, constructing a first objective function based on the rank function and the norm function includes:
根据下式构建所述第一目标函数：The first objective function is constructed according to the following formula:
其中，S表示所述目标信号，M表示所述干扰信号，rank()表示求秩函数，λ表示第一超参数，||||0表示l0范数，min()表示取最小值。Wherein, S represents the target signal, M represents the interference signal, rank() represents the rank function, λ represents the first hyperparameter, ||||0 represents the l0 norm, and min() represents taking the minimum value.
所述基于所述雷达回波信号构建第一约束函数包括：The constructing a first constraint function based on the radar echo signal comprises:
根据下式构建所述约束函数：The constraint function is constructed according to the following formula:
其中，Y表示所述雷达回波信号，S表示所述目标信号，M表示所述干扰信号，δ表示噪声容限，||||F表示张量的Frobenius范数。Wherein, Y represents the radar echo signal, S represents the target signal, M represents the interference signal, δ represents the noise margin, and ||||F represents the Frobenius norm of the tensor.
示例性地，其中，rank()表示求秩函数，rank(S)为构建的秩函数，‖M‖0为构建的范数函数。Exemplarily, rank() represents the rank function, rank(S) is the constructed rank function, and ‖M‖0 is the constructed norm function.
进一步地，所述根据所述虚拟目标信号范数和所述干扰信号范数生成所述第二目标函数包括：Further, generating the second objective function according to the virtual target signal norm and the interference signal norm includes:
根据下式构建所述第二目标函数：The second objective function is constructed according to the following formula:
其中，S′表示所述虚拟目标信号，M表示所述干扰信号，λ表示第一超参数，||||l表示l2,1范数或l1范数，||||1表示l1范数，min()表示取最小值。Among them, S′ represents the virtual target signal, M represents the interference signal, λ represents the first hyperparameter, ||||l represents the l2,1 norm or the l1 norm, ||||1 represents the l1 norm, and min() represents taking the minimum value.
所述基于所述雷达回波信号、所述干扰信号、所述虚拟目标信号和所述矩阵字典生成所述第二约束函数包括：The generating the second constraint function based on the radar echo signal, the interference signal, the virtual target signal and the matrix dictionary comprises:
根据下式构建所述第二约束函数：The second constraint function is constructed according to the following formula:
其中，Y表示所述雷达回波信号，Dbeat表示所述矩阵字典，S′表示所述虚拟目标信号，M表示所述干扰信号，δ表示噪声容限，||||F表示张量的Frobenius范数。Wherein, Y represents the radar echo signal, Dbeat represents the matrix dictionary, S′ represents the virtual target signal, M represents the interference signal, δ represents the noise margin, and ||||F represents the Frobenius norm of the tensor.
示例性地，将第一目标函数松弛为凸问题，并引入过完备矩阵字典Dbeat，用虚拟目标信号和矩阵字典表示所述目标信号，即S＝DbeatS′。将该式带入第一目标函数和第一约束函数，以得到第二目标函数和第二约束函数。Exemplarily, the first objective function is relaxed into a convex problem, and an overcomplete matrix dictionary Dbeat is introduced, and the target signal is represented by a virtual target signal and a matrix dictionary, that is, S=Dbeat S′. Substitute this formula into the first objective function and the first constraint function to obtain the second objective function and the second constraint function.
进一步地，所述通过交替方向乘子法对所述干扰抑制模型进行求解包括：Further, solving the interference suppression model by an alternating direction multiplier method includes:
根据所述第二目标函数和所述第二约束函数构建增广拉格朗日函数；constructing an augmented Lagrangian function according to the second objective function and the second constraint function;
当所述虚拟目标信号范数为l2,1范数时，构建软阈值函数和范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解；When the norm of the virtual target signal is a l2,1 norm, constructing a soft threshold function and a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method;
当所述虚拟目标信号范数为l1范数时，构建范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解。When the norm of the virtual target signal is the l1 norm, a norm threshold function is constructed and the augmented Lagrangian function is solved by the alternating direction multiplier method.
示例性地，为了约束目标回波在时频域的行稀疏性，有两种松弛选择，第一种，虚拟目标信号范数为l1范数，第二种，虚拟目标信号范数为是l2,1范数，其中For example, in order to constrain the row sparsity of the target echo in the time-frequency domain, there are two relaxation options. In the first, the virtual target signal norm is the l1 norm, and in the second, the virtual target signal norm is the l2,1 norm, where
当确定的范数不同时，求解的方法对应不同，虚拟目标信号范数为l1范数时，需要构建范数阈值函数来求解；虚拟目标信号范数为是l2,1范数时，需要构建软阈值函数和范数阈值函数来求解。When the determined norm is different, the solution method is different. When the norm of the virtual target signal is l1 norm, it is necessary to construct a norm threshold function to solve it; when the norm of the virtual target signal is l2,1 norm, it is necessary to construct a soft threshold function and a norm threshold function to solve it.
进一步地，所述根据所述第二目标函数和所述第二约束函数构建增广拉格朗日函数包括：Further, constructing an augmented Lagrangian function according to the second objective function and the second constraint function includes:
以虚拟目标信号、干扰信号、拉格朗日变量和超参数为变量，根据所述第二目标函数和所述第二约束函数构建所述增广拉格朗日函数。The augmented Lagrangian function is constructed according to the second objective function and the second constraint function, with the virtual target signal, the interference signal, the Lagrangian variable and the hyperparameter as variables.
示例性地，上述优化模型的增广拉格朗日函数如下式表示：Exemplarily, the augmented Lagrangian function of the above optimization model is expressed as follows:
其中，S′表示虚拟目标信号，M表示干扰信号，Y1表示拉格朗日变量，λ表示第一超参数，μ表示第二超参数，Dbeat表示矩阵字典，||||1表示l1范数，||||F表示张量的Frobenius范数。Among them, S′ represents the virtual target signal, M represents the interference signal, Y1 represents the Lagrangian variable, λ represents the first hyperparameter, μ represents the second hyperparameter, Dbeat represents the matrix dictionary, ||||1 represents the l1 norm, and ||||F represents the Frobenius norm of the tensor.
可选地，所述当所述虚拟目标信号范数为l2,1范数时，构建软阈值函数和范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解包括：Optionally, when the norm of the virtual target signal is a l2,1 norm, constructing a soft threshold function and a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method comprises:
针对所述虚拟目标信号范数进行多次迭代，其中，在每次迭代时执行如下操作：Perform multiple iterations on the virtual target signal norm, wherein the following operations are performed in each iteration:
基于所述软阈值函数得到更新的虚拟目标信号闭式解；Obtaining an updated closed-form solution of the virtual target signal based on the soft threshold function;
根据所述虚拟目标信号闭式解和所述范数阈值函数得到干扰信号闭式解；Obtaining a closed-form solution for an interference signal according to the closed-form solution for the virtual target signal and the norm threshold function;
根据所述虚拟目标信号闭式解和所述干扰信号闭式解得到拉格朗日变量闭式解；Obtaining a Lagrangian variable closed-form solution according to the virtual target signal closed-form solution and the interference signal closed-form solution;
基于所述虚拟目标信号闭式解和所述干扰信号闭式解计算终止条件函数；Calculate a termination condition function based on the virtual target signal closed-form solution and the interference signal closed-form solution;
当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。When the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, the iteration is stopped.
示例性地，对于l2,1范数约束的行稀疏方法，下面给出具体的求解方法：For example, for the row sparse method with l2,1 norm constraint, the specific solution method is given below:
(1)基于所述软阈值函数得到第t+1次迭代交替更新的虚拟目标信号闭式解S′(t+1)。(1) Based on the soft threshold function, a closed-form solution S′(t+1) of the virtual target signal updated alternately at the t+1th iteration is obtained.
其中，S′(t+1)为第t+1次迭代时的虚拟目标信号闭式解，St2,1(·)为软阈值函数，S′(t)为第t次迭代时的虚拟目标信号闭式解，表示矩阵字典的转置，Y表示所述雷达回波信号，为第t次迭代时的拉格朗日变量闭式解，μ(t)为第t次迭代时的超变量闭式解，M(t)表示第t次迭代时的干扰信号闭式解。Where S′(t+1) is the closed-form solution of the virtual target signal at the t+1th iteration, St2,1 (·) is the soft threshold function, S′(t) is the closed-form solution of the virtual target signal at the tth iteration, represents the transpose of the matrix dictionary, Y represents the radar echo signal, is the closed-form solution of the Lagrangian variable at the t-th iteration, μ(t) is the closed-form solution of the hypervariable at the t-th iteration, and M(t) is the closed-form solution of the interference signal at the t-th iteration.
在上述公式中，软阈值函数St2,1(·)具体定义如下：In the above formula, the soft threshold function St2,1 (·) is specifically defined as follows:
其中，A表示矩阵，δ表示预设的参数，“：”表示全部数据。Where A represents a matrix, δ represents a preset parameter, and “:” represents all data.
(2)基于第t+1次迭代时的虚拟目标信号闭式解和范数阈值函数得到干扰信号闭式解M(t+1)。(2) Based on the closed-form solution of the virtual target signal at the t+1th iteration and the norm threshold function, the closed-form solution of the interference signal M(t+1) is obtained.
其中，M(t+1)为第t+1次迭代时的干扰信号闭式解，St1(·)为范数阈值函数，Y表示所述雷达回波信号，为第t次迭代时的拉格朗日变量闭式解，μ(t)为第t次迭代时的超变量闭式解，表示矩阵字典的转置，S′(t+1)为第t+1次迭代时的虚拟目标信号闭式解。Wherein, M(t+1) is the closed-form solution of the interference signal at the t+1th iteration, St1 (·) is the norm threshold function, Y represents the radar echo signal, is the closed-form solution of the Lagrangian variable at the t-th iteration, μ(t) is the closed-form solution of the hypervariable at the t-th iteration, represents the transpose of the matrix dictionary, and S′(t+1) is the closed-form solution of the virtual target signal at the t+1th iteration.
其中，范数阈值函数St1(·)进行如下定义：The norm threshold function St1 (·) is defined as follows:
其中，A表示矩阵，δ表示预设的参数。Wherein, A represents a matrix, and δ represents a preset parameter.
(3)根据虚拟目标信号闭式解和干扰信号闭式解得到第t+1次迭代时的拉格朗日变量闭式解(3) Based on the closed-form solution of the virtual target signal and the closed-form solution of the interference signal, the closed-form solution of the Lagrangian variable at the t+1th iteration is obtained.
其中，为第t+1次迭代时的拉格朗日变量闭式解，为第t次迭代时的拉格朗日变量闭式解，μ(t)为第t次迭代时的超变量闭式解，Y表示所述雷达回波信号，表示矩阵字典的转置，S′(t+1)为第t+1次迭代时的虚拟目标信号闭式解，M(t+1)为第t+1次迭代时的干扰信号闭式解。in, is the closed-form solution of the Lagrangian variable at the t+1th iteration, is the closed-form solution of the Lagrangian variable at the t-th iteration, μ(t) is the closed-form solution of the hypervariable at the t-th iteration, Y represents the radar echo signal, represents the transpose of the matrix dictionary, S′(t+1) is the closed-form solution of the virtual target signal at the t+1th iteration, and M(t+1) is the closed-form solution of the interference signal at the t+1th iteration.
(4)根据下式计算超变量闭式解(4) Calculate the closed-form solution of the hypervariable according to the following formula
μ(t+1)＝min(ημ(t),μmax)，μ(t+1) =min(ημ(t) ,μmax ),
其中，μ(t+1)表示第t+1次迭代时的超变量闭式解，μ(t)表示第t次迭代时的超变量闭式解，η表示预设的参数。Wherein, μ(t+1) represents the closed-form solution of the hypervariable at the t+1th iteration, μ(t) represents the closed-form solution of the hypervariable at the tth iteration, and η represents the preset parameter.
(5)基于所述目标信号闭式解和所述干扰信号闭式解计算终止条件函数；当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。终止条件为：(5) Calculating a termination condition function based on the closed-form solution of the target signal and the closed-form solution of the interference signal; when the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, stopping the iteration. The termination condition is:
其中，Y表示所述雷达回波信号，S′(t+1)表示第t+1次迭代时的虚拟目标信号范数变量闭，M(t+1)表示第t+1次迭代时的干扰信号范数变量闭，||||F表示张量的Frobenius范数，τrel>0代表相对容忍度，其中，n表示张量的快时间维数，m表示张量的慢时间维数。Wherein, Y represents the radar echo signal, S′(t+1) represents the virtual target signal norm variable closed at the t+1th iteration, M(t+1) represents the interference signal norm variable closed at the t+1th iteration, ||||F represents the Frobenius norm of the tensor, τrel >0 represents relative tolerance, where n represents the fast time dimension of the tensor and m represents the slow time dimension of the tensor.
最终将数据通过行稀疏矩阵恢复，目标回波将通过字典被分开。图3a-3d为干扰抑制后的真实目标信号示意图和距离多普勒图，其中，图3a为虚拟目标信号范数为l2,范数时的真实目标信号示意图，相对应地，图3b为距离多普勒图，在干扰抑制后，可得到精度较高的目标信号。Finally, the data is restored through the row sparse matrix, and the target echo will be separated through the dictionary. Figures 3a-3d are schematic diagrams of the real target signal and the range Doppler diagram after interference suppression, where Figure 3a is a schematic diagram of the real target signal when the norm of the virtual target signal is l2, and correspondingly, Figure 3b is a range Doppler diagram. After interference suppression, a target signal with higher accuracy can be obtained.
可选地，所述当所述虚拟目标信号范数为l1范数时，构建范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解包括：Optionally, when the norm of the virtual target signal is a l1 norm, constructing a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method comprises:
针对所述虚拟目标信号范数进行多次迭代，其中，在每次迭代时执行如下操作：Perform multiple iterations on the virtual target signal norm, wherein the following operations are performed in each iteration:
基于所述范数阈值函数得到更新的虚拟目标信号闭式解；Obtaining an updated closed-form solution of the virtual target signal based on the norm threshold function;
根据所述虚拟目标信号闭式解和所述范数阈值函数得到干扰信号闭式解；Obtaining a closed-form solution for an interference signal according to the closed-form solution for the virtual target signal and the norm threshold function;
根据所述虚拟目标信号闭式解和所述干扰信号闭式解得到拉格朗日变量闭式解；Obtaining a Lagrangian variable closed-form solution according to the virtual target signal closed-form solution and the interference signal closed-form solution;
基于所述虚拟目标信号闭式解和所述干扰信号闭式解计算终止条件函数；Calculate a termination condition function based on the virtual target signal closed-form solution and the interference signal closed-form solution;
当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。When the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, the iteration is stopped.
示例性地，对于l1范数约束的元素稀疏方法，下面给出具体的求解方法：For example, for the element sparse method with l1 norm constraint, the specific solution method is given below:
(1)基于范数阈值函数得到第t+1次迭代交替更新的虚拟目标信号闭式解S′(t+1)。(1) Based on the norm threshold function, the closed-form solution S′(t+1) of the virtual target signal updated alternately at the t+1th iteration is obtained.
其中，S′(t+1)为第t+1次迭代时的虚拟目标信号闭式解，St1(·)为范数阈值函数，S′(t)为第t次迭代时的虚拟目标信号闭式解，表示矩阵字典的转置，Y表示所述雷达回波信号，为第t次迭代时的拉格朗日变量闭式解，μ(t)为第t次迭代时的超变量闭式解，M(t)表示第t次迭代时的干扰信号闭式解。Where, S′(t+1) is the closed-form solution of the virtual target signal at the t+1th iteration, St1 (·) is the norm threshold function, S′(t) is the closed-form solution of the virtual target signal at the tth iteration, represents the transpose of the matrix dictionary, Y represents the radar echo signal, is the closed-form solution of the Lagrangian variable at the t-th iteration, μ(t) is the closed-form solution of the hypervariable at the t-th iteration, and M(t) is the closed-form solution of the interference signal at the t-th iteration.
(2)基于第t+1次迭代时的虚拟目标信号闭式解和范数阈值函数得到干扰信号闭式解M(t+1)。(2) Based on the closed-form solution of the virtual target signal at the t+1th iteration and the norm threshold function, the closed-form solution of the interference signal M(t+1) is obtained.
其中，M(t+1)为第t+1次迭代时的干扰信号闭式解，St1(·)为范数阈值函数，Y表示所述雷达回波信号，为第t次迭代时的拉格朗日变量闭式解，μ(t)为第t次迭代时的超变量闭式解，表示矩阵字典的转置，S′(t+1)为第t+1次迭代时的虚拟目标信号闭式解。Wherein, M(t+1) is the closed-form solution of the interference signal at the t+1th iteration, St1 (·) is the norm threshold function, Y represents the radar echo signal, is the closed-form solution of the Lagrangian variable at the t-th iteration, μ(t) is the closed-form solution of the hypervariable at the t-th iteration, represents the transpose of the matrix dictionary, and S′(t+1) is the closed-form solution of the virtual target signal at the t+1th iteration.
(3)根据虚拟目标信号闭式解和干扰信号闭式解得到第t+1次迭代时的拉格朗日变量闭式解(3) Based on the closed-form solution of the virtual target signal and the closed-form solution of the interference signal, the closed-form solution of the Lagrangian variable at the t+1th iteration is obtained.
其中，为第t+1次迭代时的拉格朗日变量闭式解，为第t次迭代时的拉格朗日变量闭式解，μ(t)为第t次迭代时的超变量闭式解，Y表示所述雷达回波信号，表示矩阵字典的转置，S′(t+1)为第t+1次迭代时的虚拟目标信号闭式解，M(t+1)为第t+1次迭代时的干扰信号闭式解。in, is the closed-form solution of the Lagrangian variable at the t+1th iteration, is the closed-form solution of the Lagrangian variable at the t-th iteration, μ(t) is the closed-form solution of the hypervariable at the t-th iteration, Y represents the radar echo signal, represents the transpose of the matrix dictionary, S′(t+1) is the closed-form solution of the virtual target signal at the t+1th iteration, and M(t+1) is the closed-form solution of the interference signal at the t+1th iteration.
(4)根据下式计算超变量闭式解(4) Calculate the closed-form solution of the hypervariable according to the following formula
μ(t+1)＝min(ημ(t),μmax)，μ(t+1) =min(ημ(t) ,μmax ),
其中，μ(t+1)表示第t+1次迭代时的超变量闭式解，μ(t)表示第t次迭代时的超变量闭式解，η表示预设的参数。Wherein, μ(t+1) represents the closed-form solution of the hypervariable at the t+1th iteration, μ(t) represents the closed-form solution of the hypervariable at the tth iteration, and η represents the preset parameter.
(5)基于所述目标信号闭式解和所述干扰信号闭式解计算终止条件函数；当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。终止条件为：(5) Calculating a termination condition function based on the closed-form solution of the target signal and the closed-form solution of the interference signal; when the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, stopping the iteration. The termination condition is:
其中，Y表示所述雷达回波信号，S′(t+1)表示第t+1次迭代时的虚拟目标信号范数变量闭，M(t+1)表示第t+1次迭代时的干扰信号范数变量闭，||||F表示张量的Frobenius范数，τrel>0代表相对容忍度，其中，n表示张量的快时间维数，m表示张量的慢时间维数。Wherein, Y represents the radar echo signal, S′(t+1) represents the virtual target signal norm variable closed at the t+1th iteration, M(t+1) represents the interference signal norm variable closed at the t+1th iteration, ||||F represents the Frobenius norm of the tensor, τrel >0 represents relative tolerance, where n represents the fast time dimension of the tensor and m represents the slow time dimension of the tensor.
最终将数据通过元素稀疏矩阵恢复，目标回波将通过字典被分开。其中，图3c为虚拟目标信号范数为l1范数时的真实目标信号示意图，相对应地，图3d为距离多普勒图，在干扰抑制后，可得到精度较高的目标信号。Finally, the data is restored through the element sparse matrix, and the target echo will be separated through the dictionary. Among them, Figure 3c is a schematic diagram of the real target signal when the norm of the virtual target signal is the l1 norm. Correspondingly, Figure 3d is a range Doppler diagram. After interference suppression, a target signal with higher accuracy can be obtained.
进一步地，所述方法还包括：Furthermore, the method further comprises:
在所述得到干扰抑制后的真实目标信号之后，通过逆短时傅里叶变换将所述真实目标信号转换为时域信号。After obtaining the interference-suppressed real target signal, the real target signal is converted into a time domain signal by inverse short-time Fourier transform.
示例性地，将干扰抑制得到的真实目标信号通过逆短时傅里叶变换转换到时域。时频域分析采用短时傅里叶变换，通过在原始的真实目标信号x[n]上滑动长度为m的窗函数w[n]，并应用离散傅里叶变换(DFT)，将时域信号转移到时频域上，具体通过下式实现：Exemplarily, the real target signal obtained by interference suppression is converted to the time domain by inverse short-time Fourier transform. The time-frequency domain analysis uses short-time Fourier transform, by sliding a window function w[n] of length m on the original real target signal x[n] and applying discrete Fourier transform (DFT), the time domain signal is transferred to the time-frequency domain, which is specifically implemented by the following formula:
其中，x[n]表示真实目标信号，STFT{}表示时频域数据，m表示滑动长度，w[n]表示窗函数，矩阵为n行m列的矩阵。Among them, x[n] represents the true target signal, STFT{} represents the time-frequency domain data, m represents the sliding length, w[n] represents the window function, and the matrix is a matrix with n rows and m columns.
通过本发明中的上述实施例中的一个实施例或多个实施例，至少可以实现如下技术效果：Through one or more of the above embodiments of the present invention, at least the following technical effects can be achieved:
在本发明所公开的技术方案中，利用短时傅里叶变换将雷达回波信号转移到时频域，分析干扰信号和目标信号的不同性质，构造干扰抑制问题来分离具有稀疏特性的干扰信号和具有低秩特性的目标信号。引入矩阵字典作为具有低秩特性的目标信号的向量基，在优化问题中以正则项的形式约束有用目标信号，矩阵字典能够有效降低计算复杂度，简化算法，然后通过交替方向乘子法求解模型。该干扰抑制方法适用于干扰持续时间较长、干扰数目较多的多种应用场景，较传统方法能明显提高抑制干扰信号的精确度。In the technical solution disclosed in the present invention, the radar echo signal is transferred to the time-frequency domain by using short-time Fourier transform, the different properties of the interference signal and the target signal are analyzed, and the interference suppression problem is constructed to separate the interference signal with sparse characteristics and the target signal with low-rank characteristics. A matrix dictionary is introduced as the vector basis of the target signal with low-rank characteristics, and the useful target signal is constrained in the form of a regular term in the optimization problem. The matrix dictionary can effectively reduce the computational complexity, simplify the algorithm, and then solve the model by the alternating direction multiplication method. This interference suppression method is suitable for a variety of application scenarios with long interference duration and a large number of interferences, and can significantly improve the accuracy of suppressing interference signals compared with traditional methods.
基于与本发明实施例的一种雷达干扰的抑制方法同样的发明构思，本发明实施例提供了一种雷达干扰的抑制装置，请参考图4，所述装置包括：Based on the same inventive concept as the radar interference suppression method of the embodiment of the present invention, the embodiment of the present invention provides a radar interference suppression device, please refer to FIG4, the device includes:
函数构建模块201，用于通过短傅里叶变换将雷达回波信号由时域转换到时频域，根据所述雷达回波信号中的目标信号在时频域的低秩特性构建所述目标信号的秩函数，根据雷达回波信号中的干扰信号在时域的稀疏特性，用范数函数约束所述干扰信号；A function construction module 201 is used to convert the radar echo signal from the time domain to the time-frequency domain by short Fourier transform, construct a rank function of the target signal in the radar echo signal according to the low rank characteristic of the target signal in the time-frequency domain, and constrain the interference signal with a norm function according to the sparse characteristic of the interference signal in the radar echo signal in the time domain;
模型构建模块202，用于基于所述秩函数和所述范数函数构建第一目标函数，并基于所述雷达回波信号构建第一约束函数，通过凸松弛优化方法将所述第一目标函数和所述第一约束函数转换为第二目标函数和第二约束函数，根据所述第二目标函数和所述第二约束函数构建干扰抑制模型；A model building module 202 is used to build a first objective function based on the rank function and the norm function, and to build a first constraint function based on the radar echo signal, convert the first objective function and the first constraint function into a second objective function and a second constraint function through a convex relaxation optimization method, and build an interference suppression model according to the second objective function and the second constraint function;
计算模块203，用于通过交替方向乘子法对所述干扰抑制模型进行求解，以得到干扰抑制后的真实目标信号。The calculation module 203 is used to solve the interference suppression model by using an alternating direction multiplier method to obtain a real target signal after interference suppression.
进一步地，所述模型构建模块202还用于：Furthermore, the model building module 202 is also used for:
用虚拟目标信号和矩阵字典表示所述目标信号；Representing the target signal using a virtual target signal and a matrix dictionary;
将所述秩函数转换为基于所述虚拟目标信号生成的虚拟目标信号范数，将所述范数函数转换为干扰信号范数，根据所述虚拟目标信号范数和所述干扰信号范数生成所述第二目标函数；Converting the rank function into a virtual target signal norm generated based on the virtual target signal, converting the norm function into an interference signal norm, and generating the second target function according to the virtual target signal norm and the interference signal norm;
基于所述雷达回波信号、所述干扰信号、所述虚拟目标信号和所述矩阵字典生成所述第二约束函数。The second constraint function is generated based on the radar echo signal, the interference signal, the virtual target signal and the matrix dictionary.
进一步地，所述模型构建模块202还用于：Furthermore, the model building module 202 is also used for:
根据下式构建所述第一目标函数：The first objective function is constructed according to the following formula:
其中，S表示所述目标信号，M表示所述干扰信号，rank()表示求秩函数，λ表示第一超参数，||||0表示l0范数，min()表示取最小值。Wherein, S represents the target signal, M represents the interference signal, rank() represents the rank function, λ represents the first hyperparameter, ||||0 represents the l0 norm, and min() represents taking the minimum value.
所述基于所述雷达回波信号构建第一约束函数包括：The constructing a first constraint function based on the radar echo signal comprises:
根据下式构建所述约束函数：The constraint function is constructed according to the following formula:
其中，Y表示所述雷达回波信号，S表示所述目标信号，M表示所述干扰信号，δ表示噪声容限，||||F表示张量的Frobenius范数。Wherein, Y represents the radar echo signal, S represents the target signal, M represents the interference signal, δ represents the noise margin, and ||||F represents the Frobenius norm of the tensor.
进一步地，所述模型构建模块202还用于：Furthermore, the model building module 202 is also used for:
根据下式构建所述第二目标函数：The second objective function is constructed according to the following formula:
其中，S′表示所述虚拟目标信号，M表示所述干扰信号，λ表示第一超参数，||||l表示l2,1范数或l1范数，||||1表示l1范数，min()表示取最小值。Among them, S′ represents the virtual target signal, M represents the interference signal, λ represents the first hyperparameter, ||||l represents the l2,1 norm or the l1 norm, ||||1 represents the l1 norm, and min() represents taking the minimum value.
所述基于所述雷达回波信号、所述干扰信号、所述虚拟目标信号和所述矩阵字典生成所述第二约束函数包括：The generating the second constraint function based on the radar echo signal, the interference signal, the virtual target signal and the matrix dictionary comprises:
根据下式构建所述第二约束函数：The second constraint function is constructed according to the following formula:
其中，Y表示所述雷达回波信号，Dbeat表示所述矩阵字典，S′表示所述虚拟目标信号，M表示所述干扰信号，δ表示噪声容限，||||F表示张量的Frobenius范数。Wherein, Y represents the radar echo signal, Dbeat represents the matrix dictionary, S′ represents the virtual target signal, M represents the interference signal, δ represents the noise margin, and ||||F represents the Frobenius norm of the tensor.
进一步地，所述计算模块203还用于：Furthermore, the calculation module 203 is also used for:
根据所述第二目标函数和所述第二约束函数构建增广拉格朗日函数；constructing an augmented Lagrangian function according to the second objective function and the second constraint function;
当所述虚拟目标信号范数为l2,1范数时，构建软阈值函数和范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解；When the norm of the virtual target signal is a l2,1 norm, constructing a soft threshold function and a norm threshold function and solving the augmented Lagrangian function by an alternating direction multiplier method;
当所述虚拟目标信号范数为l1范数时，构建范数阈值函数并通过交替方向乘子法对所述增广拉格朗日函数进行求解。When the norm of the virtual target signal is the l1 norm, a norm threshold function is constructed and the augmented Lagrangian function is solved by the alternating direction multiplier method.
进一步地，所述计算模块203还用于：Furthermore, the calculation module 203 is also used for:
以虚拟目标信号、干扰信号、拉格朗日变量和超参数为变量，根据所述第二目标函数和所述第二约束函数构建所述增广拉格朗日函数。The augmented Lagrangian function is constructed according to the second objective function and the second constraint function, with the virtual target signal, the interference signal, the Lagrangian variable and the hyperparameter as variables.
可选地，所述计算模块203还用于：Optionally, the calculation module 203 is further used for:
针对所述虚拟目标信号范数进行多次迭代，其中，在每次迭代时执行如下操作：Perform multiple iterations on the virtual target signal norm, wherein the following operations are performed in each iteration:
基于所述软阈值函数得到更新的虚拟目标信号闭式解；Obtaining an updated closed-form solution of the virtual target signal based on the soft threshold function;
根据所述虚拟目标信号闭式解和所述范数阈值函数得到干扰信号闭式解；Obtaining a closed-form solution for an interference signal according to the closed-form solution for the virtual target signal and the norm threshold function;
根据所述虚拟目标信号闭式解和所述干扰信号闭式解得到拉格朗日变量闭式解；Obtaining a Lagrangian variable closed-form solution according to the virtual target signal closed-form solution and the interference signal closed-form solution;
基于所述虚拟目标信号闭式解和所述干扰信号闭式解计算终止条件函数；Calculate a termination condition function based on the virtual target signal closed-form solution and the interference signal closed-form solution;
当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。When the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, the iteration is stopped.
可选地，所述计算模块203还用于：Optionally, the calculation module 203 is further used for:
针对所述虚拟目标信号范数进行多次迭代，其中，在每次迭代时执行如下操作：Perform multiple iterations on the virtual target signal norm, wherein the following operations are performed in each iteration:
基于所述范数阈值函数得到更新的虚拟目标信号闭式解；Obtaining an updated closed-form solution of the virtual target signal based on the norm threshold function;
根据所述虚拟目标信号闭式解和所述范数阈值函数得到干扰信号闭式解；Obtaining a closed-form solution for an interference signal according to the closed-form solution for the virtual target signal and the norm threshold function;
根据所述虚拟目标信号闭式解和所述干扰信号闭式解得到拉格朗日变量闭式解；Obtaining a Lagrangian variable closed-form solution according to the virtual target signal closed-form solution and the interference signal closed-form solution;
基于所述虚拟目标信号闭式解和所述干扰信号闭式解计算终止条件函数；Calculate a termination condition function based on the virtual target signal closed-form solution and the interference signal closed-form solution;
当迭代数量达到预设的迭代次数或所述终止条件函数的值小于预设的误差容忍度时，停止迭代。When the number of iterations reaches a preset number of iterations or the value of the termination condition function is less than a preset error tolerance, the iteration is stopped.
进一步地，所述装置还用于：Furthermore, the device is also used for:
在所述得到干扰抑制后的真实目标信号之后，通过逆短时傅里叶变换将所述真实目标信号转换为时域信号。After obtaining the interference-suppressed real target signal, the real target signal is converted into a time domain signal by inverse short-time Fourier transform.
其中，所述雷达干扰的抑制装置的其它方面以及实现细节与前面所描述的雷达干扰的抑制方法相同或相似，在此不再赘述。Among them, other aspects and implementation details of the radar interference suppression device are the same as or similar to the radar interference suppression method described above, and will not be repeated here.
根据本发明的另一方面，本发明还提供一种存储介质，所述存储介质中存储有多条指令，所述指令适于由处理器加载以执行如上所述的任一雷达干扰的抑制方法。According to another aspect of the present invention, the present invention further provides a storage medium, wherein a plurality of instructions are stored in the storage medium, and the instructions are suitable for being loaded by a processor to execute any radar interference suppression method as described above.
综上所述，虽然本发明已以优选实施例揭露如上，但上述优选实施例并非用以限制本发明，本领域的普通技术人员，在不脱离本发明的精神和范围内，均可作各种更动与润饰，因此本发明的保护范围以权利要求界定的范围为准。In summary, although the present invention has been disclosed as above in terms of preferred embodiments, the above preferred embodiments are not intended to limit the present invention. A person skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope defined in the claims.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN118884366A (en)* | 2024-09-29 | 2024-11-01 | 南京隼眼电子科技有限公司 | Interference suppression method, device, equipment and medium for multi-polarization channel SAR system |
| CN119828117A (en)* | 2024-12-19 | 2025-04-15 | 西北工业大学 | Reverberation suppression method based on time-frequency patch tensor model |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111273238A (en)* | 2020-01-06 | 2020-06-12 | 中国航天科工集团八五一一研究所 | SAR (synthetic aperture radar) wide-band and narrow-band interference simultaneous inhibition method based on low-rank recovery |
| CN113866724A (en)* | 2021-09-28 | 2021-12-31 | 海华电子企业(中国)有限公司 | A radar target detection method under the background of sea clutter based on the alternating direction method |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111273238A (en)* | 2020-01-06 | 2020-06-12 | 中国航天科工集团八五一一研究所 | SAR (synthetic aperture radar) wide-band and narrow-band interference simultaneous inhibition method based on low-rank recovery |
| CN113866724A (en)* | 2021-09-28 | 2021-12-31 | 海华电子企业(中国)有限公司 | A radar target detection method under the background of sea clutter based on the alternating direction method |
| Title |
|---|
| YAN HUANG 等: "A Fast RFI Mitigation Approach via Alternating Projection in Real SAR Data", 《3RD URSI AT-AP-RASC》, 3 June 2022 (2022-06-03), pages 1 - 4* |
| 黄岩: "复杂电磁环境下合成孔径雷达动目标检测与识别方法研究", 《中国博士学位论文全文数据库 信息科技辑》, no. 7, 15 July 2019 (2019-07-15), pages 136 - 61* |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN118884366A (en)* | 2024-09-29 | 2024-11-01 | 南京隼眼电子科技有限公司 | Interference suppression method, device, equipment and medium for multi-polarization channel SAR system |
| CN119828117A (en)* | 2024-12-19 | 2025-04-15 | 西北工业大学 | Reverberation suppression method based on time-frequency patch tensor model |
| Publication | Publication Date | Title |
|---|---|---|
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