技术领域Technical Field
本申请涉及雷达、侦察技术领域，具体而言，涉及一种干扰条件下阵列单快拍多维参数估计方法及装置。The present application relates to the field of radar and reconnaissance technology, and in particular to a method and device for estimating multi-dimensional parameters of an array single snapshot under interference conditions.
背景技术Background Art
在雷达、侦察系统中，参数估计是一项至关重要的任务，其直接影响阵列对信源的探测、跟踪和识别能力。传统的阵列参数估计方法多基于空间类方法，这类方法通过采集大量的独立同分布样本以估计回波协方差矩阵，进而利用矩阵分解技术获得信号子空间和噪声子空间，从而实现信源参数的超分辨估计。然而，在实践中发现，对于大规模阵列天线系统，进行高维矩阵分解需要消耗大量的计算资源，导致算法的计算成本过高，并且由于信源/干扰的运动和天线波束的快速扫描，采集大量的独立同分布样本变得不现实，这进一步限制了空间类方法在实际应用中的使用。此外，信源之间存在相干性时，直接使用子空间类算法无法正确测量参数。可见，现有方法计算成本高、不适用于相干信源且难以满足实时性要求。In radar and reconnaissance systems, parameter estimation is a crucial task that directly affects the array's ability to detect, track and identify sources. Traditional array parameter estimation methods are mostly based on spatial methods, which collect a large number of independent and identically distributed samples to estimate the echo covariance matrix, and then use matrix decomposition technology to obtain signal subspace and noise subspace, thereby achieving super-resolution estimation of source parameters. However, in practice, it is found that for large-scale array antenna systems, high-dimensional matrix decomposition requires a lot of computing resources, resulting in excessively high computational costs of the algorithm. In addition, due to the movement of the source/interference and the rapid scanning of the antenna beam, it becomes unrealistic to collect a large number of independent and identically distributed samples, which further limits the use of spatial methods in practical applications. In addition, when there is coherence between sources, the subspace algorithm cannot correctly measure the parameters directly. It can be seen that the existing methods have high computational costs, are not suitable for coherent sources, and are difficult to meet real-time requirements.
发明内容Summary of the invention
本申请实施例的目的在于提供一种干扰条件下阵列单快拍多维参数估计方法及装置，能够直接处理多个相干接收信号，无需进行矩阵分解和网格搜索，从而实现实时、快速、准确的多维参数估计。The purpose of the embodiments of the present application is to provide a method and device for estimating multidimensional parameters of an array single snapshot under interference conditions, which can directly process multiple coherent received signals without matrix decomposition and grid search, thereby realizing real-time, fast and accurate multidimensional parameter estimation.
本申请第一方面提供了一种干扰条件下阵列单快拍多维参数估计方法，包括：The first aspect of the present application provides a method for estimating multi-dimensional parameters of an array single snapshot under interference conditions, comprising:
获取干扰条件下的阵列接收信号；Acquire array received signals under interference conditions;
将所述阵列接收信号的信源多维参数估计问题转化为多维频率估计问题；Converting the problem of estimating the multidimensional parameters of the source of the array received signal into a problem of estimating the multidimensional frequency;
基于所述多维频率估计问题对所述阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果；Based on the multi-dimensional frequency estimation problem, a multi-dimensional frequency rough estimation is performed on the array received signal to obtain a multi-dimensional frequency rough estimation result;
根据所述多维频率粗估计结果对所述阵列接收信号进行多维频率精估计，得到多维频率精估计结果；Performing a multi-dimensional frequency precise estimation on the array received signal according to the multi-dimensional frequency rough estimation result to obtain a multi-dimensional frequency precise estimation result;
根据所述多维频率粗估计结果和所述多维频率精估计结果，计算频率估计结果；Calculating a frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result;
将所述频率估计结果转化为参数估计结果。The frequency estimation result is converted into a parameter estimation result.
在上述实现过程中，先获取干扰条件下的阵列接收信号；将信源多维参数估计问题转化为多维频率估计问题；再对阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果；最后，根据多维频率粗估计结果和多维频率精估计结果，计算频率估计结果，并将频率估计结果转化为参数估计结果。可见，该方法无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。In the above implementation process, the array receiving signal under interference conditions is first obtained; the multi-dimensional parameter estimation problem of the signal source is converted into a multi-dimensional frequency estimation problem; then the multi-dimensional frequency rough estimation of the array receiving signal is performed to obtain the multi-dimensional frequency rough estimation result; finally, the frequency estimation result is calculated based on the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result, and the frequency estimation result is converted into a parameter estimation result. It can be seen that this method does not require matrix decomposition and grid search, and can quickly and accurately measure the distance, angle, speed and other dimensional parameters of the coherent signal source using only single snapshot data.
进一步地，所述基于所述多维频率估计问题对所述阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果，包括：Further, performing a multi-dimensional frequency rough estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency rough estimation result includes:
基于所述多维频率估计问题对所述阵列接收信号进行多维快速傅里叶变换处理，得到多维频谱矩阵块；Based on the multi-dimensional frequency estimation problem, multi-dimensional fast Fourier transform processing is performed on the array received signal to obtain a multi-dimensional spectrum matrix block;
根据所述频谱矩阵块获取信号频谱峰值点坐标；Acquire the coordinates of the peak point of the signal spectrum according to the spectrum matrix block;
根据所述信号频谱峰值点坐标进行复正弦波的多维频率粗估计，得到多维频率粗估计结果。A multi-dimensional frequency rough estimation of the complex sine wave is performed according to the coordinates of the peak points of the signal spectrum to obtain a multi-dimensional frequency rough estimation result.
进一步地，所述多维频率粗估计结果为：Furthermore, the multi-dimensional frequency rough estimation result is:
其中，表示Q个复正弦波的K维频率粗估计结果；lk为正整数，表示扩展因子。in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; lk is a positive integer, representing the expansion factor.
进一步地，所述根据所述多维频率粗估计结果对所述阵列接收信号进行多维频率精估计，得到多维频率精估计结果，包括：Further, performing multi-dimensional frequency precise estimation on the array received signal according to the multi-dimensional frequency rough estimation result to obtain a multi-dimensional frequency precise estimation result includes:
根据预设的采样长度计算最大迭代次数和偏移量；Calculate the maximum number of iterations and offset according to the preset sampling length;
确定当前迭代次数；Determine the current iteration number;
根据所述当前迭代次数获取上一次迭代频谱精估计值和上一次迭代多个复正弦波的复幅度系数；According to the current number of iterations, the accurate estimated value of the spectrum of the previous iteration and the complex amplitude coefficients of the multiple complex sine waves of the previous iteration are obtained;
根据所述多维频率粗估计结果、所述上一次迭代频谱精估计值、所述偏移量和所述阵列接收信号，计算多个复正弦波的频谱泄漏系数和多个复正弦信号的多维偏移频谱值；Calculate spectrum leakage coefficients of multiple complex sinusoidal waves and multidimensional offset spectrum values of multiple complex sinusoidal signals according to the multidimensional frequency rough estimation result, the previous iterative spectrum precise estimation value, the offset and the array received signal;
根据所述上一次迭代多个复正弦波的复幅度系数、所述多个复正弦波的频谱泄漏系数以及所述多个复正弦信号的多维偏移频谱值，计算多个复正弦波的多维偏移后频谱泄漏校正系数；Calculating multidimensional offset spectrum leakage correction coefficients of the plurality of complex sinusoidal waves according to the complex amplitude coefficients of the plurality of complex sinusoidal waves of the previous iteration, the spectrum leakage coefficients of the plurality of complex sinusoidal waves, and the multidimensional offset spectrum values of the plurality of complex sinusoidal signals;
根据所述多个复正弦波的多维偏移后频谱泄漏校正系数和所述上一次迭代频谱精估计值，计算本次频率精估计值；Calculate the current frequency precise estimation value according to the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sinusoidal waves and the previous iterative spectrum precise estimation value;
判断所述当前迭代次数是否达到所述最大迭代次数；Determine whether the current number of iterations reaches the maximum number of iterations;
如果是，则将所述本次频率精估计值确定为多维频率精估计结果。If yes, the current frequency precise estimation value is determined as the multi-dimensional frequency precise estimation result.
进一步地，所述方法还包括：Furthermore, the method further comprises:
当判断出所述当前迭代次数未达到所述最大迭代次数时，根据所述多维频率粗估计结果和所述上一次迭代频谱精估计值计算信号在多个复正弦信号频率估计点的频谱值；When it is determined that the current number of iterations has not reached the maximum number of iterations, the spectrum values of the signal at a plurality of complex sinusoidal signal frequency estimation points are calculated according to the multi-dimensional frequency rough estimation result and the spectrum precise estimation value of the previous iteration;
根据所述多维频率粗估计结果，计算所述当前迭代次数对应的频谱泄漏系数；Calculating the spectrum leakage coefficient corresponding to the current number of iterations according to the multi-dimensional frequency rough estimation result;
根据所述信号在多个复正弦信号频率估计点的频谱值、所述当前迭代次数对应的频谱泄漏系数和所述上一次迭代多个复正弦波的复幅度系数，计算所述当前迭代次数对应的多个复正弦波的复幅度系数；Calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves of the previous iteration;
将所述当前迭代次数的数值增加1，作为新的当前迭代次数，并执行所述的确定当前迭代次数。The value of the current iteration number is increased by 1 to obtain a new current iteration number, and the process of determining the current iteration number is performed.
本申请第二方面提供了一种干扰条件下阵列单快拍多维参数估计装置，所述干扰条件下阵列单快拍多维参数估计装置包括：A second aspect of the present application provides a device for estimating multidimensional parameters of an array single snapshot under interference conditions, wherein the device for estimating multidimensional parameters of an array single snapshot under interference conditions comprises:
获取单元，用于获取干扰条件下的阵列接收信号；An acquisition unit, used for acquiring array receiving signals under interference conditions;
第一转化单元，用于将所述阵列接收信号的信源多维参数估计问题转化为多维频率估计问题；A first conversion unit, configured to convert a multi-dimensional parameter estimation problem of a signal source of the array receiving signal into a multi-dimensional frequency estimation problem;
粗估计单元，用于基于所述多维频率估计问题对所述阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果；A coarse estimation unit, configured to perform a coarse multi-dimensional frequency estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a coarse multi-dimensional frequency estimation result;
精估计单元，用于根据所述多维频率粗估计结果对所述阵列接收信号进行多维频率精估计，得到多维频率精估计结果；A precise estimation unit, configured to perform a precise multidimensional frequency estimation on the array received signal according to the rough multidimensional frequency estimation result to obtain a precise multidimensional frequency estimation result;
计算单元，用于根据所述多维频率粗估计结果和所述多维频率精估计结果，计算频率估计结果；A calculation unit, used for calculating a frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result;
第二转化单元，用于将所述频率估计结果转化为参数估计结果。The second conversion unit is used to convert the frequency estimation result into a parameter estimation result.
在上述实现过程中，获取单元先获取干扰条件下的阵列接收信号；粗估计单元再对阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果；以及精估计单元根据多维频率粗估计结果对阵列接收信号进行多维频率精估计，得到多维频率精估计结果；最后，计算单元根据多维频率粗估计结果和多维频率精估计结果，计算频率估计结果。可见，该装置无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。In the above implementation process, the acquisition unit first acquires the array receiving signal under interference conditions; the rough estimation unit then performs a multi-dimensional frequency rough estimation on the array receiving signal to obtain a multi-dimensional frequency rough estimation result; and the fine estimation unit performs a multi-dimensional frequency fine estimation on the array receiving signal according to the multi-dimensional frequency rough estimation result to obtain a multi-dimensional frequency fine estimation result; finally, the calculation unit calculates the frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency fine estimation result. It can be seen that the device does not need to perform matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of the coherent signal source using only single snapshot data.
进一步地，所述粗估计单元包括：Further, the rough estimation unit comprises:
信号变换子单元，用于基于所述多维频率估计问题对所述阵列接收信号进行多维快速傅里叶变换处理，得到多维频谱矩阵块；A signal conversion subunit, configured to perform a multi-dimensional fast Fourier transform process on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional spectrum matrix block;
获取子单元，用于根据所述频谱矩阵块获取信号频谱峰值点坐标；An acquisition subunit, used for acquiring the coordinates of the peak point of the signal spectrum according to the spectrum matrix block;
粗估计子单元，用于根据所述信号频谱峰值点坐标进行复正弦波的多维频率粗估计，得到多维频率粗估计结果。The rough estimation subunit is used to perform a rough estimation of the multi-dimensional frequency of the complex sine wave according to the coordinates of the peak points of the signal spectrum to obtain a rough estimation result of the multi-dimensional frequency.
进一步地，所述多维频率粗估计结果为：Furthermore, the multi-dimensional frequency rough estimation result is:
其中，表示Q个复正弦波的K维频率粗估计结果；lk为正整数，表示扩展因子。in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; lk is a positive integer, representing the expansion factor.
进一步地，所述精估计单元包括：Furthermore, the precise estimation unit comprises:
第一计算子单元，用于根据预设的采样长度计算最大迭代次数和偏移量；A first calculation subunit, used for calculating a maximum number of iterations and an offset according to a preset sampling length;
第一确定子单元，用于确定当前迭代次数；A first determining subunit, used to determine the current number of iterations;
获取子单元，用于根据所述当前迭代次数获取上一次迭代频谱精估计值和上一次迭代多个复正弦波的复幅度系数；An acquisition subunit, used for acquiring a precise estimation value of the spectrum of the previous iteration and complex amplitude coefficients of a plurality of complex sine waves of the previous iteration according to the current iteration number;
第二计算子单元，用于根据所述多维频率粗估计结果、所述上一次迭代频谱精估计值、所述偏移量和所述阵列接收信号，计算多个复正弦波的频谱泄漏系数和多个复正弦信号的多维偏移频谱值；A second calculation subunit is used to calculate the spectrum leakage coefficients of multiple complex sine waves and the multidimensional offset spectrum values of multiple complex sine signals according to the multidimensional frequency rough estimation result, the previous iterative spectrum precise estimation value, the offset and the array received signal;
所述第二计算子单元，还用于根据所述上一次迭代多个复正弦波的复幅度系数、所述多个复正弦波的频谱泄漏系数以及所述多个复正弦信号的多维偏移频谱值，计算多个复正弦波的多维偏移后频谱泄漏校正系数；The second calculation subunit is further used to calculate the multi-dimensional offset spectrum leakage correction coefficients of the multiple complex sine waves according to the complex amplitude coefficients of the multiple complex sine waves of the previous iteration, the spectrum leakage coefficients of the multiple complex sine waves, and the multi-dimensional offset spectrum values of the multiple complex sine signals;
所述第二计算子单元，还用于根据所述多个复正弦波的多维偏移后频谱泄漏校正系数和所述上一次迭代频谱精估计值，计算本次频率精估计值；The second calculation subunit is further used to calculate the current frequency precise estimation value according to the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the previous iterative spectrum precise estimation value;
判断子单元，用于判断所述当前迭代次数是否达到所述最大迭代次数；A judging subunit, used to judge whether the current number of iterations reaches the maximum number of iterations;
第二确定子单元，用于当判断出达到所述最大迭代次数时，则将所述本次频率精估计值确定为多维频率精估计结果。The second determining subunit is used to determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result when it is determined that the maximum number of iterations has been reached.
进一步地，所述精估计单元还包括：Furthermore, the precise estimation unit further includes:
第三计算子单元，还用于当判断出所述当前迭代次数未达到所述最大迭代次数时，根据所述多维频率粗估计结果和所述上一次迭代频谱精估计值计算信号在多个复正弦信号频率估计点的频谱值；The third calculation subunit is further configured to calculate the spectrum values of the signal at a plurality of complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency rough estimation result and the spectrum precise estimation value of the previous iteration when it is determined that the current iteration number has not reached the maximum iteration number;
所述第三计算子单元，还用于根据所述多维频率粗估计结果，计算所述当前迭代次数对应的频谱泄漏系数；The third calculation subunit is further used to calculate the spectrum leakage coefficient corresponding to the current iteration number according to the multi-dimensional frequency rough estimation result;
所述第三计算子单元，还用于根据所述信号在多个复正弦信号频率估计点的频谱值、所述当前迭代次数对应的频谱泄漏系数和所述上一次迭代多个复正弦波的复幅度系数，计算所述当前迭代次数对应的多个复正弦波的复幅度系数；The third calculation subunit is further used to calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number and the complex amplitude coefficients of the multiple complex sine waves in the previous iteration;
数值增加子单元，用于将所述当前迭代次数的数值增加1，作为新的当前迭代次数，并触发所述第一确定子单元确定当前迭代次数。The value increasing subunit is used to increase the value of the current iteration number by 1 as the new current iteration number, and trigger the first determining subunit to determine the current iteration number.
本申请第三方面提供了一种电子设备，包括存储器以及处理器，所述存储器用于存储计算机程序，所述处理器运行所述计算机程序以使所述电子设备执行本申请第一方面中任一项所述的干扰条件下阵列单快拍多维参数估计方法。A third aspect of the present application provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the array single-snapshot multi-dimensional parameter estimation method under interference conditions described in any one of the first aspect of the present application.
本申请第四方面提供了一种计算机可读存储介质，其存储有计算机程序指令，所述计算机程序指令被一处理器读取并运行时，执行本申请第一方面中任一项所述的干扰条件下阵列单快拍多维参数估计方法。According to a fourth aspect of the present application, a computer-readable storage medium is provided, which stores computer program instructions. When the computer program instructions are read and executed by a processor, the method for estimating multi-dimensional parameters of an array single snapshot under interference conditions described in any one of the first aspect of the present application is executed.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
为了更清楚地说明本申请实施例的技术方案，下面将对本申请实施例中所需要使用的附图作简单地介绍，应当理解，以下附图仅示出了本申请的某些实施例，因此不应被看作是对范围的限定，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他相关的附图。In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.
图1为本申请实施例提供的一种干扰条件下阵列单快拍多维参数估计方法的流程示意图；FIG1 is a flow chart of a method for estimating multi-dimensional parameters of an array single snapshot under interference conditions provided by an embodiment of the present application;
图2为本申请实施例提供的另一种干扰条件下阵列单快拍多维参数估计方法的流程示意图；FIG2 is a schematic flow chart of another method for estimating multi-dimensional parameters of an array single snapshot under interference conditions provided by an embodiment of the present application;
图3为本申请实施例提供的一种三维频率估计结果示意图；FIG3 is a schematic diagram of a three-dimensional frequency estimation result provided in an embodiment of the present application;
图4为本申请实施例提供的一种1-2维度频率估计结果示意图；FIG4 is a schematic diagram of a 1-2 dimensional frequency estimation result provided in an embodiment of the present application;
图5为本申请实施例提供的一种1-3维度频率估计结果示意图；FIG5 is a schematic diagram of a 1-3 dimensional frequency estimation result provided in an embodiment of the present application;
图6示出了不同迭代次数下所提算法的估计性能；Fig. 6 shows the estimated performance of the proposed algorithm at different numbers of iterations;
图7示出了不同SNR下MKFE算法的RMSE；Figure 7 shows the RMSE of the MKFE algorithm under different SNRs;
图8示出了不同采样长度MKFE算法的RMSE；Fig. 8 shows the RMSE of the MKFE algorithm with different sampling lengths;
图9为本申请实施例提供的二维单快拍参数估计FDA-MIMO阵列信号重排示意图；FIG9 is a schematic diagram of a two-dimensional single-snapshot parameter estimation FDA-MIMO array signal rearrangement according to an embodiment of the present application;
图10为本申请实施例提供的三维单快拍参数估计FDA-MIMO阵列信号重排示意图；FIG10 is a schematic diagram of a FDA-MIMO array signal rearrangement for three-dimensional single snapshot parameter estimation provided by an embodiment of the present application;
图11为本申请实施例提供的发射、接收维2D-FFT处理示意图；FIG11 is a schematic diagram of 2D-FFT processing in the transmitting and receiving dimensions provided in an embodiment of the present application;
图12为本申请实施例提供的发射、接收和脉冲维3D-FFT处理示意图；FIG12 is a schematic diagram of 3D-FFT processing in the transmission, reception and pulse dimensions provided in an embodiment of the present application;
图13示出了角度估计算法的性能；Figure 13 shows the performance of the angle estimation algorithm;
图14示出了距离估计算法的性能；Figure 14 shows the performance of the distance estimation algorithm;
图15示出了角度估计算法的性能；Figure 15 shows the performance of the angle estimation algorithm;
图16示出了距离估计算法的性能；Figure 16 shows the performance of the distance estimation algorithm;
图17示出了速度估计算法的性能；Figure 17 shows the performance of the velocity estimation algorithm;
图18为本申请实施例提供的一种干扰条件下阵列单快拍多维参数估计装置的结构示意图；FIG18 is a schematic diagram of the structure of a device for estimating multi-dimensional parameters of an array single snapshot under interference conditions provided by an embodiment of the present application;
图19为本申请实施例提供的另一种干扰条件下阵列单快拍多维参数估计装置的结构示意图。FIG19 is a schematic diagram of the structure of another array single-snapshot multi-dimensional parameter estimation device under interference conditions provided in an embodiment of the present application.
具体实施方式DETAILED DESCRIPTION
下面将结合本申请实施例中的附图，对本申请实施例中的技术方案进行描述。The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application.
应注意到：相似的标号和字母在下面的附图中表示类似项，因此，一旦某一项在一个附图中被定义，则在随后的附图中不需要对其进行进一步定义和解释。同时，在本申请的描述中，术语“第一”、“第二”等仅用于区分描述，而不能理解为指示或暗示相对重要性。It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.
实施例1Example 1
请参看图1，图1为本实施例提供的一种干扰条件下阵列单快拍多维参数估计方法的流程示意图。其中，该干扰条件下阵列单快拍多维参数估计方法包括：Please refer to Figure 1, which is a flow chart of a method for estimating multidimensional parameters of an array single snapshot under interference conditions provided by this embodiment. The method for estimating multidimensional parameters of an array single snapshot under interference conditions includes:
S101、获取干扰条件下的阵列接收信号。S101. Acquire an array receiving signal under interference conditions.
S102、将阵列接收信号的信源多维参数估计问题转化为多维频率估计问题。S102, converting the problem of estimating the multi-dimensional parameters of the source of the array received signal into a problem of estimating the multi-dimensional frequency.
S103、基于多维频率估计问题对阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果。S103 . Based on the multi-dimensional frequency estimation problem, perform multi-dimensional frequency rough estimation on the array received signal to obtain a multi-dimensional frequency rough estimation result.
S104、根据多维频率粗估计结果对阵列接收信号进行多维频率精估计，得到多维频率精估计结果。S104 , performing multi-dimensional frequency precise estimation on the array received signal according to the multi-dimensional frequency rough estimation result to obtain a multi-dimensional frequency precise estimation result.
S105、根据多维频率粗估计结果和多维频率精估计结果，计算频率估计结果。S105. Calculate a frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result.
S106、将频率估计结果转化为参数估计结果。S106: Convert the frequency estimation result into a parameter estimation result.
本实施例中，该方法的执行主体可以为计算机、服务器等计算装置，对此本实施例中不作任何限定。In this embodiment, the execution subject of the method may be a computing device such as a computer or a server, and no limitation is made in this embodiment.
在本实施例中，该方法的执行主体还可以为智能手机、平板电脑等智能设备，对此本实施例中不作任何限定。In this embodiment, the execution subject of the method may also be a smart device such as a smart phone, a tablet computer, etc., which is not limited in this embodiment.
可见，本实施例所描述的干扰条件下阵列单快拍多维参数估计方法，无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。It can be seen that the array single snapshot multi-dimensional parameter estimation method under interference conditions described in this embodiment does not require matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of coherent signal sources using only single snapshot data.
实施例2Example 2
请参看图2，图2为本实施例提供的一种干扰条件下阵列单快拍多维参数估计方法的流程示意图。其中，该干扰条件下阵列单快拍多维参数估计方法包括：Please refer to Figure 2, which is a flow chart of a method for estimating multidimensional parameters of an array single snapshot under interference conditions provided by this embodiment. The method for estimating multidimensional parameters of an array single snapshot under interference conditions includes:
S201、获取干扰条件下的阵列接收信号。S201: Acquire array receiving signals under interference conditions.
S202、将阵列接收信号的信源多维参数估计问题转化为多维频率估计问题。S202, converting the problem of estimating the multi-dimensional parameters of the source of the array received signal into a problem of estimating the multi-dimensional frequency.
本实施例中，假设阵列接收信号S是由Q个复正弦波组成的复信号，其每个正弦波由K个频率确定。在加性高斯白噪声信号背景下，信号S可以被建模为：In this embodiment, it is assumed that the array receiving signal S is a complex signal composed of Q complex sine waves, each of which is determined by K frequencies. In the background of additive white Gaussian noise signal, the signal S can be modeled as:
其中，表示第q个正弦波、第k个维度的频率，Aq表示第q个正弦波的复幅度系数，n(m1，...，mK)表示高斯白噪声信号；in, represents the frequency of the qth sine wave and the kth dimension, Aq represents the complex amplitude coefficient of the qth sine wave, and n(m1 , ..., mK ) represents a Gaussian white noise signal;
根据式(1.1)定义，接收信号S可以被重新表示为如下向量形式：According to the definition of formula (1.1), the received signal S can be re-expressed as the following vector form:
其中，in,
在本实施例中，定义一组Vandermonde矩阵其表达式为：In this embodiment, a set of Vandermonde matrices is defined Its expression is:
其中，表示一个具有Vandermonde结构的向量，其表达式为：in, represents a vector with a Vandermonde structure, which is expressed as:
利用式(1.3)，式(1.2)可以被重构为Using formula (1.3), formula (1.2) can be reconstructed as
其中，表示Khatri-Rao积运算，n假定为服从零均值，协方差矩阵的复高斯白噪声信号，表示噪声功率。in, represents the Khatri-Rao product operation, n is assumed to have zero mean, and the covariance matrix The complex white Gaussian noise signal is Represents the noise power.
本实施例中，基于阵列接收信号进行K维频率估计所得到的频率估计结果包括多个复正弦波的多维估计频率；In this embodiment, the frequency estimation result obtained by performing K-dimensional frequency estimation based on the array received signal includes multi-dimensional estimated frequencies of multiple complex sine waves;
其中，复正弦信号K维频率估计(Multiple Sinusoids K-D FrequencyEstimation，MKFE)算法是通过粗估计和精估计两部分来进行的。具体的，定义第q个正弦信号，第k个维度的频率表示为：The Multiple Sinusoids KD Frequency Estimation (MKFE) algorithm is performed through two parts: rough estimation and fine estimation. Specifically, the qth sinusoidal signal, the frequency of the kth dimension is defined as It is expressed as:
其中，为第q个正弦信号、第k个维度的估计频率；in, is the estimated frequency of the qth sinusoidal signal and the kth dimension;
定义为整数频率，表示频率粗估计结果； Defined as integer frequency, it represents the rough frequency estimation result;
定义为分数阶残差频率，表示频率精估计结果。 Defined as the fractional-order residual frequency, it represents the frequency estimation result.
S203、基于多维频率估计问题对阵列接收信号进行多维快速傅里叶变换处理，得到多维频谱矩阵块。S203 , performing multi-dimensional fast Fourier transform processing on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional spectrum matrix block.
本实施例中，该方法可以先对接收信号进行K维快速傅里叶变换(Fast FourierTransform,FFT)运算，可以得到信号的K维频谱矩阵块PK，其表达式为：In this embodiment, the method may first perform a K-dimensional Fast Fourier Transform (FFT) operation on the received signal to obtain a K-dimensional spectrum matrix block PK of the signal, which is expressed as follows:
其中，nk＝0，1，...，lkMk-1；Wherein, nk =0, 1, ..., lk Mk -1;
lk为正整数，表示扩展因子，用于在K维FFT处理时执行零填充，执行零填充后的取值范围变为[-0.5/lk，0.5/lk]。lk is a positive integer, indicating the expansion factor, which is used to perform zero padding in K-dimensional FFT processing. The value range becomes [-0.5/lk , 0.5/lk ].
S204、根据频谱矩阵块获取信号频谱峰值点坐标。S204 , obtaining the coordinates of the peak points of the signal spectrum according to the spectrum matrix block.
本实施例中，假设输入SNR大于SNR阈值门限(DFT类频率估计算法具有阈值效应，当SNR超过阈值门限时，算法的均方根误差会迅速减小并接近CRB)，在进行K维FFT处理后，即可得到信号的频谱峰值点，记峰值点的坐标为：In this embodiment, assuming that the input SNR is greater than the SNR threshold (the DFT-type frequency estimation algorithm has a threshold effect. When the SNR exceeds the threshold, the root mean square error of the algorithm will decrease rapidly and approach the CRB), after performing K-dimensional FFT processing, the spectrum peak point of the signal can be obtained. The coordinates of the peak point are recorded as:
S205、根据信号频谱峰值点坐标进行复正弦波的多维频率粗估计，得到多维频率粗估计结果。S205 , performing a rough estimation of the multi-dimensional frequency of the complex sine wave according to the coordinates of the peak points of the signal spectrum to obtain a rough estimation result of the multi-dimensional frequency.
本实施例中，多维频率粗估计结果为：In this embodiment, the multi-dimensional frequency rough estimation result is:
其中，表示Q个复正弦波的K维频率粗估计结果；lk为正整数，表示扩展因子。in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; lk is a positive integer, representing the expansion factor.
需要说明的是，DFT类频率估计算法的阈值效应是由算法估计的步骤决定的。DFT类频率估计算法分粗估计和精估计两部分，精估计的初始值依赖于粗估计的结果。粗估计部分是通过FFT实现的，若SNR较低，则无法凝聚出信号正确的峰值点，不能为精估计提供正确的初始值，从而无法准确地估计信号频率。而一旦SNR超越某一阈值门限，则可以正确地凝聚出峰值点，为精估计提供正确的初始值。因此，在SNR超越某一阈值门限后，算法的估计性能会迅速提高，该阈值也称为DFT类算法的SNR击穿阈值。在实际应用中，通过执行零填充，可以有效地降低算法的SNR击穿阈值，提高低SNR下算法的估计性能。It should be noted that the threshold effect of the DFT-type frequency estimation algorithm is determined by the algorithm estimation step. The DFT-type frequency estimation algorithm is divided into two parts: coarse estimation and fine estimation. The initial value of the fine estimation depends on the result of the coarse estimation. The coarse estimation part is implemented by FFT. If the SNR is low, the correct peak point of the signal cannot be condensed, and the correct initial value cannot be provided for the fine estimation, so the signal frequency cannot be accurately estimated. Once the SNR exceeds a certain threshold, the peak point can be correctly condensed to provide the correct initial value for the fine estimation. Therefore, after the SNR exceeds a certain threshold, the estimation performance of the algorithm will increase rapidly. This threshold is also called the SNR breakdown threshold of the DFT-type algorithm. In practical applications, by performing zero padding, the SNR breakdown threshold of the algorithm can be effectively reduced, thereby improving the estimation performance of the algorithm under low SNR.
S206、根据预设的采样长度计算最大迭代次数和偏移量。S206: Calculate the maximum number of iterations and the offset according to the preset sampling length.
本实施例中，由于频率精估计算法的性能会受到迭代次数的影响。因此，为了避免过多的迭代导致的计算复杂度的增加(此时并不会提高性能)，该方法提出了计算最大迭代次数Iopt的算法，其计算表达式为：In this embodiment, since the performance of the frequency estimation algorithm is affected by the number of iterations, in order to avoid the increase in computational complexity caused by too many iterations (which does not improve the performance), the method proposes an algorithm for calculating the maximum number of iterations Iopt , and its calculation expression is:
其中，表示向上取整。in, Indicates rounding up.
此外，偏移量是不确定的，它的取值会影响算法的性能，其取值准则为：In addition, the offset is uncertain, and its value will affect the performance of the algorithm. Its value selection criteria are:
在本实施例中，在确定了算法的迭代次数I和偏移量的取值后，就可以得到Q个复正弦波K个维度的频率估计值。In this embodiment, after determining the number of iterations I and the offset of the algorithm, After taking the value of , we can get the frequency estimation values of Q complex sine waves in K dimensions.
S207、确定当前迭代次数。S207: Determine the current number of iterations.
S208、根据当前迭代次数获取上一次迭代频谱精估计值和上一次迭代多个复正弦波的复幅度系数。S208. Obtain, according to the current iteration number, a precise frequency spectrum estimation value of the previous iteration and complex amplitude coefficients of a plurality of complex sine waves of the previous iteration.
本实施例中，对于Q个复正弦波不同维度的分数阶残差频率，该方法对该频率逐一进行精估计。In this embodiment, for the fractional-order residual frequencies of different dimensions of Q complex sine waves, the method accurately estimates the frequencies one by one.
在本实施例中，假定在第i次迭代(即当前迭代次数)后，已经得到了第q个复正弦波第k个维度的分数阶残差频率估计值(即上一次迭代频谱精估计值，初始值设置为零)，期望在下一次迭代过程中更新频率估计结果。In this embodiment, it is assumed that after the i-th iteration (i.e., the current iteration number), the fractional-order residual frequency estimate of the k-th dimension of the q-th complex sine wave has been obtained. (i.e. the accurate estimate of the spectrum in the previous iteration, the initial value It is set to zero), and the frequency estimation result is expected to be updated in the next iteration.
在本实施例中，αr(i-1)表示在第i-1次迭代，第r个复正弦波的复幅度系数(即上一次迭代多个复正弦波的复幅度系数，其初始值αr(0)设置为0)。In this embodiment, αr(i-1) represents the complex amplitude coefficient of the rth complex sine wave in the i-1th iteration (ie, the complex amplitude coefficients of multiple complex sine waves in the previous iteration, whose initial value αr(0) is set to 0).
S209、根据多维频率粗估计结果、上一次迭代频谱精估计值、偏移量和阵列接收信号，计算多个复正弦波的频谱泄漏系数和多个复正弦信号的多维偏移频谱值。S209, calculating spectrum leakage coefficients of multiple complex sinusoidal waves and multidimensional offset spectrum values of multiple complex sinusoidal signals according to the multidimensional frequency coarse estimation result, the spectrum precise estimation value of the previous iteration, the offset and the array received signal.
本实施例中，表示第r个复正弦波的频谱泄漏系数。其中，的计算表达式为：In this embodiment, represents the spectrum leakage coefficient of the rth complex sine wave. Among them, The calculation expression is:
本实施例中，表示信号S在第q个复正弦信号，第k个维度偏移了后的频谱值。其中，的计算表达式为：In this embodiment, It means that the signal S is a complex sinusoidal signal in the qth dimension, and the kth dimension is offset by The spectrum value after . Among them, The calculation expression is:
S210、根据上一次迭代多个复正弦波的复幅度系数、多个复正弦波的频谱泄漏系数以及多个复正弦信号的多维偏移频谱值，计算多个复正弦波的多维偏移后频谱泄漏校正系数。S210, calculating multidimensional offset spectrum leakage correction coefficients of the multiple complex sinusoids according to the complex amplitude coefficients of the multiple complex sinusoids, the spectrum leakage coefficients of the multiple complex sinusoids and the multidimensional offset spectrum values of the multiple complex sinusoidal signals in the previous iteration.
本实施例中，由于信号S包含了Q个复正弦波，在估计第q个复正弦波的频率时，其余Q-1个复正弦波会对估计性能造成影响。因此，计算第q个复正弦波的频谱泄漏校正系数时，需要消除其余Q-1个信源分量，其计算表达式为：In this embodiment, since the signal S contains Q complex sinusoids, when estimating the frequency of the qth complex sinusoid, the remaining Q-1 complex sinusoids will affect the estimation performance. Therefore, the spectrum leakage correction coefficient of the qth complex sinusoid is calculated as When , the remaining Q-1 source components need to be eliminated, and the calculation expression is:
其中，αr(i-1)表示在第i-1次迭代，第r个复正弦波的复幅度系数(即上一次迭代多个复正弦波的复幅度系数，其初始值αr(0)设置为0)。表示第r个复正弦波的频谱泄漏系数。表示信号S在第q个复正弦信号，第k个维度偏移了后的频谱值。Wherein, αr(i-1) represents the complex amplitude coefficient of the rth complex sine wave in the i-1th iteration (i.e., the complex amplitude coefficients of multiple complex sine waves in the previous iteration, whose initial value αr(0) is set to 0). represents the spectrum leakage coefficient of the rth complex sine wave. It means that the signal S is a complex sinusoidal signal in the qth dimension, and the kth dimension is offset by The subsequent spectrum value.
S211、根据多个复正弦波的多维偏移后频谱泄漏校正系数和上一次迭代频谱精估计值，计算本次频率精估计值。S211, calculating the current frequency precise estimation value according to the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the previous iterative spectrum precise estimation value.
其中，根据第i-1次的估计结果(即上一次迭代频谱精估计值)，第i次迭代频率精估计值的计算表达式为：Among them, according to the i-1th estimation result (i.e., the accurate value of the spectrum in the previous iteration), the calculation expression for the accurate value of the frequency in the i-th iteration is:
其中，Re(·)表示取实部操作，表示第q个复正弦波在第k个维度偏移了后的频谱泄漏校正系数，表示归一化系数。Among them, Re(·) represents the real part operation, It means that the qth complex sine wave is shifted in the kth dimension The spectrum leakage correction coefficient after Represents the normalization coefficient.
的表达式为 The expression is
其中，表示偏移量。in, Indicates the offset.
S212、判断当前迭代次数是否达到最大迭代次数，若是，则执行步骤S213；若否，则执行步骤S207。S212: Determine whether the current number of iterations reaches the maximum number of iterations. If so, execute step S213; if not, execute step S207.
本实施例中，在执行步骤S207之前，该方法为了执行下一次的迭代，可以对每个信源的复幅度值αq(i)进行更新，其可以利用最大似然估计计算得到，相应的计算表达式为：In this embodiment, before executing step S207, the method may update the complex amplitude value αq(i) of each information source in order to perform the next iteration, which may be calculated using maximum likelihood estimation, and the corresponding calculation expression is:
其中，表示第i次迭代后，信号s在第q个复正弦信号频率估计点的频谱值，表示第i次估计后的频谱泄漏系数。in, It represents the spectrum value of signal s at the qth complex sinusoidal signal frequency estimation point after the i-th iteration. Represents the spectrum leakage coefficient after the i-th estimation.
的计算表达式为 The calculation expression is
的计算表达式为 The calculation expression is
作为一种可选的实施方式，在判断出当前迭代次数未达到最大迭代次数时，且在执行步骤S207之前，该方法还包括：As an optional implementation, when it is determined that the current number of iterations has not reached the maximum number of iterations and before executing step S207, the method further includes:
(当判断出当前迭代次数未达到最大迭代次数时)根据多维频率粗估计结果和上一次迭代频谱精估计值计算信号在多个复正弦信号频率估计点的频谱值；(When it is determined that the current number of iterations has not reached the maximum number of iterations) calculating the spectrum values of the signal at multiple complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency rough estimation result and the spectrum precise estimation value of the previous iteration;
根据多维频率粗估计结果，计算当前迭代次数对应的频谱泄漏系数(即基于上述方式计算得到)；According to the multi-dimensional frequency rough estimation result, the spectrum leakage coefficient corresponding to the current iteration number is calculated (that is, the spectrum leakage coefficient corresponding to the current iteration number is calculated based on the above method). );
根据信号在多个复正弦信号频率估计点的频谱值、当前迭代次数对应的频谱泄漏系数和上一次迭代多个复正弦波的复幅度系数，计算当前迭代次数对应的多个复正弦波的复幅度系数；Calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves in the previous iteration;
将当前迭代次数的数值增加1，作为新的当前迭代次数，并执行确定当前迭代次数(即执行步骤S207)。The value of the current iteration number is increased by 1 to be used as the new current iteration number, and the current iteration number is determined (ie, step S207 is executed).
S213、将本次频率精估计值确定为多维频率精估计结果。S213: Determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result.
S214、根据多维频率粗估计结果和多维频率精估计结果，计算频率估计结果。S214. Calculate a frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result.
S215、将频率估计结果转化为参数估计结果。S215: Convert the frequency estimation result into a parameter estimation result.
本实施例中，该方法可以通过重复上述步骤，对不同复正弦信号的频率和幅值依次进行估计。其中，随着迭代次数的增加，估计误差将逐渐减小，频率估计值将逐渐收敛于一个稳定的结果。假设总共执行了I次迭代，得到了第q个复正弦波第k个维度的分数阶残差频率估计值In this embodiment, the method can estimate the frequency and amplitude of different complex sinusoidal signals in turn by repeating the above steps. As the number of iterations increases, the estimation error will gradually decrease, and the frequency estimation value will gradually converge to a stable result. Assuming that a total of I iterations are performed, the fractional-order residual frequency estimation value of the kth dimension of the qth complex sinusoidal wave is obtained.
综上，根据频率粗估计和精估计的结果，第q个复正弦波第k个维度的频率估计值表示为：In summary, based on the results of rough and precise frequency estimation, the frequency estimate of the kth dimension of the qth complex sine wave is It is expressed as:
综上，该方法总结给出了单快拍K维单快拍相干信源多维参数估计算法的伪代码。具体如下：In summary, this method summarizes and gives the pseudo code of the multi-dimensional parameter estimation algorithm of a single-snapshot K-dimensional single-snapshot coherent signal source. The details are as follows:
输入：单快拍多复正弦信号s，采样长度Mk。Input: single snapshot multi-complex sinusoidal signal s, sampling length Mk .
初始化：设置I＝Iopt，l1≥1，...，lK≥1，α1(0)＝...＝αQ(0)＝0，Initialization: set I = Iopt , l1 ≥1,..., lK ≥1, α1(0) =...=αQ(0) =0,
通过式(1.7)执行K维FFT得到频谱矩阵块PK。Performing K-dimensional FFT through equation (1.7) yields the spectrum matrix block PK .
通过式(1.9)得到频率粗估计值The rough frequency estimate is obtained by formula (1.9):
For i＝1，...，IdoFor i=1,...,Ido
For q＝1，...，QdoFor q＝1，...，Qdo
通过式(1.12)计算Calculated by formula (1.12)
For k＝1，...，KdoFor k=1, ..., Kdo
通过式(1.13)计算Calculated by formula (1.13)
通过式(1.14)计算Calculated by formula (1.14)
根据式(1.15)计算Calculate according to formula (1.15)
EndEnd
根据式(1.18)和(1.19)分别计算和According to formula (1.18) and (1.19), we can calculate and
根据式(1.17)更新αq(i)。Update αq(i) according to formula (1.17).
endend
endend
输出：频率估计结果Output: Frequency estimation result
本实施例中，该方法实施前采用数值仿真验证所提算法的性能，并将所提算法的性能与参数估计的克拉美罗界进行比较。考虑复信号由两个相干信源组成，每个信源分别由三个频率来决定，其频率分别为由于算法的目的主要在于频率估计，为了方便起见，两个信源的幅度系数Aq都设置为1。在后续仿真中设置M1＝M2＝M3＝M，l1＝l2＝l3＝l，并采用M和l来替代Mk和lk(k＝1，2，3)。In this embodiment, numerical simulation is used to verify the performance of the proposed algorithm before the method is implemented, and the performance of the proposed algorithm is compared with the Cramer-Rao bound of parameter estimation. Consider that the complex signal consists of two coherent sources, each of which is determined by three frequencies, and their frequencies are Since the purpose of the algorithm is mainly frequency estimation, for convenience, the amplitude coefficientAq of the two sources is set to 1. In the subsequent simulation,M1 =M2 =M3 =M,l1 =l2 =l3 =l are set, and M and l are used to replaceMk andlk (k=1, 2, 3).
仿真利用频率估计的RMSE来评估算法的性能，其定义为：The simulation uses the RMSE of frequency estimation to evaluate the performance of the algorithm, which is defined as:
其中，Nc＝20000表示蒙特卡洛仿真次数，表示第nc次蒙特卡洛仿真第q个信源第k个维度的频率估计值。Where, Nc = 20000 represents the number of Monte Carlo simulations. It represents the frequency estimate of the kth dimension of the qth source in thenth Monte Carlo simulation.
在本实施例中，对算法有效性验证的过程如下：In this embodiment, the process of verifying the validity of the algorithm is as follows:
设置采样长度M＝17，信号SNR＝10dB，图3、图4和图5给出了两个信源的频率估计结果，其中，图3示出了三维频率估计结果，图4示出了1-2维度频率估计结果，图5示出了1-3维度频率估计结果。由图可以看出，所提算法能够在不同的维度上准确地估计了两个信源的频率，从而以此验证了算法的有效性。Set the sampling length M = 17, signal SNR = 10dB, Figures 3, 4 and 5 show the frequency estimation results of the two sources, where Figure 3 shows the three-dimensional frequency estimation result, Figure 4 shows the 1-2 dimensional frequency estimation result, and Figure 5 shows the 1-3 dimensional frequency estimation result. It can be seen from the figure that the proposed algorithm can accurately estimate the frequencies of the two sources in different dimensions, thereby verifying the effectiveness of the algorithm.
在本实施例中，为了验证最优迭代次数的有效性，图6给出了所提算法在不同迭代次数下的RMSE(即图6示出了不同迭代次数下所提算法的估计性能)。由图6可以看出，对于所有信噪比值，MKFE算法都能收敛于Iopt＝3，因此证明了算法的有效性。此外，还可以发现增加迭代次数并不能提高性能，反而增加了计算复杂度，故在实际应用中不需要设置过高的迭代次数。In this embodiment, in order to verify the effectiveness of the optimal number of iterations, FIG6 shows the RMSE of the proposed algorithm at different numbers of iterations (i.e., FIG6 shows the estimated performance of the proposed algorithm at different numbers of iterations). As can be seen from FIG6, for all signal-to-noise ratio values, the MKFE algorithm can converge to Iopt = 3, thus proving the effectiveness of the algorithm. In addition, it can be found that increasing the number of iterations does not improve the performance, but increases the computational complexity, so it is not necessary to set too high a number of iterations in practical applications.
在本实施例中，对不同采样长度下算法的性能的验证如下：In this embodiment, the performance of the algorithm under different sampling lengths is verified as follows:
设置扩展因子l＝3，图7给出了MKFE算法在不同SNR下，不同采样长度的RMSE(即图7示出了不同SNR下MKFE算法的RMSE)。如图7所示，在信噪比较低的情况下，MKFE算法的估计性能较差。当信噪比超过SNR阈值后，MKFE算法的性能接近CRB，能够准确的估计出信号的频率。比如，当信噪比大于2dB时，RMSE近似于CRB，在转换为dB之前，MKFE算法的RMSE是CRB的1.7倍。此外，还可以发现随着采样长度从17增加到48，信噪比阈值从4dB下降到0dB。Set the expansion factor l=3, and Figure 7 shows the RMSE of the MKFE algorithm at different SNRs and different sampling lengths (i.e., Figure 7 shows the RMSE of the MKFE algorithm at different SNRs). As shown in Figure 7, when the signal-to-noise ratio is low, the estimation performance of the MKFE algorithm is poor. When the signal-to-noise ratio exceeds the SNR threshold, the performance of the MKFE algorithm is close to that of the CRB, and the frequency of the signal can be accurately estimated. For example, when the signal-to-noise ratio is greater than 2dB, the RMSE is similar to that of the CRB, and before conversion to dB, the RMSE of the MKFE algorithm is 1.7 times that of the CRB. In addition, it can be found that as the sampling length increases from 17 to 48, the signal-to-noise ratio threshold drops from 4dB to 0dB.
图8给出了在不同信噪比下，MKFE算法在不同采样长度下的RMSE性能(即图8示出了不同采样长度MKFE算法的RMSE)。从图8可以发现，当SNR＝10dB或SNR＝20dB时，MKFE算法的RMSE更接近CRB。此外，当SNR＝0dB时，若采样长度M小于48，算法的估计性能较差。这因为较短的采样长度对应了较高的SNR击穿阈值，从而导致在低信噪比条件下采样数目较小场景的RMSE性能较差，与图7的现象一致。Figure 8 shows the RMSE performance of the MKFE algorithm at different sampling lengths under different signal-to-noise ratios (i.e., Figure 8 shows the RMSE of the MKFE algorithm at different sampling lengths). It can be seen from Figure 8 that when SNR = 10dB or SNR = 20dB, the RMSE of the MKFE algorithm is closer to CRB. In addition, when SNR = 0dB, if the sampling length M is less than 48, the estimation performance of the algorithm is poor. This is because a shorter sampling length corresponds to a higher SNR breakdown threshold, which leads to poor RMSE performance in scenarios with a small number of samples under low signal-to-noise ratio conditions, which is consistent with the phenomenon in Figure 7.
本实施例中，该方法的执行主体可以为计算机、服务器等计算装置，对此本实施例中不作任何限定。In this embodiment, the execution subject of the method may be a computing device such as a computer or a server, and no limitation is made in this embodiment.
在本实施例中，该方法的执行主体还可以为智能手机、平板电脑等智能设备，对此本实施例中不作任何限定。In this embodiment, the execution subject of the method may also be a smart device such as a smart phone, a tablet computer, etc., which is not limited in this embodiment.
可见，本实施例所描述的干扰条件下阵列单快拍多维参数估计方法，无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。It can be seen that the array single snapshot multi-dimensional parameter estimation method under interference conditions described in this embodiment does not require matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of coherent signal sources using only single snapshot data.
实施例3Example 3
本实施例示出了一种在FDA-MIMO阵列中实施该方法的过程。其中，FDA-MIMO的信源多维参数估计问题可以转换为复正弦信号的多维频率估计问题。发射、接收和多普勒频率分别定义为：This embodiment shows a process of implementing this method in an FDA-MIMO array. The multidimensional parameter estimation problem of the FDA-MIMO source can be converted into a multidimensional frequency estimation problem of a complex sinusoidal signal. The transmit, receive and Doppler frequencies are defined as:
f1＝dsinθ/λ-2r△f/cf1 = dsinθ/λ-2r△f/c
f2＝dsinθ/λf2 = dsinθ/λ
f3＝2vTp/λf3 = 2vTp /λ
其中，d表示阵元间距，λ＝c/f0表示信号波长，c表示光速，f0表示第一个发射阵元的载频，λ表示信号波长，Δf表示频率偏移。Tp表示脉冲重复周期。(r，θ，v)表示信源距离、角度和速度。Where d represents the array element spacing, λ=c/f0 represents the signal wavelength, c represents the speed of light,f0 represents the carrier frequency of the first transmitting array element, λ represents the signal wavelength, and Δf represents the frequency offset.Tp represents the pulse repetition period. (r, θ, v) represents the source distance, angle, and speed.
首先，定义第q个信源的发射、接收和多普勒频率分别表示为：First, the transmission, reception and Doppler frequencies of the qth source are defined as:
其中，和为整数频率，表示频率粗估计结果。和为分数阶残差频率，表示频率精估计结果，取值范围为[-0.5，0.5]。in, and is an integer frequency, which indicates the rough frequency estimation result. and is the fractional-order residual frequency, which indicates the frequency estimation result, and its value range is [-0.5, 0.5].
首先，进行信源参数粗估计：First, make a rough estimate of the source parameters:
在进行信源参数粗估计之前，首先对阵列接收的单信号进行重排。在不考虑信源速度的情况下，对于FDA-MIMO阵列信源距离、角度二维联合估计问题，将M1M2×1维单快拍回波信号重新排列为M1×M2维矩阵Y2，表示为：Before making a rough estimate of the source parameters, the single signals received by the array are first rearranged. Without considering the source speed, for the two-dimensional joint estimation of the source distance and angle of the FDA-MIMO array, the M1 M2 ×1-dimensional single snapshot echo signal is reordered. Rearranged into M1 ×M2 -dimensional matrix Y2 , expressed as:
其中，表示噪声信号的重构矩阵；in, Reconstructed matrix representing the noisy signal;
表示发射导向矢量； represents the launch steering vector;
表示接收导向矢量。 Represents the receive steering vector.
为了便于理解，图9给出了FDA-MIMO阵列二维参数估计中多快拍数据、单快拍数据和单快拍重排后数据的示意图(即图9为二维单快拍参数估计FDA-MIMO阵列信号重排示意图)。For ease of understanding, FIG9 shows a schematic diagram of multi-snapshot data, single-snapshot data, and single-snapshot rearranged data in two-dimensional parameter estimation of the FDA-MIMO array (ie, FIG9 is a schematic diagram of signal rearrangement of a two-dimensional single-snapshot parameter estimation FDA-MIMO array).
对于FDA-MIMO阵列信源距离、角度及速度三维联合估计问题，将M1M2M3×1维单快拍回波信号重新排列为M1×M2×M3维矩阵Y3，表示为：For the three-dimensional joint estimation of source distance, angle and velocity of FDA-MIMO array, the M1 M2 M3 × 1-dimensional single snapshot echo signal is transformed into Rearranged into M1 ×M2 ×M3 -dimensional matrix Y3 , expressed as:
其中，表示噪声信号的重构矩阵，表示的第一个元素，表示时间导向矢量。in, represents the reconstruction matrix of the noisy signal, express The first element of Represents a time-oriented vector.
图10给出了FDA-MIMO阵列三维参数估计中多快拍数据、单快拍数据和单快拍重排后数据的示意图(即图10为三维单快拍参数估计FDA-MIMO阵列信号重排示意图)。FIG10 shows a schematic diagram of multi-snapshot data, single-snapshot data and single-snapshot rearranged data in three-dimensional parameter estimation of FDA-MIMO array (ie, FIG10 is a schematic diagram of signal rearrangement of FDA-MIMO array for three-dimensional single-snapshot parameter estimation).
对于FDA-MIMO阵列，无论是二维估计还是三维参数估计，算法的参数粗估计都是通过FFT来实现的。用重排后的接收信号Y2和Y3分别替换式(1.7)中的信号S进行2D-FFT和3D-FFT计算，分别得到信源的二维频谱矩阵块P2和三维频谱矩阵块P3。假设输入SNR大于SNR阈值门限，那么在进行2D-FFT或3D-FFT处理后，即可得到信源的峰值点。For FDA-MIMO arrays, whether it is two-dimensional estimation or three-dimensional parameter estimation, the rough estimation of the algorithm parameters is achieved through FFT. The rearranged received signals Y2 and Y3 are used to replace the signal S in equation (1.7) for 2D-FFT and 3D-FFT calculations, respectively, to obtain the two-dimensional spectrum matrix block P2 and the three-dimensional spectrum matrix block P3 of the signal source. Assuming that the input SNR is greater than the SNR threshold, the peak point of the signal source can be obtained after 2D-FFT or 3D-FFT processing.
图11和图12分别给出了2D-FFT和3D-FFT处理后回波信号的二维或三维频谱图，此时信源峰值点已经凸显出来。FIG11 and FIG12 respectively show the two-dimensional or three-dimensional spectrograms of the echo signal after 2D-FFT and 3D-FFT processing, where the peak point of the signal source has been highlighted.
具体的，图11为发射、接收维2D-FFT处理示意图；图12为发射、接收和脉冲维3D-FFT处理示意图。Specifically, FIG11 is a schematic diagram of 2D-FFT processing in the transmission and reception dimensions; FIG12 is a schematic diagram of 3D-FFT processing in the transmission, reception and pulse dimensions.
其中，记频谱矩阵块中第q个峰值点的坐标为：Among them, the coordinates of the qth peak point in the spectrum matrix block are recorded as:
其中，K的大小由所解决的问题来确定。若为信源距离、角度二维联合估计问题，则K＝2；若为信源距离、角度及速度三维联合估计问题，则K＝3。The size of K is determined by the problem to be solved. If it is a two-dimensional joint estimation problem of source distance and angle, then K = 2; if it is a three-dimensional joint estimation problem of source distance, angle and speed, then K = 3.
在进行FFT处理后，第q个信源每个维度的频率粗估计结果可以表示为：After FFT processing, the rough frequency estimation result of each dimension of the qth signal source can be expressed as:
其次，进行信源参数精估计：Secondly, the source parameters are precisely estimated:
对于多信源场景，FDA-MIMO阵列接收回波即可以视为多个复正弦信号的叠加。若K＝2，即为多信源单快拍距离、角度二维联合估计场景；若K＝3即为多信源单快拍距离、角度及速度三维联合估计场景。For multi-source scenarios, the echo received by the FDA-MIMO array can be regarded as the superposition of multiple complex sinusoidal signals. If K = 2, it is a multi-source single snapshot distance, angle two-dimensional joint estimation scenario; if K = 3, it is a multi-source single snapshot distance, angle and speed three-dimensional joint estimation scenario.
基于上述内容，该方法进行以下的仿真实验及结果分析：Based on the above content, this method conducts the following simulation experiments and result analysis:
采用数值仿真来验证所提算法的性能，并将所提算法的性能与DFT搜索算法、PARAFAC算法及CRB进行比较。由于算法在单信源场景下和多信源场景下采用的算法流程不同，因此分单信源和多信源场景分别进行仿真实验。Numerical simulation is used to verify the performance of the proposed algorithm, and the performance of the proposed algorithm is compared with that of the DFT search algorithm, PARAFAC algorithm and CRB. Since the algorithm uses different algorithm processes in single-source and multi-source scenarios, simulation experiments are performed separately for single-source and multi-source scenarios.
仿真采用经典的均匀频偏FDA-MIMO阵列系统，发射阵列和接收阵列都采用阵元间距为半波长的均匀线阵。表1给出了相应的阵列仿真参数。设置执行零填充的扩展因子仿真所给出的RMSE是执行了20000次蒙特卡洛仿真后的结果。The simulation uses the classic uniform frequency offset FDA-MIMO array system. Both the transmitting array and the receiving array use uniform linear arrays with an array element spacing of half a wavelength. Table 1 gives the corresponding array simulation parameters. Set the expansion factor for zero padding The RMSE given by the simulation is the result of executing 20,000 Monte Carlo simulations.
表1FDA-MIMO阵列系统参数Table 1FDA-MIMO array system parameters
实验1：二维参数估计的RMSEExperiment 1: RMSE of 2D parameter estimation
对于二维参数估计问题，考虑两个相干信源分别位于(0.5km，-10°)、(1.5km，20°)。由于DFT搜索算法性能受离散量化数的影响，故分别仿真了离散量化数nθ和nr为512和1024时算法的RMSE性能。图13和图14给出了多信源场景下，天线维度分别为24和48时，不同算法随SNR变化的RMSE性能(即图13示出了角度估计算法的性能、图14示出了距离估计算法的性能)。For the two-dimensional parameter estimation problem, consider two coherent signal sources located at (0.5km, -10°) and (1.5km, 20°). Since the performance of the DFT search algorithm is affected by the discrete quantization number, the RMSE performance of the algorithm is simulated when the discrete quantization numbers nθ and nr are 512 and 1024, respectively. Figures 13 and 14 show the RMSE performance of different algorithms with SNR changes when the antenna dimensions are 24 and 48, respectively, in a multi-source scenario (i.e., Figure 13 shows the performance of the angle estimation algorithm, and Figure 14 shows the performance of the distance estimation algorithm).
对比所提算法和DFT搜索算法，从图13和图14可以看出所提算法的估计性能优于DFT搜索算法。具体来讲，所提算法的SNR击穿阈值明显小于DFT搜索算法，这意味着算法能够在低信噪比场景下能够获得更优的估计精度。从图13和图14还可以发现DFT搜索算法的性能会受到角度维和距离维离散量化数nθ和nr的影响。这是因为该算法是一种网格搜索算法，增大离散量化数可以提升算法的运算性能，但此时也会导致算法的运算复杂度升高。相比之下，所提算法在进行精细估计时不需要进行网格搜索，且具有更好的估计性能。Comparing the proposed algorithm with the DFT search algorithm, it can be seen from Figures 13 and 14 that the proposed algorithm has better estimation performance than the DFT search algorithm. Specifically, the SNR breakdown threshold of the proposed algorithm is significantly lower than that of the DFT search algorithm, which means that the algorithm can obtain better estimation accuracy in low signal-to-noise ratio scenarios. It can also be found from Figures 13 and 14 that the performance of the DFT search algorithm is affected by the discrete quantization numbers nθ and nr in the angle dimension and distance dimension. This is because the algorithm is a grid search algorithm. Increasing the discrete quantization number can improve the algorithm's computational performance, but this will also increase the algorithm's computational complexity. In contrast, the proposed algorithm does not require grid search when performing fine estimation and has better estimation performance.
实验2：三维参数估计的RMSEExperiment 2: RMSE of 3D parameter estimation
对于三维参数估计问题，设置两个相干信源参数分别为(20°,5km,100m/s)、(-10°,0.5km,50m/s)。考虑到现有已公开文献尚无成熟的FDA-MIMO阵列单快拍相干信源三维参数估计算法，因此本实验将已公开发表的PARAFAC算法与所提算法进行对比。由于PARAFAC方法是一种多快拍算法，无法在单快拍条件下进行相干信源参数估计。故PARAFAC算法的实验中设置了两个非相干信源，仿真给出了采样数据分别为5个快拍和20个快拍时PARAFAC算法的估计性能。图15、图16、图17给出了多信源场景下，天线维度分别为24和48时，不同算法随SNR变化的RMSE性能(即，图15示出了角度估计算法的性能，图16示出了距离估计算法的性能，图17示出了速度估计算法的性能)。For the three-dimensional parameter estimation problem, the parameters of two coherent signal sources are set to (20°, 5km, 100m/s) and (-10°, 0.5km, 50m/s). Considering that there is no mature three-dimensional parameter estimation algorithm for single-snap coherent signal sources in the existing public literature, this experiment compares the publicly published PARAFAC algorithm with the proposed algorithm. Since the PARAFAC method is a multi-snap algorithm, it is impossible to estimate the parameters of the coherent signal source under single-snap conditions. Therefore, two incoherent signal sources are set in the experiment of the PARAFAC algorithm, and the simulation gives the estimation performance of the PARAFAC algorithm when the sampling data is 5 snapshots and 20 snapshots respectively. Figures 15, 16, and 17 show the RMSE performance of different algorithms with SNR changes when the antenna dimensions are 24 and 48 respectively in the multi-source scenario (that is, Figure 15 shows the performance of the angle estimation algorithm, Figure 16 shows the performance of the distance estimation algorithm, and Figure 17 shows the performance of the speed estimation algorithm).
对于距离估计，所提算法的估计性能优于5个快拍PARAFAC算法的估计性能，与20个快拍时PARAFAC算法的性能基本一致(需要说明的是，此处给出的CRB是基于单快拍得到的，故PARAFAC算法在快拍数较多时的估计性能可能会低于CRB)。对于速度估计，所提算法的估计性能优于5个或20个快拍下PARAFAC算法的估计性能。特别是在低信噪比条件下，所提算法具有更好的距离和速度估计性能。For distance estimation, the estimation performance of the proposed algorithm is better than that of the PARAFAC algorithm with 5 snapshots, and is basically consistent with the performance of the PARAFAC algorithm with 20 snapshots (it should be noted that the CRB given here is based on a single snapshot, so the estimation performance of the PARAFAC algorithm may be lower than that of the CRB when the number of snapshots is large). For speed estimation, the estimation performance of the proposed algorithm is better than that of the PARAFAC algorithm with 5 or 20 snapshots. Especially under low signal-to-noise ratio conditions, the proposed algorithm has better distance and speed estimation performance.
可见，实施本实施例所描述的干扰条件下阵列单快拍多维参数估计方法，无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。It can be seen that the single-snapshot multi-dimensional parameter estimation method for an array under interference conditions described in this embodiment does not require matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters of a coherent source, such as distance, angle, and speed, using only single-snapshot data.
实施例4Example 4
请参看图18，图18为本实施例提供的一种干扰条件下阵列单快拍多维参数估计装置的结构示意图。如图18所示，该干扰条件下阵列单快拍多维参数估计装置包括：Please refer to Figure 18, which is a schematic diagram of the structure of a device for estimating multidimensional parameters of an array single snapshot under interference conditions provided by this embodiment. As shown in Figure 18, the device for estimating multidimensional parameters of an array single snapshot under interference conditions includes:
获取单元310，用于获取干扰条件下的阵列接收信号；An acquisition unit 310 is used to acquire an array receiving signal under interference conditions;
第一转化单元320，用于将阵列接收信号的信源多维参数估计问题转化为多维频率估计问题；A first conversion unit 320, configured to convert a multi-dimensional parameter estimation problem of a signal source of an array receiving signal into a multi-dimensional frequency estimation problem;
粗估计单元330，用于基于多维频率估计问题对阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果；A coarse estimation unit 330, configured to perform a multi-dimensional frequency coarse estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency coarse estimation result;
精估计单元340，用于根据多维频率粗估计结果对阵列接收信号进行多维频率精估计，得到多维频率精估计结果；The precise estimation unit 340 is used to perform a precise multi-dimensional frequency estimation on the array received signal according to the rough multi-dimensional frequency estimation result to obtain a precise multi-dimensional frequency estimation result;
计算单元350，用于根据多维频率粗估计结果和多维频率精估计结果，计算频率估计结果；A calculation unit 350, configured to calculate a frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result;
第二转化单元360，用于将频率估计结果转化为参数估计结果。The second conversion unit 360 is used to convert the frequency estimation result into a parameter estimation result.
本实施例中，对于干扰条件下阵列单快拍多维参数估计装置的解释说明可以参照实施例1或实施例2中的描述，对此本实施例中不再多加赘述。In this embodiment, the explanation of the array single-snapshot multi-dimensional parameter estimation device under interference conditions can refer to the description in Embodiment 1 or Embodiment 2, which will not be described in detail in this embodiment.
可见，实施本实施例所描述的干扰条件下阵列单快拍多维参数估计装置，无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。It can be seen that the array single snapshot multi-dimensional parameter estimation device under interference conditions described in this embodiment does not need to perform matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of coherent signal sources using only single snapshot data.
实施例5Example 5
请参看图19，图19为本实施例提供的一种干扰条件下阵列单快拍多维参数估计装置的结构示意图。如图19所示，该干扰条件下阵列单快拍多维参数估计装置包括：Please refer to Figure 19, which is a schematic diagram of the structure of a device for estimating multidimensional parameters of an array single snapshot under interference conditions provided by this embodiment. As shown in Figure 19, the device for estimating multidimensional parameters of an array single snapshot under interference conditions includes:
获取单元310，用于获取干扰条件下的阵列接收信号；An acquisition unit 310 is used to acquire an array receiving signal under interference conditions;
第一转化单元320，用于将阵列接收信号的信源多维参数估计问题转化为多维频率估计问题；A first conversion unit 320, configured to convert a multi-dimensional parameter estimation problem of a signal source of an array receiving signal into a multi-dimensional frequency estimation problem;
粗估计单元330，用于基于多维频率估计问题对阵列接收信号进行多维频率粗估计，得到多维频率粗估计结果；A coarse estimation unit 330, configured to perform a multi-dimensional frequency coarse estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency coarse estimation result;
精估计单元340，用于根据多维频率粗估计结果对阵列接收信号进行多维频率精估计，得到多维频率精估计结果；The precise estimation unit 340 is used to perform a precise multi-dimensional frequency estimation on the array received signal according to the rough multi-dimensional frequency estimation result to obtain a precise multi-dimensional frequency estimation result;
计算单元350，用于根据多维频率粗估计结果和多维频率精估计结果，计算频率估计结果；A calculation unit 350, configured to calculate a frequency estimation result according to the multi-dimensional frequency rough estimation result and the multi-dimensional frequency precise estimation result;
第二转化单元360，用于将频率估计结果转化为参数估计结果。The second conversion unit 360 is used to convert the frequency estimation result into a parameter estimation result.
作为一种可选的实施方式，粗估计单元330包括：As an optional implementation manner, the coarse estimation unit 330 includes:
信号变换子单元331，用于对阵列接收信号进行多维快速傅里叶变换处理，得到多维频谱矩阵块；The signal conversion subunit 331 is used to perform multi-dimensional fast Fourier transform processing on the array received signal to obtain a multi-dimensional spectrum matrix block;
获取子单元332，用于根据频谱矩阵块获取信号频谱峰值点坐标；An acquisition subunit 332 is used to acquire the coordinates of the peak point of the signal spectrum according to the spectrum matrix block;
粗估计子单元333，用于根据信号频谱峰值点坐标进行复正弦波的多维频率粗估计，得到多维频率粗估计结果。The rough estimation subunit 333 is used to perform a rough estimation of the multi-dimensional frequency of the complex sine wave according to the coordinates of the peak points of the signal spectrum to obtain a rough estimation result of the multi-dimensional frequency.
本实施例中，多维频率粗估计结果为：In this embodiment, the multi-dimensional frequency rough estimation result is:
其中，表示Q个复正弦波的K维频率粗估计结果；lk为正整数，表示扩展因子。in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; lk is a positive integer, representing the expansion factor.
作为一种可选的实施方式，精估计单元340包括：As an optional implementation, the precise estimation unit 340 includes:
第一计算子单元341，用于根据预设的采样长度计算最大迭代次数和偏移量；A first calculation subunit 341 is used to calculate a maximum number of iterations and an offset according to a preset sampling length;
第一确定子单元342，用于确定当前迭代次数；A first determining subunit 342, used to determine the current number of iterations;
获取子单元343，用于根据当前迭代次数获取上一次迭代频谱精估计值和上一次迭代多个复正弦波的复幅度系数；An acquisition subunit 343 is used to acquire the spectrum accurate estimation value of the previous iteration and the complex amplitude coefficients of multiple complex sine waves of the previous iteration according to the current iteration number;
第二计算子单元344，用于根据多维频率粗估计结果、上一次迭代频谱精估计值、偏移量和阵列接收信号，计算多个复正弦波的频谱泄漏系数和多个复正弦信号的多维偏移频谱值；The second calculation subunit 344 is used to calculate the spectrum leakage coefficients of multiple complex sinusoidal waves and the multidimensional offset spectrum values of multiple complex sinusoidal signals according to the multidimensional frequency rough estimation result, the spectrum precise estimation value of the previous iteration, the offset and the array received signal;
第二计算子单元344，还用于根据上一次迭代多个复正弦波的复幅度系数、多个复正弦波的频谱泄漏系数以及多个复正弦信号的多维偏移频谱值，计算多个复正弦波的多维偏移后频谱泄漏校正系数；The second calculation subunit 344 is further used to calculate the multi-dimensional offset spectrum leakage correction coefficients of the multiple complex sine waves according to the complex amplitude coefficients of the multiple complex sine waves in the previous iteration, the spectrum leakage coefficients of the multiple complex sine waves, and the multi-dimensional offset spectrum values of the multiple complex sine signals;
第二计算子单元344，还用于根据多个复正弦波的多维偏移后频谱泄漏校正系数和上一次迭代频谱精估计值，计算本次频率精估计值；The second calculation subunit 344 is further used to calculate the current frequency precision estimation value according to the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the previous iterative spectrum precision estimation value;
判断子单元345，用于判断当前迭代次数是否达到最大迭代次数；A judging subunit 345 is used to judge whether the current number of iterations reaches the maximum number of iterations;
第二确定子单元346，用于当判断出达到最大迭代次数时，则将本次频率精估计值确定为多维频率精估计结果。The second determining subunit 346 is used to determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result when it is determined that the maximum number of iterations has been reached.
作为一种可选的实施方式，精估计单元340还包括：As an optional implementation manner, the precise estimation unit 340 further includes:
第三计算子单元347，用于当判断出当前迭代次数未达到最大迭代次数时，根据多维频率粗估计结果和上一次迭代频谱精估计值计算信号在多个复正弦信号频率估计点的频谱值；The third calculation subunit 347 is used to calculate the spectrum value of the signal at multiple complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency rough estimation result and the spectrum precise estimation value of the previous iteration when it is determined that the current iteration number has not reached the maximum iteration number;
第三计算子单元347，还用于根据多维频率粗估计结果，计算当前迭代次数对应的频谱泄漏系数；The third calculation subunit 347 is further used to calculate the spectrum leakage coefficient corresponding to the current iteration number according to the multi-dimensional frequency rough estimation result;
第三计算子单元347，还用于根据信号在多个复正弦信号频率估计点的频谱值、当前迭代次数对应的频谱泄漏系数和上一次迭代多个复正弦波的复幅度系数，计算当前迭代次数对应的多个复正弦波的复幅度系数；The third calculation subunit 347 is further used to calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves in the previous iteration;
数值增加子单元348，用于将当前迭代次数的数值增加1，作为新的当前迭代次数，并触发第一确定子单元342确定当前迭代次数。The value increasing subunit 348 is used to increase the value of the current iteration number by 1 as the new current iteration number, and trigger the first determining subunit 342 to determine the current iteration number.
本实施例中，对于干扰条件下阵列单快拍多维参数估计装置的解释说明可以参照实施例1或实施例2中的描述，对此本实施例中不再多加赘述。In this embodiment, the explanation of the array single-snapshot multi-dimensional parameter estimation device under interference conditions can refer to the description in Embodiment 1 or Embodiment 2, which will not be described in detail in this embodiment.
可见，实施本实施例所描述的干扰条件下阵列单快拍多维参数估计装置，无需进行矩阵分解和网格搜索，仅利用单快拍数据就能够快速、准确的测量相干信源的距离、角度、速度等多个维度参数。It can be seen that the array single snapshot multi-dimensional parameter estimation device under interference conditions described in this embodiment does not need to perform matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of coherent signal sources using only single snapshot data.
本申请实施例提供了一种电子设备，包括存储器以及处理器，存储器用于存储计算机程序，处理器运行计算机程序以使电子设备执行本申请实施例1或实施例2中的干扰条件下阵列单快拍多维参数估计方法。An embodiment of the present application provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the array single-snapshot multi-dimensional parameter estimation method under interference conditions in Embodiment 1 or Embodiment 2 of the present application.
本申请实施例提供了一种计算机可读存储介质，其存储有计算机程序指令，所述计算机程序指令被一处理器读取并运行时，执行本申请实施例1或实施例2中的干扰条件下阵列单快拍多维参数估计方法。An embodiment of the present application provides a computer-readable storage medium storing computer program instructions. When the computer program instructions are read and executed by a processor, the method for estimating multi-dimensional parameters of a single-snapshot array under interference conditions in Embodiment 1 or Embodiment 2 of the present application is executed.
在本申请所提供的几个实施例中，应该理解到，所揭露的装置和方法，也可以通过其它的方式实现。以上所描述的装置实施例仅仅是示意性的，例如，附图中的流程图和框图显示了根据本申请的多个实施例的装置、方法和计算机程序产品的可能实现的体系架构、功能和操作。在这点上，流程图或框图中的每个方框可以代表一个模块、程序段或代码的一部分，所述模块、程序段或代码的一部分包含一个或多个用于实现规定的逻辑功能的可执行指令。也应当注意，在有些作为替换的实现方式中，方框中所标注的功能也可以以不同于附图中所标注的顺序发生。例如，两个连续的方框实际上可以基本并行地执行，它们有时也可以按相反的顺序执行，这依所涉及的功能而定。也要注意的是，框图和/或流程图中的每个方框、以及框图和/或流程图中的方框的组合，可以用执行规定的功能或动作的专用的基于硬件的系统来实现，或者可以用专用硬件与计算机指令的组合来实现。In several embodiments provided in the present application, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device embodiments described above are merely schematic. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the devices, methods and computer program products according to multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, a program segment or a part of a code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and/or flowchart, and the combination of boxes in the block diagram and/or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.
另外，在本申请各个实施例中的各功能模块可以集成在一起形成一个独立的部分，也可以是各个模块单独存在，也可以两个或两个以上模块集成形成一个独立的部分。In addition, the functional modules in the various embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
所述功能如果以软件功能模块的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读存储介质中。基于这样的理解，本申请的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本申请各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(ROM，Read-Only Memory)、随机存取存储器(RAM，Random Access Memory)、磁碟或者光盘等各种可以存储程序代码的介质。If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.
以上所述仅为本申请的实施例而已，并不用于限制本申请的保护范围，对于本领域的技术人员来说，本申请可以有各种更改和变化。凡在本申请的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。应注意到：相似的标号和字母在下面的附图中表示类似项，因此，一旦某一项在一个附图中被定义，则在随后的附图中不需要对其进行进一步定义和解释。The above description is only an embodiment of the present application and is not intended to limit the scope of protection of the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.
以上所述，仅为本申请的具体实施方式，但本申请的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本申请揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本申请的保护范围之内。因此，本申请的保护范围应所述以权利要求的保护范围为准。The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.
需要说明的是，在本文中，诸如第一和第二等之类的关系术语仅仅用来将一个实体或者操作与另一个实体或操作区分开来，而不一定要求或者暗示这些实体或操作之间存在任何这种实际的关系或者顺序。而且，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、物品或者设备不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、物品或者设备所固有的要素。在没有更多限制的情况下，由语句“包括一个……”限定的要素，并不排除在包括所述要素的过程、方法、物品或者设备中还存在另外的相同要素。It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.
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| CN202411104644.5AActiveCN118897252B (en) | 2024-08-13 | 2024-08-13 | Method and device for estimating array single snapshot multidimensional parameters under interference condition |
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| CN (1) | CN118897252B (en) |
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|---|---|---|---|---|
| DE102004016937A1 (en)* | 2003-04-07 | 2004-11-04 | Rohde & Schwarz Gmbh & Co. Kg | Estimation method for determining frequency and phase shift in a data transmission network whereby an estimation algorithm is derived from a suitable cost function determined from a likelihood function in a non-data aided approach |
| CN110113075A (en)* | 2018-10-29 | 2019-08-09 | 西安电子科技大学 | Hybrid network platform frequency parameter blind estimating method based on STFT-SPWVD |
| CN110333389A (en)* | 2019-05-07 | 2019-10-15 | 东南大学 | Frequency Estimation Method of Sine Signal Based on Interpolation DFT |
| CN112816779A (en)* | 2021-01-23 | 2021-05-18 | 中国人民解放军陆军勤务学院 | Harmonic real signal parameter estimation method for analytic signal generation |
| CN116626645A (en)* | 2023-07-21 | 2023-08-22 | 西安电子科技大学 | A Coherent Accumulation Grating Lobe Suppression Method for Broadband Radar High Speed Targets |
| CN116722892A (en)* | 2023-03-21 | 2023-09-08 | 中国人民解放军63892部队 | Frequency hopping signal parameter estimation method based on time-frequency transformation and waveform shaping |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102004016937A1 (en)* | 2003-04-07 | 2004-11-04 | Rohde & Schwarz Gmbh & Co. Kg | Estimation method for determining frequency and phase shift in a data transmission network whereby an estimation algorithm is derived from a suitable cost function determined from a likelihood function in a non-data aided approach |
| CN110113075A (en)* | 2018-10-29 | 2019-08-09 | 西安电子科技大学 | Hybrid network platform frequency parameter blind estimating method based on STFT-SPWVD |
| CN110333389A (en)* | 2019-05-07 | 2019-10-15 | 东南大学 | Frequency Estimation Method of Sine Signal Based on Interpolation DFT |
| CN112816779A (en)* | 2021-01-23 | 2021-05-18 | 中国人民解放军陆军勤务学院 | Harmonic real signal parameter estimation method for analytic signal generation |
| CN116722892A (en)* | 2023-03-21 | 2023-09-08 | 中国人民解放军63892部队 | Frequency hopping signal parameter estimation method based on time-frequency transformation and waveform shaping |
| CN116626645A (en)* | 2023-07-21 | 2023-08-22 | 西安电子科技大学 | A Coherent Accumulation Grating Lobe Suppression Method for Broadband Radar High Speed Targets |
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| 吴伟: "阵列天线系统中的空频域参数估计算法研究", 《中国博士学位论文全文数据库信息科技辑》, 15 February 2023 (2023-02-15), pages 63 - 81* |
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| CN118897252B (en) | 2025-09-19 |
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