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CN116908802A - Skywave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm - Google Patents

Skywave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm Download PDF

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CN116908802A
CN116908802A CN202310852546.9A CN202310852546A CN116908802A CN 116908802 A CN116908802 A CN 116908802A CN 202310852546 A CN202310852546 A CN 202310852546A CN 116908802 A CN116908802 A CN 116908802A
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苏洪涛
韩可欣
王兆祎
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Xidian University
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Abstract

The invention provides a sky wave beyond visual range radar distance estimation method based on a sparse Bayesian algorithm, which comprises the following implementation steps: carrying out wave beam formation on data received by an sky wave beyond visual range radar antenna array; performing pulse compression and moving target detection on echo data of the azimuth of the target to obtain a distance-Doppler matrix; performing two-dimensional constant false alarm detection on the distance-Doppler matrix; and carrying out sparse recovery on echo data of the Doppler channel where the target is positioned by using a sparse Bayesian algorithm to obtain the distance information of the target. The invention can improve the distance resolution capability and the distance estimation precision of the sky wave beyond visual range radar; the calculation amount of the algorithm and the complexity of the system are reduced, and the method is more suitable for engineering application.

Description

基于稀疏贝叶斯算法的天波超视距雷达距离估计方法Skywave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm

技术领域Technical field

本发明属于雷达技术领域,更进一步涉及雷达信号处理技术领域的一种应用于天波超视距雷达OTHR(Skywave Over-the-horizon Radar)的距离估计方法。本发明可用于对天波雷达接收到的回波数据进行参数估计,在雷达带宽有限的情况下,获得突破瑞利限的距离超分辨能力,提高目标距离估计精度。The invention belongs to the field of radar technology, and further relates to a distance estimation method applied to skywave over-the-horizon radar OTHR (Skywave Over-the-horizon Radar) in the field of radar signal processing technology. The invention can be used for parameter estimation of echo data received by sky wave radar, and in the case of limited radar bandwidth, it can obtain range super-resolution capability that breaks through the Rayleigh limit and improve the accuracy of target distance estimation.

背景技术Background technique

天波超视距雷达工作在3-30MHz之间的高频(High frequency,HF)段,天波雷达利用电离层对高频信号的反射作用自上而下的进行目标探测,因此可以突破地球曲率的限制,探测到常规体制雷达视距以外的超远距离(1000~4000km)目标。但是,高频频段频谱资源有限,各种干扰很多,因此OTHR的工作带宽有限,距离分辨率不高,一般为几公里到十几公里。受发射信号带宽的限制,OTHR的距离分辨率有限,所以在多目标情况下,由于不能正确分辨目标,导致测距精度下降很多。Skywave over-the-horizon radar works in the high frequency (HF) range between 3-30MHz. Skywave radar uses the reflection of high-frequency signals by the ionosphere to detect targets from top to bottom, so it can break through the curvature of the earth. Limitation, it can detect ultra-long-distance (1000~4000km) targets beyond the visual range of conventional system radars. However, spectrum resources in the high-frequency band are limited and there are many types of interference. Therefore, the working bandwidth of OTHR is limited and the distance resolution is not high, generally ranging from a few kilometers to more than ten kilometers. Limited by the bandwidth of the transmitted signal, the distance resolution of OTHR is limited. Therefore, in the case of multiple targets, the ranging accuracy is greatly reduced due to the inability to correctly distinguish the targets.

电子科技大学在其所申请的专利文献“一种基于OMP与DPL1算法的雷达距离超分辨计算方法”(专利申请号:202210626515.7,申请公布号:CN 115564645A)中提出了一种基于OMP与DPL1算法的雷达距离超分辨计算方法。该方法的实现步骤如下,首先对雷达的回波信号进行脉冲压缩,确定群目标的雷达信号段;再对群目标的雷达信号段进行频率去斜得到单频信号,接着利用OMP算法得到目标的粗略位置;最后利用动态参数L1正则化算法对得到的频点位置进一步超分辨处理,得到群目标的精确频点位置,将频点信息转换成距离信息,实现距离超分辨。该方法存在的不足之处是,由于对线性调频连续波信号进行数字“去斜”需要将雷达接收到的全部回波信号进行后续处理,由此导致计算量大,实时性差。而且此方法需要进行两步操作,复杂性高。同时,OMP算法容易过匹配,如果第一步估计错误,在之后的每一步中都会累计前面的误差,导致算法的稳定性差。The University of Electronic Science and Technology of China proposed a method based on OMP and DPL1 algorithms in the patent document "A radar range super-resolution calculation method based on OMP and DPL1 algorithms" (Patent application number: 202210626515.7, application publication number: CN 115564645A) Radar distance super-resolution calculation method. The implementation steps of this method are as follows: first, perform pulse compression on the radar echo signal to determine the radar signal segment of the group target; then frequency deskew the radar signal segment of the group target to obtain a single-frequency signal; and then use the OMP algorithm to obtain the target's Rough position; finally, the dynamic parameter L1 regularization algorithm is used to further super-resolution process the obtained frequency point position to obtain the precise frequency point position of the group target, and convert the frequency point information into distance information to achieve distance super-resolution. The disadvantage of this method is that the digital "deskewing" of linear frequency modulated continuous wave signals requires subsequent processing of all echo signals received by the radar, which results in a large amount of calculation and poor real-time performance. Moreover, this method requires two steps and is highly complex. At the same time, the OMP algorithm is prone to over-matching. If the first step is estimated incorrectly, the previous error will be accumulated in each subsequent step, resulting in poor stability of the algorithm.

电子科技大学在其所申请的专利文献“一种基于瞬时自相关矩阵稀疏分解的OTHR机动目标参数估计方法”(专利申请号:CN201711068233.5,申请公布号:CN107861115A)中提出了一种基于瞬时自相关矩阵稀疏分解的OTHR机动目标参数估计方法。该方法的实现步骤如下,首先对回波进行瞬时自相关变换,然后对瞬时自相关矩阵进行交叉项抑制,再对瞬时自相关矩阵进行稀疏分解,最后对分解后的稀疏矩阵进行Hough变换得到信号的瞬时频率,从而估计目标运动参数。该方法存在的不足之处是,虽然该方法提高了OTHR在多目标情况下的多普勒频率和角度的估计精度,但是没有解决OTHR由于距离分辨率较低而导致的目标距离参数估计精度不足的问题。The University of Electronic Science and Technology of China proposed a method based on instantaneous autocorrelation matrix sparse decomposition in the patent document "OTHR maneuvering target parameter estimation method based on instantaneous autocorrelation matrix" (Patent application number: CN201711068233.5, application publication number: CN107861115A). OTHR maneuvering target parameter estimation method based on sparse decomposition of autocorrelation matrix. The implementation steps of this method are as follows: first, perform instantaneous autocorrelation transformation on the echo, then perform cross-term suppression on the instantaneous autocorrelation matrix, then perform sparse decomposition of the instantaneous autocorrelation matrix, and finally perform Hough transformation on the decomposed sparse matrix to obtain the signal. instantaneous frequency to estimate the target motion parameters. The shortcoming of this method is that although this method improves the estimation accuracy of Doppler frequency and angle of OTHR in multi-target situations, it does not solve the insufficient accuracy of target range parameter estimation caused by OTHR's low range resolution. The problem.

发明内容Contents of the invention

本发明的目的在于针对上述已有技术的不足,提出一种天波雷达参数高精度估计方法,用于解决OTHR由于距离分辨率差导致的参数估计精度不足的问题,以及现有的频率去斜的距离超分辨方法计算量大、实时性差的问题。The purpose of the present invention is to propose a high-precision estimation method for sky-wave radar parameters in view of the above-mentioned shortcomings of the prior art, which is used to solve the problem of insufficient parameter estimation accuracy of OTHR due to poor range resolution, as well as the existing frequency deskewing method. The distance super-resolution method has the problem of large computational complexity and poor real-time performance.

实现本发明目的的技术方案是,本发明通过对发射的线性调频连续波信号脉冲压缩后的数据时延来构建稀疏恢复问题的基矩阵,基矩阵中的每一列都代表了不同时延下的线性调频连续波信号的脉压波形数据,将时延对应到距离上,即可得到不同距离下的脉压波形数据,基矩阵的每一列之间的距离间隔都小于一个距离分辨单元,将观测向量与基矩阵的每一列进行匹配,得到稀疏恢复向量,再将稀疏向量中各个元素的位置转换成目标的距离位置,即可克服现有技术中天波超视距雷达距离分辨率较差的问题。本发明利用天波超视距雷达天线阵列接收到的信号进行波束形成,将空间中的能量积累起来,再对目标所在方位的信号进行脉冲压缩,之后对同一距离单元的一个相干积累时间内的回波数据进行DFT,得到目标的距离-多普勒矩阵,再对距离-多普勒矩阵进行二维恒虚警检测;最后选取被检测目标所在多普勒通道的脉冲压缩后数据进行稀疏恢复,根据脉冲压缩结果,只截取包含目标信息的部分脉压信号作为观测向量,可以有效减小整个算法的计算量,克服了现有频率“去斜”距离超分辨方法运算量大、实时性差的问题。本发明采用稀疏贝叶斯算法对观测向量进行稀疏恢复,该算法可以处理单快拍数据、且不需要设置正则化参数,在信噪比较低的时候,依然有着良好的分辨力和稳定性,克服了现有技术的子空间类算法只能处理非相干源和需要多快拍数据的问题以及贪婪类稀疏恢复算法容易过匹配的缺点,由此更好地提高了天波超视距雷达的距离分辨能力。The technical solution to achieve the object of the present invention is to construct a basis matrix for the sparse recovery problem by pulse-compressing the data delay of the transmitted linear frequency modulated continuous wave signal. Each column in the basis matrix represents the data delay under different delays. For the pulse pressure waveform data of the linear frequency modulated continuous wave signal, by mapping the time delay to the distance, the pulse pressure waveform data at different distances can be obtained. The distance interval between each column of the base matrix is less than one distance resolution unit, and the observed The vector is matched with each column of the base matrix to obtain a sparse recovery vector, and then the position of each element in the sparse vector is converted into the distance position of the target, which can overcome the problem of poor distance resolution of sky-wave over-the-horizon radar in the existing technology. . This invention uses the signal received by the sky wave over-the-horizon radar antenna array to perform beam forming, accumulates the energy in space, and then performs pulse compression on the signal in the direction of the target, and then performs pulse compression on the echo within a coherent accumulation time of the same distance unit. Perform DFT on the wave data to obtain the range-Doppler matrix of the target, and then perform two-dimensional constant false alarm detection on the range-Doppler matrix; finally, select the pulse-compressed data of the Doppler channel where the detected target is located for sparse recovery. According to the pulse compression results, only part of the pulse pressure signal containing the target information is intercepted as the observation vector, which can effectively reduce the calculation amount of the entire algorithm and overcome the problems of large computational complexity and poor real-time performance of the existing frequency "deskew" distance super-resolution method. . The present invention uses a sparse Bayesian algorithm to sparsely restore the observation vector. This algorithm can process single snapshot data and does not need to set regularization parameters. When the signal-to-noise ratio is low, it still has good resolution and stability. , which overcomes the shortcomings of the existing subspace algorithm that can only handle incoherent sources and the need for multiple snapshot data, and the greedy sparse recovery algorithm that is prone to over-matching, thereby better improving the performance of sky-wave over-the-horizon radar. Distance resolution ability.

本发明的实现步骤如下:The implementation steps of the present invention are as follows:

步骤1,对天波超视距雷达天线阵列接收到的数据进行波束形成,得到目标所在方位的回波数据;Step 1: Perform beam forming on the data received by the sky wave over-the-horizon radar antenna array to obtain the echo data of the target's location;

步骤2,对目标所在方位的天波超视距雷达接收的回波数据进行脉冲压缩,得到脉压后的回波数据;Step 2: Perform pulse compression on the echo data received by the sky wave over-the-horizon radar in the azimuth of the target to obtain the echo data after pulse pressure;

步骤3,对天波超视距雷达脉压后的回波信号进行动目标检测:Step 3: Perform moving target detection on the echo signal after the sky wave over-the-horizon radar pulse pressure:

对同一距离单元的一个相干积累时间内的脉压后回波数据进行离散傅里叶变换DFT,得到目标的距离-多普勒矩阵;Perform discrete Fourier transform DFT on the pulse pressure post-echo data within a coherent accumulation time of the same range unit to obtain the range-Doppler matrix of the target;

步骤4,对目标的距离-多普勒矩阵做二维恒虚警检测,得到目标所在的距离单元和多普勒单元;Step 4: Perform two-dimensional constant false alarm detection on the range-Doppler matrix of the target to obtain the range unit and Doppler unit where the target is located;

步骤5,利用稀疏贝叶斯算法对目标所在多普勒单元的信号进行稀疏恢复:Step 5: Use the sparse Bayesian algorithm to sparsely restore the signal of the Doppler unit where the target is located:

通过对天波超视距雷达发射的线性调频连续波信号脉冲压缩后的信号时延,根据观测向量的维度,构建测量矩阵;利用稀疏贝叶斯算法对观测向量进行稀疏恢复,得到稀疏信号向量,将稀疏向量中各个元素的位置转换成目标的距离值。By compressing the signal delay of the linear frequency modulated continuous wave signal emitted by the sky wave over-the-horizon radar, a measurement matrix is constructed according to the dimensions of the observation vector; the sparse Bayesian algorithm is used to sparsely restore the observation vector to obtain a sparse signal vector. Convert the position of each element in the sparse vector into the distance value of the target.

本发明与现有技术相比具有以下优点:Compared with the prior art, the present invention has the following advantages:

第一,由于本发明利用稀疏贝叶斯算法,估计天波超视距雷达的距离参数,克服了现有技术中天波超视距雷达距离分辨率较差的问题,使得本发明能够对天波超视距雷达实现比常规距离参数估计方法高三倍以上的距离分辨能力。First, because the present invention uses the sparse Bayesian algorithm to estimate the distance parameters of the sky-wave over-the-horizon radar, it overcomes the problem of poor distance resolution of the sky-wave over-the-horizon radar in the existing technology, making the present invention able to detect sky-wave over-the-horizon radars. The range radar achieves a range resolution that is more than three times higher than conventional range parameter estimation methods.

第二,由于本发明选取被检测目标所在多普勒通道的脉冲压缩后数据进行距离超分辨处理,根据脉冲压缩结果截取部分脉压后的信号作为观测向量,克服了现有频率“去斜”距离超分辨方法运算量大、实时性差的问题,使得本发明大大减小了算法的计算量和系统复杂度,更适用于工程应用。Second, because the present invention selects the pulse compression data of the Doppler channel where the detected target is located for range super-resolution processing, and intercepts part of the pulse pressure signal according to the pulse compression result as the observation vector, it overcomes the existing frequency "deskewing" The distance super-resolution method has the problems of large computational complexity and poor real-time performance, which makes the present invention greatly reduce the computational complexity of the algorithm and the system complexity, making it more suitable for engineering applications.

第三,由于本发明采用稀疏贝叶斯算法对观测向量进行稀疏恢复,该算法可以处理单快拍数据、且不需要设置正则化参数,在信噪比较低的时候,依然有着良好的分辨力和稳定性,克服了现有技术的子空间类算法只能处理非相干源和需要多快拍数据的问题以及贪婪类稀疏恢复算法过匹配的缺点,使得本发明对天波超视距雷达的距离参数估计的更准确、稳定性更强,由此提高了天波超视距雷达的距离分辨能力。Third, since the present invention uses the sparse Bayesian algorithm to sparsely restore the observation vector, the algorithm can process single snapshot data and does not need to set regularization parameters. It still has good resolution when the signal-to-noise ratio is low. power and stability, and overcomes the problems that the existing subspace algorithm can only handle incoherent sources and requires multiple snapshot data, as well as the over-matching problem of the greedy sparse recovery algorithm, making the present invention suitable for sky-wave over-the-horizon radar. The distance parameter estimation is more accurate and more stable, thus improving the distance resolution capability of the sky wave over-the-horizon radar.

附图说明Description of the drawings

图1是本发明的流程图;Figure 1 is a flow chart of the present invention;

图2是仿真条件1下利用本发明方法对天波超视距雷达回波数据进行处理的结果图;Figure 2 is a diagram showing the results of processing sky wave over-the-horizon radar echo data using the method of the present invention under simulation condition 1;

图3是仿真条件2下利用本发明方法对天波超视距雷达回波数据进行处理的结果图;Figure 3 is a diagram showing the results of processing sky wave over-the-horizon radar echo data using the method of the present invention under simulation condition 2;

图4是仿真条件3下利用本发明方法对天波超视距雷达回波数据进行处理的结果图。Figure 4 is a diagram showing the results of processing sky wave over-the-horizon radar echo data using the method of the present invention under simulation condition 3.

具体实施方式Detailed ways

下面结合附图和实施例,对本发明做进一步的详细描述。The present invention will be described in further detail below with reference to the accompanying drawings and examples.

参照图1,本发明实施例的具体实现步骤做进一步的详细描述。Referring to Figure 1, the specific implementation steps of the embodiment of the present invention are described in further detail.

步骤1,对天波超视距雷达天线阵列接收到的数据进行波束形成,将空间中的能量积累起来,得到目标所在方位的回波数据。Step 1: Perform beam forming on the data received by the sky wave over-the-horizon radar antenna array, accumulate the energy in space, and obtain the echo data of the target's location.

步骤2,对目标所在方位的天波超视距雷达接收的回波数据进行脉冲压缩,得到脉压后的回波数据。Step 2: Perform pulse compression on the echo data received by the sky wave over-the-horizon radar in the azimuth of the target to obtain the echo data after pulse pressure.

所述对天波超视距雷达接收的回波数据进行脉冲压缩的步骤如下:The steps for pulse compression of the echo data received by sky wave over-the-horizon radar are as follows:

第一步,根据天波超视距雷达的发射信号,构建匹配滤波器的冲激响应为其中,s表示天波超视距雷达一个脉冲重复周期内发射的线性调频连续波信号s(t)经过离散采样后,得到的离散序列,s=[s1,s2,...,sG],G表示一个脉冲重复周期内离散序列的采样点数,sg表示s的第g个元素,g=1,2,…G,(·)*表示共轭操作;In the first step, based on the transmission signal of the sky wave over-the-horizon radar, the impulse response of the matched filter is constructed as Among them, s represents the discrete sequence obtained after discrete sampling of the chirp continuous wave signal s(t) emitted within one pulse repetition period of the sky-wave over-the-horizon radar, s=[s 1 , s 2 ,..., s G ], G represents the number of sampling points of the discrete sequence within a pulse repetition period, s g represents the g-th element of s, g=1,2,...G, (·) * represents the conjugate operation;

第二步,将天波超视距雷达回波数据与匹配滤波器的冲激响应进行卷积,得到脉压后的回波数据。In the second step, the sky wave over-the-horizon radar echo data is convolved with the impulse response of the matched filter to obtain the echo data after pulse pressure.

步骤3,对天波超视距雷达脉压后的回波信号进行动目标检测:Step 3: Perform moving target detection on the echo signal after the sky wave over-the-horizon radar pulse pressure:

对同一距离单元的一个相干积累时间内的脉压后回波数据进行离散傅里叶变换DFT,得到目标的距离-多普勒矩阵。Perform discrete Fourier transform DFT on the pulse pressure post-echo data within a coherent accumulation time of the same range unit to obtain the range-Doppler matrix of the target.

步骤4,对目标的距离-多普勒矩阵做二维恒虚警检测,得到目标所在的距离单元和多普勒单元。Step 4: Perform two-dimensional constant false alarm detection on the range-Doppler matrix of the target to obtain the range unit and Doppler unit where the target is located.

所述二维恒虚警检测的步骤如下:The steps of the two-dimensional constant false alarm detection are as follows:

第一步,选取距离-多普勒矩阵中未被选择过的元素作为待检测单元;The first step is to select unselected elements in the distance-Doppler matrix as units to be detected;

第二步,在待检测单元两侧分别选取N个参考单元,N的选取为2的整数幂,计算2N个参考单元的平均值,将该平均值作为背景噪声的功率估计值ZcaIn the second step, N reference units are selected on both sides of the unit to be detected, N is selected as an integer power of 2, the average value of the 2N reference units is calculated, and the average value is used as the power estimate Z ca of the background noise;

第三步,将背景噪声的功率估计值Zca乘以门限乘积因子k,得到待检测单元的门限值s;The third step is to multiply the background noise power estimate Z ca by the threshold product factor k to obtain the threshold value s of the unit to be detected;

第四步,将待检测单元的信号值与门限值s进行比较,如果待检测单元的信号值大于门限值,则判定该信号为目标信号,并为其赋值1;否则,判定该信号为噪声信号,赋值为0;The fourth step is to compare the signal value of the unit to be detected with the threshold value s. If the signal value of the unit to be detected is greater than the threshold value, the signal is determined to be the target signal and assigned a value of 1; otherwise, the signal is determined to be the target signal. For the noise signal, the value is assigned to 0;

第五步,判断是否选完距离-多普勒矩阵中的所有元素,若是,将被判定为目标信号的元素坐标值映射到距离-多普勒矩阵中,得到目标所在的距离单元和多普勒单元;否则,执行第一步。The fifth step is to determine whether all elements in the range-Doppler matrix have been selected. If so, map the coordinate values of the elements determined to be the target signals into the range-Doppler matrix to obtain the range unit and Doppler where the target is located. unit; otherwise, perform the first step.

步骤5,利用稀疏贝叶斯算法对目标所在多普勒单元的信号进行稀疏恢复:Step 5: Use the sparse Bayesian algorithm to sparsely restore the signal of the Doppler unit where the target is located:

通过对天波超视距雷达发射的线性调频连续波信号脉冲压缩后的信号时延,根据观测向量的维度,构建测量矩阵;利用稀疏贝叶斯算法对观测向量进行稀疏恢复,得到稀疏信号向量,将稀疏向量中各个元素的位置转换成目标的距离值。By compressing the signal delay of the linear frequency modulated continuous wave signal emitted by the sky wave over-the-horizon radar, a measurement matrix is constructed according to the dimensions of the observation vector; the sparse Bayesian algorithm is used to sparsely restore the observation vector to obtain a sparse signal vector. Convert the position of each element in the sparse vector into the distance value of the target.

所述的观测向量指的是,选取目标所在多普勒单元中的脉冲压缩后的回波数据,截取回波数据主瓣宽度长度的数据组成观测向量。The observation vector refers to selecting the pulse-compressed echo data in the Doppler unit where the target is located, and intercepting the data of the main lobe width and length of the echo data to form an observation vector.

所述构造测量矩阵的步骤如下:The steps to construct the measurement matrix are as follows:

第一步,构建一个维度为P×M的元素初始值均为0的测量矩阵;P的取值等于观测向量的长度,M=KP,K的取值为线性调频信号的采样频率与观测向量的采样频率的比值,本发明实施例中,K=5;The first step is to construct a measurement matrix with dimensions P×M whose initial values are all 0; the value of P is equal to the length of the observation vector, M=KP, and the value of K is the sampling frequency of the linear frequency modulation signal and the observation vector The ratio of the sampling frequency, in the embodiment of the present invention, K=5;

第二步,将线性调频连续波信号与匹配滤波器冲激响应进行脉冲压缩,得到基矢量,找到基矢量的峰值点位置q,截取基矢量主瓣的第q-b到q+b个元素,b的取值为基矢量主瓣采样点数的二分之一,将基矢量主瓣中的所有元素放到测量矩阵的第一列的第一行到第2b行,以此类推,将基矢量主瓣中的所有元素放到测量矩阵的第k列的第k行到第k+2b-1行,k=1,2,...,M;The second step is to perform pulse compression on the linear frequency modulation continuous wave signal and the matched filter impulse response to obtain the basis vector, find the peak point position q of the basis vector, and intercept the q-b to q+b elements of the main lobe of the basis vector, b The value of is one-half of the number of sampling points in the main lobe of the basis vector. Put all the elements in the main lobe of the basis vector into the first row to row 2b of the first column of the measurement matrix, and so on. Put the main lobe of the basis vector into All elements in the lobe are placed in the kth row to the k+2b-1th row of the kth column of the measurement matrix, k=1,2,...,M;

第三步,截取测量矩阵的第b到第P+b-1行,测量矩阵的第一列代表第0时刻的线性调频连续波信号的脉压波形数据,第k列代表第k×Δt时刻的线性调频连续波信号的脉压波形数据,Δt代表测量矩阵各个列之间的时间间隔;The third step is to intercept the b-th to P+b-1 rows of the measurement matrix. The first column of the measurement matrix represents the pulse pressure waveform data of the chirp continuous wave signal at time 0, and the k-th column represents the k×Δt time. The pulse pressure waveform data of linear frequency modulation continuous wave signal, Δt represents the time interval between each column of the measurement matrix;

第四步,对测量矩阵的所有列向量进行K倍抽取,使线性调频连续波信号的脉压波形数据的维度与观测向量一致。The fourth step is to perform K-fold extraction on all column vectors of the measurement matrix to make the dimensions of the pulse pressure waveform data of the linear frequency modulated continuous wave signal consistent with the observation vector.

所述利用稀疏贝叶斯算法对观测向量进行稀疏恢复得到稀疏信号向量的具体步骤如下:The specific steps of using the sparse Bayesian algorithm to sparsely restore the observation vector to obtain the sparse signal vector are as follows:

第一步,初始化超参数α、α0,α=(α12,…,αM)表示稀疏信号向量的超参数,α的每一个元素都初始化为1;α0代表噪声方差,初始化为1;The first step is to initialize the hyperparameters α and α 0 , α = (α 1 , α 2 ,…, α M ) represents the hyperparameter of the sparse signal vector, each element of α is initialized to 1; α 0 represents the noise variance, initialized to 1;

第二步,按照下式,计算待求稀疏信号向量的后验概率密度函数的方差矩阵R和均值向量μ;In the second step, according to the following formula, calculate the variance matrix R and mean vector μ of the posterior probability density function of the sparse signal vector to be found;

R=(α0ΦTΦ+Λ)-1 R=(α 0 Φ T Φ+Λ) -1

μ=α0Tyμ=α 0T y

其中,Φ表示测量矩阵,(·)T表示转置操作,Λ表示超参数α的对角矩阵,y表示观测向量,(·)-1表示求逆操作;Among them, Φ represents the measurement matrix, (·) T represents the transpose operation, Λ represents the diagonal matrix of the hyperparameter α, y represents the observation vector, and (·) -1 represents the inversion operation;

第三步,按照下式,更新超参数和αnewThe third step is to update the hyperparameters according to the following formula and α new ;

其中,表示αnew的第i列向量,γi表示量化因子的第i个元素,γi=1-αiRii,∑表示求和操作,i=1,2,…,M;in, represents the i-th column vector of α new , γ i represents the i-th element of the quantization factor, γ i =1-α i R ii , ∑ represents the summation operation, i = 1, 2,...,M;

第四步,判断当前迭代的均方根误差是否满足收敛条件或达到最大迭代次数,若是,执行第五步,否则,执行第二步;所述的收敛条件为当前迭代得到的均值向量与前一次迭代得到的均值向量的均方根误差小于e-4,最大迭代次数为1000次;The fourth step is to determine whether the root mean square error of the current iteration satisfies the convergence condition or reaches the maximum number of iterations. If so, perform step five. Otherwise, perform step two; the convergence condition is the difference between the mean vector obtained by the current iteration and the previous iteration. The root mean square error of the mean vector obtained in one iteration is less than e -4 , and the maximum number of iterations is 1000;

第五步,将当前迭代得到的均值向量作为稀疏信号向量。The fifth step is to use the mean vector obtained in the current iteration as a sparse signal vector.

所述将稀疏向量中各个元素的位置转换成目标的距离值指的是:利用公式将稀疏向量中各个元素的位置转换成目标的距离值;其中,c表示光速,L表示截取目标所在多普勒单元中的脉冲压缩后的回波数据中的起始坐标值,fs表示观测向量的采样频率。The conversion of the position of each element in the sparse vector into the distance value of the target refers to: using the formula Convert the position of each element in the sparse vector into the distance value of the target; where c represents the speed of light, L represents the starting coordinate value in the echo data after intercepting the pulse compression in the Doppler unit where the target is located, and f s represents the observation The sampling frequency of the vector.

下面结合仿真实验对本发明的效果作进一步说明:The effect of the present invention will be further explained below in combination with simulation experiments:

1.仿真实验的条件:1. Conditions for simulation experiments:

本发明的仿真实验的平台为:Windows 10操作系统和Matlab R2020b。The platform for the simulation experiment of the present invention is: Windows 10 operating system and Matlab R2020b.

仿真实验1:雷达发射的线性调频连续波信号时宽Tp=15×10-3s,带宽B为1×104Hz,常规脉压距离分辨率ΔR=c/2B=15000m。接收天线数为32,对应角度分辨率3.169。回波信号包含目标信息以及高斯白噪声,回波信号的采样频率fs=2×104Hz,两个目标的信噪比分别为SNR1=10dB,SNR2=10dB;目标分别位于1°和1.5°的方位;距离分别为R1=313500m,R2=318000m;目标速度分别为v1=39m/s,v2=39m/s,对应多普勒频率分别为fd1=2.6Hz,fd2=2.6Hz。Simulation experiment 1: The time width of the linear frequency modulated continuous wave signal emitted by the radar is T p =15×10 -3 s, the bandwidth B is 1×10 4 Hz, and the conventional pulse pressure distance resolution ΔR=c/2B=15000m. The number of receiving antennas is 32, corresponding to an angular resolution of 3.169. The echo signal contains target information and Gaussian white noise. The sampling frequency of the echo signal is f s =2×10 4 Hz. The signal-to-noise ratios of the two targets are SNR1=10dB and SNR2=10dB respectively; the targets are located at 1° and 1.5 respectively. ° bearing; the distances are R1=313500m, R2=318000m respectively; the target speeds are v1=39m/s, v2=39m/s respectively, and the corresponding Doppler frequencies are f d 1=2.6Hz, f d 2=2.6 Hz.

仿真实验2:目标速度分别为v1=39m/s,v2=62m/s,对应多普勒频率分别为fd1=2.6Hz,fd2=4.13Hz,其余参数与仿真实验1相同。Simulation experiment 2: The target velocities are v1=39m/s, v2=62m/s, and the corresponding Doppler frequencies are f d 1 = 2.6 Hz and f d 2 = 4.13 Hz respectively. The other parameters are the same as simulation experiment 1.

仿真实验3:仿真实验3的距离分别为R1=310500m,R2=318000m;目标速度分别为v1=39m/s,v2=62m/s,对应多普勒频率分别为fd1=2.6Hz,fd2=4.13Hz。其余参数与仿真实验1相同。Simulation experiment 3: The distances of simulation experiment 3 are R1=310500m, R2=318000m respectively; the target speeds are v1=39m/s, v2=62m/s respectively, and the corresponding Doppler frequencies are f d 1=2.6Hz, f d2 =4.13Hz. The remaining parameters are the same as simulation experiment 1.

2.仿真内容及其结果分析:2. Simulation content and result analysis:

本发明的仿真实验有三个。There are three simulation experiments in this invention.

仿真实验1,仿真实验1说明了当目标的多普勒速度相同,两个目标的距离间隔小于一个距离分辨单元时,无法分辨出两个目标的情况。对天线接收到的回波信号进行常规波束形成,得到目标所在的方位如图2(a)所示,图2(a)中横坐标代表角度,纵坐标代表归一化幅度,可以看到常规波束形成无法将两个目标从方位维度分开。对波束形成后的回波数据进行脉冲压缩处理,脉压结果如图2(b)所示,图2(b)横坐标代表距离值,纵坐标代表归一化幅度,得到目标所在距离信息,由于两个目标距离间隔小于一个距离分辨单元,所以只估计出一个距离值为315km,无法从距离维度将两个目标分辨开。对同一距离单元的一个相干积累时间内的回波数据进行DFT,并做恒虚警检测,得到目标的距离-多普勒图如图2(c)所示,图2(c)的x轴代表距离,y轴代表多普勒频率,z轴代表幅度,可以看出多普勒频率的值为2.60417Hz,与实际值相符,但是由于目标在同一个距离分辨单元内,所以无法分辨出两个目标的距离信息,故无法分辨出两个目标;对距离-多普勒图做二维CFAR检测结果如图2(d)所示,图2(d)的x轴代表距离,y轴代表多普勒频率,z轴代表判别值,对二维CFAR检测结果中判别值为1的多普勒通道中的脉压后回波数据利用稀疏贝叶斯算法进行距离参数估计,结果如图2(e)所示,虚线为距离的真实值,曲线峰值表示利用本发明估计的目标距离值,可以看到能够将两个目标的距离信息分辨出来,得到的距离值分别为313.5km和318km,与实际值相符。Simulation experiment 1. Simulation experiment 1 illustrates the situation where the two targets cannot be distinguished when the Doppler velocity of the target is the same and the distance interval between the two targets is less than one distance resolution unit. Perform conventional beamforming on the echo signal received by the antenna, and obtain the orientation of the target, as shown in Figure 2(a). The abscissa in Figure 2(a) represents the angle, and the ordinate represents the normalized amplitude. You can see that the conventional Beamforming cannot separate two targets in the azimuthal dimension. The echo data after beam formation is subjected to pulse compression processing. The pulse pressure results are shown in Figure 2(b). The abscissa in Figure 2(b) represents the distance value, and the ordinate represents the normalized amplitude. The distance information of the target is obtained. Since the distance between the two targets is less than one distance resolution unit, only one distance value is estimated to be 315km, and the two targets cannot be distinguished from the distance dimension. Perform DFT on the echo data within a coherent accumulation time of the same range unit, and perform constant false alarm detection to obtain the range-Doppler diagram of the target, as shown in Figure 2(c), the x-axis of Figure 2(c) represents distance, the y-axis represents Doppler frequency, and the z-axis represents amplitude. It can be seen that the value of Doppler frequency is 2.60417Hz, which is consistent with the actual value. However, because the target is in the same range resolution unit, it is impossible to distinguish the two distance information of two targets, so the two targets cannot be distinguished; the two-dimensional CFAR detection results of the range-Doppler diagram are shown in Figure 2(d). The x-axis in Figure 2(d) represents the distance, and the y-axis represents Doppler frequency, the z-axis represents the discriminant value. The sparse Bayes algorithm is used to estimate the distance parameter for the post-pulse pressure echo data in the Doppler channel with a discriminant value of 1 in the two-dimensional CFAR detection results. The results are shown in Figure 2 As shown in (e), the dotted line is the true value of the distance, and the peak value of the curve represents the target distance value estimated by the present invention. It can be seen that the distance information of the two targets can be distinguished, and the obtained distance values are 313.5km and 318km respectively. consistent with the actual value.

仿真实验2,仿真实验2说明了当目标在多普勒域上可分辨,但由于可估计的距离值受雷达回波信号采样率影响,只能估计出在采样点上的距离值,导致距离维度依旧不可分的情况。对天线接收到的回波信号进行常规波束形成,得到目标所在方位如图3(a)所示,图3(a)的横轴代表角度,纵轴代表幅度,可以看到常规波束形成无法将两个目标的方位角分开。对波束形成后的回波数据进行脉冲压缩处理,脉压结果如图3(b)所示,图3(b)横坐标代表距离值,纵坐标代表归一化幅度,得到目标所在距离信息为315km,可以看到无法从距离维度将两个目标分辨开。对同一距离单元的一个相干积累时间内的回波数据进行DFT,并做恒虚警检测,得到目标的距离-多普勒图如图3(c)所示,图3(c)的x轴代表距离,y轴代表多普勒频率,z轴代表幅度,可以看出多普勒频率的值分别为2.60417Hz和4.16667Hz,与实际值相符。虽然多普勒频率可分,但由于只能估计出采样点上对应的距离值,当两个目标的距离间隔较小时,两个目标的距离值被估计为同一个采样点上的值,都被估计为了315km,所以依然无法分辨出两个目标的具体距离信息。对距离-多普勒图做二维CFAR检测结果如图3(d)所示,图3(d)的x轴代表距离,y轴代表多普勒频率,z轴代表判别值,对二维CFAR检测结果中判别值为1的多普勒通道中的脉压后回波数据利用稀疏贝叶斯算法进行距离参数估计,结果如图3(e)所示,虚线为距离的真实值,曲线峰值表示利用本发明估计的距离值,可以看到能够将两个目标的距离信息分辨出来,得到的距离值分别为313.5km和318km,与实际值相符,可见此方法能够提高天波超视距雷达距离估计精度。Simulation experiment 2. Simulation experiment 2 illustrates that when the target is resolvable in the Doppler domain, but because the estimable distance value is affected by the sampling rate of the radar echo signal, the distance value at the sampling point can only be estimated, resulting in a Dimensions are still inseparable. Perform conventional beamforming on the echo signal received by the antenna, and obtain the target orientation as shown in Figure 3(a). The horizontal axis of Figure 3(a) represents the angle, and the vertical axis represents the amplitude. It can be seen that conventional beamforming cannot The two targets are separated in azimuth. The echo data after beam formation is subjected to pulse compression processing. The pulse pressure results are shown in Figure 3(b). The abscissa in Figure 3(b) represents the distance value, and the ordinate represents the normalized amplitude. The distance information of the target is obtained as 315km, it can be seen that the two targets cannot be distinguished from the distance dimension. Perform DFT on the echo data within a coherent accumulation time of the same range unit, and perform constant false alarm detection to obtain the range-Doppler diagram of the target, as shown in Figure 3(c), the x-axis of Figure 3(c) represents distance, the y-axis represents Doppler frequency, and the z-axis represents amplitude. It can be seen that the values of Doppler frequency are 2.60417Hz and 4.16667Hz respectively, which are consistent with the actual values. Although the Doppler frequency is separable, since only the corresponding distance value at the sampling point can be estimated, when the distance interval between the two targets is small, the distance value of the two targets is estimated as the value at the same sampling point. It is estimated to be 315km, so it is still impossible to distinguish the specific distance information of the two targets. The results of two-dimensional CFAR detection on the range-Doppler map are shown in Figure 3(d). The x-axis in Figure 3(d) represents the distance, the y-axis represents the Doppler frequency, and the z-axis represents the discriminant value. For the two-dimensional In the CFAR detection results, the pulse pressure post-echo data in the Doppler channel with a discriminant value of 1 uses the sparse Bayesian algorithm to estimate the distance parameter. The results are shown in Figure 3(e). The dotted line is the true value of the distance, and the curve The peak value represents the distance value estimated by the present invention. It can be seen that the distance information of the two targets can be distinguished. The obtained distance values are 313.5km and 318km respectively, which are consistent with the actual values. It can be seen that this method can improve the sky-wave over-the-horizon radar. Distance estimation accuracy.

仿真实验3,仿真实验3说明了当目标在多普勒域上可分辨,但由于可估计的距离值受采样率影响,只能估计出在网格点上的距离值,虽然距离维度可分辨,但是估计的距离值与实际值有误差的情况。对天线接收到的回波信号进行常规波束形成,得到目标所在的方位如图4(a)所示,图4(a)的横轴代表角度,纵轴代表幅度,可以看到常规波束形成无法将两个目标从方位的维度分开。对波束形成后的回波数据进行脉冲压缩处理,脉压结果如图4(b)所示,图4(b)横坐标代表距离值,纵坐标代表归一化幅度,得到目标所在距离信息为315km,单纯从距离维度无法将两个目标分辨开。对同一距离单元的一个相干积累时间内的回波数据进行DFT,并做恒虚警检测,得到目标的距离-多普勒图如图4(c)所示,图4(c)的x轴代表距离,y轴代表多普勒频率,z轴代表幅度,可以看出多普勒频率的值分别为2.60417Hz和4.16667Hz,与实际值相符,虽然多普勒频率可分,距离维度也可分,但两个目标的距离值被估计为离真实值最近的网格点上的值,分别为307.5km和315km,与实际距离值不符。对距离-多普勒图做二维CFAR检测结果如图4(d)所示,图4(d)的x轴代表距离,y轴代表多普勒频率,z轴代表判别值,对二维CFAR检测结果中判别值为1的多普勒通道中的脉压后回波数据利用稀疏贝叶斯算法进行距离估计,结果如图4(e)所示,虚线为距离的真实值,曲线峰值表示利用本发明估计的距离值,可以看到能够将两个目标的距离分辨出来,得到的距离值分别为310.5km和318km,与实际值相符,可见此方法能够提高天波超视距雷达距离估计精度。Simulation experiment 3. Simulation experiment 3 illustrates that when the target is resolvable in the Doppler domain, because the estimable distance value is affected by the sampling rate, the distance value at the grid point can only be estimated, although the distance dimension is resolvable. , but there is an error between the estimated distance value and the actual value. Perform conventional beamforming on the echo signal received by the antenna, and obtain the orientation of the target, as shown in Figure 4(a). The horizontal axis of Figure 4(a) represents the angle, and the vertical axis represents the amplitude. It can be seen that conventional beamforming cannot Separate two targets from the dimension of orientation. The echo data after beam formation is subjected to pulse compression processing. The pulse pressure results are shown in Figure 4(b). The abscissa in Figure 4(b) represents the distance value, and the ordinate represents the normalized amplitude. The distance information of the target is obtained as 315km, it is impossible to distinguish the two targets simply from the distance dimension. Perform DFT on the echo data within a coherent accumulation time of the same range unit, and perform constant false alarm detection to obtain the range-Doppler diagram of the target, as shown in Figure 4(c), the x-axis of Figure 4(c) represents the distance, the y-axis represents the Doppler frequency, and the z-axis represents the amplitude. It can be seen that the values of the Doppler frequency are 2.60417Hz and 4.16667Hz respectively, which are consistent with the actual values. Although the Doppler frequency can be divided, the distance dimension can also be points, but the distance values of the two targets are estimated as the values at the grid points closest to the true values, which are 307.5km and 315km respectively, which is inconsistent with the actual distance values. The results of two-dimensional CFAR detection on the range-Doppler map are shown in Figure 4(d). The x-axis in Figure 4(d) represents the distance, the y-axis represents the Doppler frequency, and the z-axis represents the discriminant value. For the two-dimensional In the CFAR detection results, the pulse pressure post-echo data in the Doppler channel with a discriminant value of 1 uses the sparse Bayes algorithm for distance estimation. The results are shown in Figure 4(e). The dotted line is the true value of the distance, and the peak value of the curve is It means that using the distance values estimated by the present invention, it can be seen that the distance between the two targets can be distinguished, and the obtained distance values are 310.5km and 318km respectively, which are consistent with the actual values. It can be seen that this method can improve the distance estimation of sky wave over-the-horizon radar. Accuracy.

以上仿真实验表明,本发明针对天波超视距雷达由于工作带宽有限,距离分辨率较低,距离估计精度不足的问题,提出基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,与天波超视距雷达的常规距离参数估计方法相比,距离估计精度可以提高三倍以上。The above simulation experiments show that the present invention proposes a distance estimation method for skywave over-the-horizon radar based on the sparse Bayesian algorithm, which is similar to the sky-wave over-the-horizon radar's limited operating bandwidth, low range resolution, and insufficient distance estimation accuracy. Compared with the conventional distance parameter estimation method of over-the-horizon radar, the distance estimation accuracy can be improved by more than three times.

Claims (7)

1.一种基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于,利用天波超视距雷达发射的线性调频连续波信号构造测量矩阵,使用稀疏贝叶斯算法对目标所在多普勒通道的脉冲压缩后数据进行稀疏恢复;该距离估计方法的步骤包括如下:1. A distance estimation method for sky-wave over-the-horizon radar based on the sparse Bayesian algorithm, which is characterized by using the linear frequency modulated continuous wave signal emitted by the sky-wave over-the-horizon radar to construct a measurement matrix, and using the sparse Bayesian algorithm to estimate the location of the target. The pulse compression data of the Doppler channel is sparsely restored; the steps of the distance estimation method include the following: 步骤1,对天波超视距雷达天线阵列接收到的数据进行波束形成,得到目标所在方位的回波数据;Step 1: Perform beam forming on the data received by the sky wave over-the-horizon radar antenna array to obtain the echo data of the target's location; 步骤2,对目标所在方位的天波超视距雷达接收的回波数据进行脉冲压缩,得到脉压后的回波数据;Step 2: Perform pulse compression on the echo data received by the sky wave over-the-horizon radar in the azimuth of the target to obtain the echo data after pulse pressure; 步骤3,对天波超视距雷达脉压后的回波信号进行动目标检测:Step 3: Perform moving target detection on the echo signal after the sky wave over-the-horizon radar pulse pressure: 对同一距离单元的一个相干积累时间内的脉压后回波数据进行离散傅里叶变换DFT,得到目标的距离-多普勒矩阵;Perform discrete Fourier transform DFT on the pulse pressure post-echo data within a coherent accumulation time of the same range unit to obtain the range-Doppler matrix of the target; 步骤4,对目标的距离-多普勒矩阵做二维恒虚警检测,得到目标所在的距离单元和多普勒单元;Step 4: Perform two-dimensional constant false alarm detection on the range-Doppler matrix of the target to obtain the range unit and Doppler unit where the target is located; 步骤5,利用稀疏贝叶斯算法对目标所在多普勒单元的信号进行稀疏恢复:Step 5: Use the sparse Bayesian algorithm to sparsely restore the signal of the Doppler unit where the target is located: 通过对天波超视距雷达发射的线性调频连续波信号脉冲压缩后的信号时延,根据观测向量的维度,构建测量矩阵;利用稀疏贝叶斯算法对观测向量进行稀疏恢复,得到稀疏信号向量,将稀疏向量中各个元素的位置转换成目标的距离值。By compressing the signal delay of the linear frequency modulated continuous wave signal emitted by the sky wave over-the-horizon radar, a measurement matrix is constructed according to the dimensions of the observation vector; the sparse Bayesian algorithm is used to sparsely restore the observation vector to obtain a sparse signal vector. Convert the position of each element in the sparse vector into the distance value of the target. 2.根据权利要求1所述基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于:步骤2中所述对天波超视距雷达接收的回波数据进行脉冲压缩的步骤如下:2. The sky wave over-the-horizon radar distance estimation method based on the sparse Bayesian algorithm according to claim 1, characterized in that: the step of performing pulse compression on the echo data received by the sky wave over-the-horizon radar in step 2 is as follows : 第一步,根据天波超视距雷达的发射信号,构建匹配滤波器的冲激响应为其中,s表示天波超视距雷达一个脉冲重复周期内发射的线性调频连续波信号s(t)经过离散采样后,得到的离散序列,s=[s1,s2,...,sG],G表示一个脉冲重复周期内离散序列的采样点数,sg表示s的第g个元素,g=1,2,G,(·)*表示共轭操作;In the first step, based on the transmission signal of the sky wave over-the-horizon radar, the impulse response of the matched filter is constructed as Among them, s represents the discrete sequence obtained after discrete sampling of the chirp continuous wave signal s(t) emitted within one pulse repetition period of the sky-wave over-the-horizon radar, s=[s 1 , s 2 ,..., s G ], G represents the number of sampling points of the discrete sequence within a pulse repetition period, s g represents the g-th element of s, g=1,2,G, (·) * represents the conjugate operation; 第二步,将天波超视距雷达回波数据与匹配滤波器的冲激响应进行卷积,得到脉压后的回波数据。In the second step, the sky wave over-the-horizon radar echo data is convolved with the impulse response of the matched filter to obtain the echo data after pulse pressure. 3.根据权利要求1所述基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于:步骤4中所述二维恒虚警检测的步骤如下:3. The sky-wave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm according to claim 1, characterized in that: the steps of two-dimensional constant false alarm detection in step 4 are as follows: 第一步,选取距离-多普勒矩阵中未被选择过的元素作为待检测单元;The first step is to select unselected elements in the distance-Doppler matrix as units to be detected; 第二步,在待检测单元两侧分别选取N个参考单元,N的选取为2的整数幂,计算2N个参考单元的平均值,将该平均值作为背景噪声的功率估计值ZcaIn the second step, N reference units are selected on both sides of the unit to be detected, N is selected as an integer power of 2, the average value of the 2N reference units is calculated, and the average value is used as the power estimate Z ca of the background noise; 第三步,将背景噪声的功率估计值Zca乘以门限乘积因子k,得到待检测单元的门限值s;The third step is to multiply the background noise power estimate Z ca by the threshold product factor k to obtain the threshold value s of the unit to be detected; 第四步,将待检测单元的信号值与门限值s进行比较,如果待检测单元的信号值大于门限值,则判定该信号为目标信号,并为其赋值1;否则,判定该信号为噪声信号,赋值为0;The fourth step is to compare the signal value of the unit to be detected with the threshold value s. If the signal value of the unit to be detected is greater than the threshold value, the signal is determined to be the target signal and assigned a value of 1; otherwise, the signal is determined to be the target signal. For the noise signal, the value is assigned to 0; 第五步,判断是否选完距离-多普勒矩阵中的所有元素,若是,将被判定为目标信号的元素坐标值映射到距离-多普勒矩阵中,得到目标所在的距离单元和多普勒单元;否则,执行第一步。The fifth step is to determine whether all elements in the range-Doppler matrix have been selected. If so, map the coordinate values of the elements determined to be the target signals into the range-Doppler matrix to obtain the range unit and Doppler where the target is located. unit; otherwise, perform the first step. 4.根据权利要求1所述的基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于:步骤5中所述的观测向量指的是,选取目标所在多普勒单元中的脉冲压缩后的回波数据,截取回波数据主瓣宽度长度的数据组成观测向量。4. The sky-wave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm according to claim 1, characterized in that: the observation vector described in step 5 refers to selecting the Doppler unit where the target is located. After pulse compression, the echo data is intercepted and the main lobe width and length of the echo data are intercepted to form an observation vector. 5.根据权利要求1所述的基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于:步骤5中所述构造测量矩阵的步骤如下:5. The sky-wave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm according to claim 1, characterized in that: the steps of constructing the measurement matrix in step 5 are as follows: 第一步,构建一个维度为P×M的元素初始值均为0的测量矩阵;P的取值等于观测向量的长度,M=KP,K的取值为线性调频信号的采样频率与观测向量的采样频率的比值;The first step is to construct a measurement matrix with dimensions P×M whose initial values are all 0; the value of P is equal to the length of the observation vector, M=KP, and the value of K is the sampling frequency of the linear frequency modulation signal and the observation vector The ratio of sampling frequencies; 第二步,将线性调频连续波信号与匹配滤波器冲激响应进行脉冲压缩,得到基矢量,找到基矢量的峰值点位置q,截取基矢量主瓣的第q-b到q+b个元素,b的取值为基矢量主瓣采样点数的二分之一,将基矢量主瓣中的所有元素放到测量矩阵的第一列的第一行到第2b行,以此类推,将基矢量主瓣中的所有元素放到测量矩阵的第k列的第k行到第k+2b-1行,k=1,2,...,M;The second step is to perform pulse compression on the linear frequency modulation continuous wave signal and the matched filter impulse response to obtain the basis vector, find the peak point position q of the basis vector, and intercept the q-b to q+b elements of the main lobe of the basis vector, b The value of is one-half of the number of sampling points in the main lobe of the basis vector. Put all the elements in the main lobe of the basis vector into the first row to row 2b of the first column of the measurement matrix, and so on. Put the main lobe of the basis vector into All elements in the lobe are placed in the kth row to the k+2b-1th row of the kth column of the measurement matrix, k=1,2,...,M; 第三步,截取测量矩阵的第b到第P+b-1行,测量矩阵的第一列代表第0时刻的线性调频连续波信号的脉压波形数据,第k列代表第k×Δt时刻的线性调频连续波信号的脉压波形数据,Δt代表测量矩阵各个列之间的时间间隔;The third step is to intercept the b-th to P+b-1 rows of the measurement matrix. The first column of the measurement matrix represents the pulse pressure waveform data of the chirp continuous wave signal at time 0, and the k-th column represents the k×Δt time. The pulse pressure waveform data of linear frequency modulation continuous wave signal, Δt represents the time interval between each column of the measurement matrix; 第四步,对测量矩阵的所有列向量进行K倍抽取,使线性调频连续波信号的脉压波形数据的维度与观测向量一致。The fourth step is to perform K-fold extraction on all column vectors of the measurement matrix to make the dimensions of the pulse pressure waveform data of the linear frequency modulated continuous wave signal consistent with the observation vector. 6.根据权利要求1所述的基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于:步骤5中所述利用稀疏贝叶斯算法对观测向量进行稀疏恢复得到稀疏信号向量的具体步骤如下:6. The sky-wave over-the-horizon radar distance estimation method based on the sparse Bayesian algorithm according to claim 1, characterized in that: using the sparse Bayesian algorithm in step 5 to sparsely restore the observation vector to obtain the sparse signal vector The specific steps are as follows: 第一步,初始化超参数α、α0,α=(α12,,αM)表示稀疏信号向量的超参数,α的每一个元素都初始化为1;α0代表噪声方差,初始化为1;The first step is to initialize the hyperparameters α and α 0 , α = (α 1 , α 2 ,, α M ) represents the hyperparameter of the sparse signal vector, each element of α is initialized to 1; α 0 represents the noise variance, initialization is 1; 第二步,按照下式,计算待求稀疏信号向量的后验概率密度函数的方差矩阵R和均值向量μ;In the second step, according to the following formula, calculate the variance matrix R and mean vector μ of the posterior probability density function of the sparse signal vector to be found; R=(α0ΦTΦ+Λ)-1 R=(α 0 Φ T Φ+Λ) -1 μ=α0Tyμ=α 0T y 其中,Φ表示测量矩阵,(·)T表示转置操作,Λ表示超参数α的对角矩阵,y表示观测向量,(·)-1表示求逆操作;Among them, Φ represents the measurement matrix, (·) T represents the transpose operation, Λ represents the diagonal matrix of the hyperparameter α, y represents the observation vector, and (·) -1 represents the inversion operation; 第三步,按照下式,更新超参数和αnewThe third step is to update the hyperparameters according to the following formula and α new ; 其中,表示αnew的第i列向量,γi表示量化因子的第i个元素,γi=1-αiRii,∑表示求和操作,i=1,2,,M;in, represents the i-th column vector of α new , γ i represents the i-th element of the quantization factor, γ i =1-α i R ii , ∑ represents the summation operation, i = 1, 2,,M; 第四步,判断当前迭代的均方根误差是否满足收敛条件或达到最大迭代次数,若是,执行第五步,否则,执行第二步;所述的收敛条件为当前迭代得到的均值向量与前一次迭代得到的均值向量的均方根误差小于e-4,最大迭代次数为1000次;The fourth step is to determine whether the root mean square error of the current iteration satisfies the convergence condition or reaches the maximum number of iterations. If so, perform step five. Otherwise, perform step two; the convergence condition is the difference between the mean vector obtained by the current iteration and the previous iteration. The root mean square error of the mean vector obtained in one iteration is less than e -4 , and the maximum number of iterations is 1000; 第五步,将当前迭代得到的均值向量作为稀疏信号向量。The fifth step is to use the mean vector obtained in the current iteration as a sparse signal vector. 7.根据权利要求5所述的基于稀疏贝叶斯算法的天波超视距雷达距离估计方法,其特征在于:步骤5中所述将稀疏向量中各个元素的位置转换成目标的距离值指的是:利用公式将稀疏向量中各个元素的位置转换成目标的距离值;其中,c表示光速,L表示截取目标所在多普勒单元中的脉冲压缩后的回波数据中的起始坐标值,fs表示观测向量的采样频率。7. The sky-wave over-the-horizon radar distance estimation method based on sparse Bayesian algorithm according to claim 5, characterized in that: in step 5, the position of each element in the sparse vector is converted into the distance value of the target. Yes: Use the formula Convert the position of each element in the sparse vector into the distance value of the target; where c represents the speed of light, L represents the starting coordinate value in the echo data after intercepting the pulse compression in the Doppler unit where the target is located, and f s represents the observation The sampling frequency of the vector.
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