米波数字阵列雷达低仰角测高方法研究
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摘要
米波雷达波长较长，在反隐身、抗反辐射导弹等方面具有独特的优势，且作用距离远，衰减比微波小，近年来受到世界各国的普遍重视。但受天线尺寸的限制，米波阵列雷达天线主瓣波束较宽，角分辨率差，天线副瓣高，抗干扰能力差。在探测远距离目标时，由于波束较宽，俯仰维波束会打地，雷达接收信号中除了直接从目标反射回来的信号外，还有从多径效应产生的镜面反射和漫反射等多径信号。多径效应对低空目标的仰角测量影响较大，从而影响了对目标高度的准确测量。因此提高米波雷达在低仰角区的测角和测高精度是亟待解决的关键难题。
本人在前人工作的基础上，结合目前承担的科研任务，从若干方面围绕米波数字阵列雷达的低仰角测高问题展开工作，具体工作概括如下：
1.在综合考虑数字阵列雷达信号处理系统的基础上，采用DSP和FPGA相结合的方法，设计一种高性能软件化数字信号处理机，整个信号处理机基于CPCI总线，采用高速串行通道提高板间数据传输速率，采用交叉开关技术实现信号处理板间的动态互联，提高雷达信号处理机的性能。该系统结构简单，具有很好的通用性和可扩展性，具有较高的实用价值。另外，研究两维数字阵列雷达的数字单脉冲测角方法，分析基本单脉冲测角过程中存在的问题，提出一种改进的基于窗函数的二维数字阵列雷达单脉冲测角方法。该方法在差波束形成过程中考虑不同工作频率、不同波位的天线等效孔径的变化。针对测角误差信号的非线性特征，在根据误差信号计算目标角度时采用多阶多项式拟合的方法，不仅减少单脉冲误差曲线的数目，而且简化数据处理中大量的数据存储和查表的运算，便于工程实现，更重要的是消除建立误差曲线表时的量化误差和减小线性近似时的测量误差。
2.研究基于广义约束MUSIC算法的低仰角测高方法。约束MUSIC算法利用已知的信源方向来提高未知信源估计精度，而且不受信源相干的影响。把该算法应用于米波雷达低仰角测高中，提出一种广义约束MUSIC算法，将多径方向的导向矢量构成约束矩阵，生成投影算子，通过对协方差矩阵的投影来消除多径信号对协方差矩阵的影响，从而提高直达波的DOA估计精度。该算法的优点在于能直接处理相干信号，并且不用考虑地面反射系数的影响。再结合雷达测高的特点，对该算法进行改进，将二维搜索降为一维搜索，在保持良好性能的同时降低运算量。该方法在快拍数大于阵元数时就能超过空间平滑MUSIC的测角精度。
3.研究基于精确多径信号模型的合成导向矢量测高方法。精确多径信号模型考虑入射信号极化信息、镜面反射、散射、漫反射、地形及掠射角等因素对多径信号的影响，利用天线高度、目标和雷达之间的距离、地球曲率、大气折射等先验信息，给出球面模型复杂地形下反射系数以及直达波、反射波波程的计算方法，提出基于地形匹配的合成导向矢量超分辨算法，将搜索导向矢量表示为直达波和反射波导向矢量之和的形式，然后使用超分辨算法进行DOA估计，提高角度估计精度。另外，当地面粗糙度增加到不能满足瑞利准则时，雷达天线接收的信号应该看成是镜面反射分量与漫反射分量之和，表面越粗糙，雷达仰角越低，漫散射功率越占主导地位，建立存在地面漫反射时的信号模型，将多径信号认为是相干分布源，提出利用多维交替投影和合成导向矢量超分辨算法进行低仰角测高。但是实际中，地面反射区的多径分布源模型很难确定，需要通过大量的实验来进行验证。
4.将稀疏分析应用于米波数字阵列雷达低仰角测高中，利用实际空间中被测目标在空域内分布的稀疏性，利用压缩感知思想来进行低仰角估计。提出协方差矩阵压缩感知、内插阵压缩感知和波束空间压缩感知DOA估计算法，分别在协方差矩阵、虚拟内插阵和波束空间上进行压缩采样，构建出新的DOA估计压缩感知模型，最后通过稀疏重建算法来进行信号重构，得到目标的高分辨DOA估计。该方法突破阵列分辨率的瑞利限，降低信号功率谱和空间谱的旁瓣，在低信噪比和快拍数较少的环境下也能达到较好的效果，而且对空域信号的相关性不敏感，可以直接用于相干信号的DOA估计，具有较高的角度分辨力。
5.研究干涉式APES算法在分布式相参阵列DOA估计中的应用。利用干涉式APES算法得到的空间谱和模型阶数选择准则获得目标个数和目标方向余弦的粗估计，同时利用子阵间的相位中心偏移来获得目标方向余弦的精估计，再使用双尺度解模糊算法得到高精度且无模糊的目标DOA估计。该算法不依赖于信源数、信源相关性等参数，是一种盲DOA估计方法，而且在样本少时性能较好。该算法以增大运算量为代价来得到更高的角度分辨率和测角精度，能有效地应用于米波雷达低仰角多径环境下的测高问题。同时对分布式阵列中的基线模糊门限与信噪比门限进行讨论，并对算法的运算量和克拉美罗界进行分析。
论文针对这些方法，在仿真分析的基础上，结合了实际雷达的实测数据结果。因此，论文理论紧密联系实际，解决了某型米波雷达在一些典型阵地上遇到的实际问题，并给出了实际的测高结果。本论文为该型雷达的研制发挥了重要作用。
As a kind of meter-wave radar, it has good anti-stealth effect, anti-arm capacity, lessattenuation compared with microwave radar, and large detection range. In recent years,the research in VHF radar has been attached great importance. Limited by aperture,meter-wave radar has wide beam, which usually causes bad angular resolution.Furthermore, high sidelobe excludes good anti-interference capacity. Because of thebeam wideness, the beam often reflects to the ground when radar detects the long rangetargets, the received signal in the mainlobe includes the direct path echo from the targetdirectly and the reflection multipath echo which are reflected from the ground (sea)surface. The reflection multipath echo cause the measurement accuracy of elevationdeteriorates sharply. The key technology to be solved is improving the low-elevationangle accuracy.
On the basis of the achievements obtained by now, combined with my researchproject, this dissertation starts from low angle estimation in meter-wave radar. The maincontent of this dissertation is summarized as follows.
1. Considering the demand and technical characteristic of radar signal processingsystem, a new high-powered radar signal processing system architecture based onFPGA and DSP is proposed. The architecture is based on cPCI standard platform.High-speed serial channel improves data Transmission rate. The crosspoint switch isable to make circuit boards connection dynamically. These greatly improve theperformance of the radar signal processor. This system is simple in structure and hasgood universality and extendibility which is in agreement with the forthcomingdirection of radar signal processors and has high engineering value. Additionally, theangle measurement method with digital monopulse for2-Dimensional digital arrayradar is studied in the paper. The variations of equivalent aperture of antenna array withdifferent frequencies and different beam positions are taken into account in the processof difference patterns synthesis. Multi-order polynomial fitting method is adopted tocalculate the target’s angle according to the angle error signal whose characteristic isnonlinear. This technique decreases the number of monopulse error cures and simplifiesthe huge data storage and the calculation of lookup table, facilitated engineeringimplementation. It is important to eliminate the quantized error of error curve tables anddecrease the measuring error of linear approximation.
2. A generalized constrained MUSIC is studied for low-angle altitude estimation.Constrained MUSIC improves the estimation precision of unknown source directions byincorporating the prior known source directions and has no influence caused bycoherence of sources. A generalized constrained MUSIC is proposed, which is modifiedin terms of the low-angle environment of VHF radar, improves the estimation precisionof direct signal with multi-path signal as a constraint. The proposed method deal withcoherent sources directly and doesn’t considering the affect caused by reflectioncoefficient. According to the characteristic of height-finding, some improvement ismade on the proposed algorithm, change2-D search to1-D search, which reducescomputation complexity and gets good performances. The proposed method obtainsgood performance while the number of snapshot is more than the number of elementcompared with the spatial smoothing MUSIC.
3. A synthetic steering vector superresolution algorithm based on a highlydeterministic multipath signal model is proposed. To model the signal more accurately,signal polarization, mirror reflection, dispersion, diffuse reflection, the terrainparameters of the reflection region and grazing angle must be taken into account, inaddition to antenna height, distance between target and array, the curvature of the signalpath due to refraction in the troposphere and the curvature of the earth itself. Thecalculation methods of the reflection coefficient and lengths of the direct path andindirect path are given. A synthetic steering vector superresolution algorithm based onterrain matching is proposed. The accuracy DOA is obtained by superresolutionalgorithm that makes use of the synthetic steering vector which is the sum of directsteering vector and indirect steering vector. In additional, if the roughness dissatisfiesthe Reileigh rule, the received signal includes the direct component and diffusereflection component. The reflection surface is rougher; the power of diffuse reflectioncomponent is stronger. The diffuse reflection component in signal module can be takenfor coherent distributed source. The DOA could be obtained by multi-dimensionalternating projection and synthetic steering vector superresolution algorithm. But inpractice, it is hard to ascertain the multipath distributed source model that should bevalidated by lots of experiments.
4. Making use of the sparsity of targets, some novel direction-of-arrival models forlow-angel estimation in VHF radar based on compressive sensing are proposed.Covariance matrix compressive sensing, interpolated array compressive sensing andbeam space compressive sensing carry out compressive sampling on covariance matrix,interpolated array and beam space, respectively, and three new three new direction-of-arrival models based on compressive sensing are built. The accuracy DOAestimation is achieved by sparse reconstruction algorithm. The proposed methodsachieve resolution beyond Rayleigh limit, get low sidelobe in spatial spectrum andobtain good performance at low SNR and less snapshots environment. The proposedmethods are conceptually different from subspace-based methods and provide highresolution using a uniform linear array without restricting requirements on the spatialand temporal stationary and correlation properties of the sources and the noise and gethigh angular resolution.
5. An interferometric-like APES algorithm is studied for DOA estimation ofdistributed coherent arrays. The number of targets and coarse direction cosine estimatesare obtained from interferometric-like APES spatial spectral and model-order selectioncriterion. The high accuracy direction cosine estimates are derived from phase centershift between subarrays. A dual-size algorithm is used to resolve the ambiguity in DOAestimation resulted from the distributed coherent arrays. Then the low variance andunambiguous DOA estimates are achieved. The proposed approach is a blind DOAestimation method and is independent of the number of sources and the coherence ofsources and has good performance while the sample is less. The algorithm enhancesangle resolution and accuracy at the cost of huge computation and can be applied inVHF radar low-angle DOA problem. Also the baseline ambiguity threshold and SNRambiguity threshold in distributed coherent arrays are demonstrated, the computationcost and CRB of the proposed method are analysed.
On the basis of simulations and analysis, the real data of some VHF radar isincorporated into these methods above. Therefore, this dissertation realizes the closerelation between the theory and practice or implementation, and solve some practicalissues of the VHF radar in some typical positions.This dissertation is of vast importancefor the research and development of this VHF radar.
本人在前人工作的基础上，结合目前承担的科研任务，从若干方面围绕米波数字阵列雷达的低仰角测高问题展开工作，具体工作概括如下：
1.在综合考虑数字阵列雷达信号处理系统的基础上，采用DSP和FPGA相结合的方法，设计一种高性能软件化数字信号处理机，整个信号处理机基于CPCI总线，采用高速串行通道提高板间数据传输速率，采用交叉开关技术实现信号处理板间的动态互联，提高雷达信号处理机的性能。该系统结构简单，具有很好的通用性和可扩展性，具有较高的实用价值。另外，研究两维数字阵列雷达的数字单脉冲测角方法，分析基本单脉冲测角过程中存在的问题，提出一种改进的基于窗函数的二维数字阵列雷达单脉冲测角方法。该方法在差波束形成过程中考虑不同工作频率、不同波位的天线等效孔径的变化。针对测角误差信号的非线性特征，在根据误差信号计算目标角度时采用多阶多项式拟合的方法，不仅减少单脉冲误差曲线的数目，而且简化数据处理中大量的数据存储和查表的运算，便于工程实现，更重要的是消除建立误差曲线表时的量化误差和减小线性近似时的测量误差。
2.研究基于广义约束MUSIC算法的低仰角测高方法。约束MUSIC算法利用已知的信源方向来提高未知信源估计精度，而且不受信源相干的影响。把该算法应用于米波雷达低仰角测高中，提出一种广义约束MUSIC算法，将多径方向的导向矢量构成约束矩阵，生成投影算子，通过对协方差矩阵的投影来消除多径信号对协方差矩阵的影响，从而提高直达波的DOA估计精度。该算法的优点在于能直接处理相干信号，并且不用考虑地面反射系数的影响。再结合雷达测高的特点，对该算法进行改进，将二维搜索降为一维搜索，在保持良好性能的同时降低运算量。该方法在快拍数大于阵元数时就能超过空间平滑MUSIC的测角精度。
3.研究基于精确多径信号模型的合成导向矢量测高方法。精确多径信号模型考虑入射信号极化信息、镜面反射、散射、漫反射、地形及掠射角等因素对多径信号的影响，利用天线高度、目标和雷达之间的距离、地球曲率、大气折射等先验信息，给出球面模型复杂地形下反射系数以及直达波、反射波波程的计算方法，提出基于地形匹配的合成导向矢量超分辨算法，将搜索导向矢量表示为直达波和反射波导向矢量之和的形式，然后使用超分辨算法进行DOA估计，提高角度估计精度。另外，当地面粗糙度增加到不能满足瑞利准则时，雷达天线接收的信号应该看成是镜面反射分量与漫反射分量之和，表面越粗糙，雷达仰角越低，漫散射功率越占主导地位，建立存在地面漫反射时的信号模型，将多径信号认为是相干分布源，提出利用多维交替投影和合成导向矢量超分辨算法进行低仰角测高。但是实际中，地面反射区的多径分布源模型很难确定，需要通过大量的实验来进行验证。
4.将稀疏分析应用于米波数字阵列雷达低仰角测高中，利用实际空间中被测目标在空域内分布的稀疏性，利用压缩感知思想来进行低仰角估计。提出协方差矩阵压缩感知、内插阵压缩感知和波束空间压缩感知DOA估计算法，分别在协方差矩阵、虚拟内插阵和波束空间上进行压缩采样，构建出新的DOA估计压缩感知模型，最后通过稀疏重建算法来进行信号重构，得到目标的高分辨DOA估计。该方法突破阵列分辨率的瑞利限，降低信号功率谱和空间谱的旁瓣，在低信噪比和快拍数较少的环境下也能达到较好的效果，而且对空域信号的相关性不敏感，可以直接用于相干信号的DOA估计，具有较高的角度分辨力。
5.研究干涉式APES算法在分布式相参阵列DOA估计中的应用。利用干涉式APES算法得到的空间谱和模型阶数选择准则获得目标个数和目标方向余弦的粗估计，同时利用子阵间的相位中心偏移来获得目标方向余弦的精估计，再使用双尺度解模糊算法得到高精度且无模糊的目标DOA估计。该算法不依赖于信源数、信源相关性等参数，是一种盲DOA估计方法，而且在样本少时性能较好。该算法以增大运算量为代价来得到更高的角度分辨率和测角精度，能有效地应用于米波雷达低仰角多径环境下的测高问题。同时对分布式阵列中的基线模糊门限与信噪比门限进行讨论，并对算法的运算量和克拉美罗界进行分析。
论文针对这些方法，在仿真分析的基础上，结合了实际雷达的实测数据结果。因此，论文理论紧密联系实际，解决了某型米波雷达在一些典型阵地上遇到的实际问题，并给出了实际的测高结果。本论文为该型雷达的研制发挥了重要作用。
As a kind of meter-wave radar, it has good anti-stealth effect, anti-arm capacity, lessattenuation compared with microwave radar, and large detection range. In recent years,the research in VHF radar has been attached great importance. Limited by aperture,meter-wave radar has wide beam, which usually causes bad angular resolution.Furthermore, high sidelobe excludes good anti-interference capacity. Because of thebeam wideness, the beam often reflects to the ground when radar detects the long rangetargets, the received signal in the mainlobe includes the direct path echo from the targetdirectly and the reflection multipath echo which are reflected from the ground (sea)surface. The reflection multipath echo cause the measurement accuracy of elevationdeteriorates sharply. The key technology to be solved is improving the low-elevationangle accuracy.
On the basis of the achievements obtained by now, combined with my researchproject, this dissertation starts from low angle estimation in meter-wave radar. The maincontent of this dissertation is summarized as follows.
1. Considering the demand and technical characteristic of radar signal processingsystem, a new high-powered radar signal processing system architecture based onFPGA and DSP is proposed. The architecture is based on cPCI standard platform.High-speed serial channel improves data Transmission rate. The crosspoint switch isable to make circuit boards connection dynamically. These greatly improve theperformance of the radar signal processor. This system is simple in structure and hasgood universality and extendibility which is in agreement with the forthcomingdirection of radar signal processors and has high engineering value. Additionally, theangle measurement method with digital monopulse for2-Dimensional digital arrayradar is studied in the paper. The variations of equivalent aperture of antenna array withdifferent frequencies and different beam positions are taken into account in the processof difference patterns synthesis. Multi-order polynomial fitting method is adopted tocalculate the target’s angle according to the angle error signal whose characteristic isnonlinear. This technique decreases the number of monopulse error cures and simplifiesthe huge data storage and the calculation of lookup table, facilitated engineeringimplementation. It is important to eliminate the quantized error of error curve tables anddecrease the measuring error of linear approximation.
2. A generalized constrained MUSIC is studied for low-angle altitude estimation.Constrained MUSIC improves the estimation precision of unknown source directions byincorporating the prior known source directions and has no influence caused bycoherence of sources. A generalized constrained MUSIC is proposed, which is modifiedin terms of the low-angle environment of VHF radar, improves the estimation precisionof direct signal with multi-path signal as a constraint. The proposed method deal withcoherent sources directly and doesn’t considering the affect caused by reflectioncoefficient. According to the characteristic of height-finding, some improvement ismade on the proposed algorithm, change2-D search to1-D search, which reducescomputation complexity and gets good performances. The proposed method obtainsgood performance while the number of snapshot is more than the number of elementcompared with the spatial smoothing MUSIC.
3. A synthetic steering vector superresolution algorithm based on a highlydeterministic multipath signal model is proposed. To model the signal more accurately,signal polarization, mirror reflection, dispersion, diffuse reflection, the terrainparameters of the reflection region and grazing angle must be taken into account, inaddition to antenna height, distance between target and array, the curvature of the signalpath due to refraction in the troposphere and the curvature of the earth itself. Thecalculation methods of the reflection coefficient and lengths of the direct path andindirect path are given. A synthetic steering vector superresolution algorithm based onterrain matching is proposed. The accuracy DOA is obtained by superresolutionalgorithm that makes use of the synthetic steering vector which is the sum of directsteering vector and indirect steering vector. In additional, if the roughness dissatisfiesthe Reileigh rule, the received signal includes the direct component and diffusereflection component. The reflection surface is rougher; the power of diffuse reflectioncomponent is stronger. The diffuse reflection component in signal module can be takenfor coherent distributed source. The DOA could be obtained by multi-dimensionalternating projection and synthetic steering vector superresolution algorithm. But inpractice, it is hard to ascertain the multipath distributed source model that should bevalidated by lots of experiments.
4. Making use of the sparsity of targets, some novel direction-of-arrival models forlow-angel estimation in VHF radar based on compressive sensing are proposed.Covariance matrix compressive sensing, interpolated array compressive sensing andbeam space compressive sensing carry out compressive sampling on covariance matrix,interpolated array and beam space, respectively, and three new three new direction-of-arrival models based on compressive sensing are built. The accuracy DOAestimation is achieved by sparse reconstruction algorithm. The proposed methodsachieve resolution beyond Rayleigh limit, get low sidelobe in spatial spectrum andobtain good performance at low SNR and less snapshots environment. The proposedmethods are conceptually different from subspace-based methods and provide highresolution using a uniform linear array without restricting requirements on the spatialand temporal stationary and correlation properties of the sources and the noise and gethigh angular resolution.
5. An interferometric-like APES algorithm is studied for DOA estimation ofdistributed coherent arrays. The number of targets and coarse direction cosine estimatesare obtained from interferometric-like APES spatial spectral and model-order selectioncriterion. The high accuracy direction cosine estimates are derived from phase centershift between subarrays. A dual-size algorithm is used to resolve the ambiguity in DOAestimation resulted from the distributed coherent arrays. Then the low variance andunambiguous DOA estimates are achieved. The proposed approach is a blind DOAestimation method and is independent of the number of sources and the coherence ofsources and has good performance while the sample is less. The algorithm enhancesangle resolution and accuracy at the cost of huge computation and can be applied inVHF radar low-angle DOA problem. Also the baseline ambiguity threshold and SNRambiguity threshold in distributed coherent arrays are demonstrated, the computationcost and CRB of the proposed method are analysed.
On the basis of simulations and analysis, the real data of some VHF radar isincorporated into these methods above. Therefore, this dissertation realizes the closerelation between the theory and practice or implementation, and solve some practicalissues of the VHF radar in some typical positions.This dissertation is of vast importancefor the research and development of this VHF radar.
引文
[1]董玫.米波雷达测高算法及应用研究[D].西安:西安电子科技大学博士学位论文,2008.
[2]吴向东.米波雷达低仰角测高算法及相关技术研究[D].西安:西安电子科技大学博士学位论文,2008.
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