分布式阵列米波雷达高精度测角问题研究
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摘要
米波雷达的波长特性使米波雷达具有反隐身、抗反辐射导弹及作用距离远等突出优势，但米波雷达带宽窄、波束宽、角分辨率低、定位精度低等缺点也较为明显。如何提高米波雷达的角度分辨率及定位精度是米波雷达发展需解决的突出问题。而增大天线孔径是一种比较有效的解决方法，但是天线孔径的增大不仅不利于雷达或雷达平台的隐身需求，而且降低了系统的机动性、抗摧毁能力和战场生存能力。本文提出分布式阵列米波雷达系统的解决方案，该系统采用密布的主阵列发射、分布式阵列接收的配置结构，通过分布式接收阵列的相参处理可得到等效的大孔径天线。
因此，结合某米波雷达课题，本文围绕分布式阵列米波雷达的高精度测角问题展开，对分布式阵列的稳健自适应波束形成、高精度方向估计、流形解模糊和低仰角估计等方面进行深入研究，具体工作概括如下：
1.研究分布式阵列米波雷达的稳健自适应波束形成技术。首先针对分布式阵列的结构特征，提出分散式与集中式两种数字波束形成的实现结构；再分析波束指向误差、阵元幅相误差等对分布式阵列的各种稳健自适应波束形成算法的性能影响，为分布式阵列的波束形成选择合理算法提供理论指导；最后，针对子阵相位中心未知或存在扰动的部分校正的分布式阵列，提出其导向矢量的结构化不确定集模型，将其波束形成问题转换成非凸的伪半正定优化(SDP)问题，由于非凸优化问题的难以求解，本文采用优化理论中的松弛方法求解，从而提出了部分校正的分布式阵列的半正定松弛(SDR)波束形成器，并通过计算机仿真验证其正确性与有效性。
2.提出三种分布式阵列结构及其高精度DOA估计方法。为了实现二维的高精度角度估计，本文依次提出干涉式L形阵、分布式相参阵列及斜线型分布式阵列三种分布式阵列结构及其高精度DOA估计方法。针对干涉式L形阵的结构特点，本文提出采用一维双尺度酉ESPRIT算法及基于子空间正交特性的配对算法实现无模糊高精度的方向估计，并简要地分析基线阵列基线长度对其DOA估计性能的影响。为了提高天线的增益、孔径，本文以干涉式L形阵为基础，将其一维线阵扩展为二维面阵，提出了分布式相参阵列。根据分布式相参阵列的面阵特征，本文采用二维双尺度ESPRIT算法及配对算法实现高精度的DOA估计。针对以上两种阵列的方向估计性能的明显门限效应，本文利用分段误差法(MIE)法分析分布式阵列的门限性能，并给出了SNR门限与基线门限的近似计算方法。最后，本文提出了斜线型分布式阵列，由于存在孔径耦合，斜线型分布式阵列的二维方向余弦精估计耦合并形成直线簇，因此本文提出基于点线间垂线距离最短准则的解模糊算法，且孔径耦合使斜线型阵列的方向估计性能存在明显的方位角与俯仰角分辨力得益区，并由分辨力得益区说明斜线型阵列仅能在方位维或俯仰维获得高精度性能，而无法同时获得二维方向的高精度估计性能。
3.研究阵列流形模糊及干涉阵列的矩阵完型解模糊算法。流形模糊并不表示不可识别，本文从模式识别理论分析流形解模糊的两种基本方法，即关联法与模型拟合法或解卷积法。分布式阵列对空间场的欠采样是产生流形模糊的根本原因。由Caratheodory定理及Pisarenko谐波分解理论可知，若能得到与稀疏阵列同孔径的虚拟均匀线阵的正定厄密Toeplitz协方差矩阵，则可自动解模糊，即将解模糊问题转换成正定Toeplitz矩阵完型的纯数学问题。因此本文先简要地分析并比较已有正定Toeplitz矩阵完型算法的性能及适用条件。针对干涉阵列米波雷达的阵列结构的特殊性及已有完型算法的不稳定性，本文提出辅助阵元与Toeplitz矩阵完型相结合的矩阵完型解模糊算法，实现软件算法的硬件化，提高解模糊算法的稳定性，仿真与实测数据证明了算法的有效性与正确性。
4.研究干涉式阵列米波雷达的高精度低仰角估计。由于地(海)面反射的多径反射信号严重影响了米波雷达的仰角估计性能，本文利用干涉式阵列扩展俯仰孔径，并提出了干涉式阵列的前后向空间平滑(IFBSS)解相干方法，以实现多径信号与直达信号的解相干，再采用ESPRIT算法提高米波雷达的仰角估计精度。仿真与实测数据验证了该阵列结构及IFBSS算法的有效性与正确性。针对常用的两目标近似模型与实际的多径信号的失配问题，本文研究了基于非参数化的MTM法的米波雷达多径信号自适应波数谱特征，实测数据分析结果表明了多径信号的色噪声特性及近似模型的不合理性。
VHF radar has the prominent advantages over the microwave radar of anti-stealth,anti-ARM and long detection range, while some distinct disadvantages such asnarrower bandwidth, wider beamwidth, lower angular resolution and lower localizationprecision are also severe. How to enhance the angular resolution and localizationprecision is indispensable for the development of VHF radar. An increase in the antennaaperture is an effective measurement for the problems mentioned above, but the stealthrequirement of radar or radar platforms, transportability, and battlefield survivingcapacity are adversely affected. As a solution to these problems, an array system withdistributed subarrays for VHF radar is proposed, consisting of a main transmit subarrayand distributed receive subarrays. Coherently Combination of the signals received bythe individual subarray can achieve high angular resolution of equivalent large antenna.
This dissertation addresses some issues of distributed subarrays array VHF radarwith the research task of given VHF radar. The research concentrates on the robustadaptive beamforming, high accuracy DOA estimation, manifold ambiguity resolutionand low elevation angle estimation.
The main content of this dissertation is summarized as follows.
1. The techniques of robust adaptive beamforming for distributed subarrays arrayVHF radar are studied. Firstly, In terms of the configuration of distributed subarrays,centralized and distributed structures for digital beamforming are proposed. Secondly,An analysis of effects of mismatches caused by look direction/pointing error, sensorsgains and phase errors on the performance of robust adaptive beamformers is made, ascould be used to provide theoretical guidance for selecting appropriate beamformeralgorithem.Lastly, A structured uncertainty model of steering vector is proposed fordistributed array composed of partly calibrated subarrays in which cases the phasecenters of the subarrays are unknown or disturbed. Then, the robust adaptivebeamforming is converted into a non-convex Pseudo-SDP problem, and a Semi-DefiniteRelaxation(SDR)-based beamformer is proposed.
2. High accuracy2-Dimensional DOA estimation methods for threeconfiguarations of distributed array are presented. Firstly, direction finding for aninterfermetric-like L shaped array and the effect of the baseline on accuracy of DOA areinvestigated. According to the array structure and the ambiguity caused by grating lobes, one-dimensional unitary ESPRIT algorithm is utilized to achieve lower variance andnon-ambiguous DOA estimates. Secondly,2-Dimensional unitary ESPRIT algorithm isused to estimate DOA for distributed coherent array. Threshold effect in DOAestimation is analyzed by Method of Interval Error(MIE), and the methods toapproximately compute threshold baseline and threshold SNR are presented. Lastly,aperture coupling between azimuthal and elevational aperture of slanting array leads tofine direction cosine estimate standing at a family of straight lines. Then, the directioncosine ambiguity can be resolved by the rule that the vectical distance between a dotand a line is the shortest. Simultaneously, aperture coupling causes the presence ofazimuthal and elevational resolution gain regions for slanting array.
3.Manifold ambiguity and matrix completion-based ambiguity resolution algorithmof an interferometric array are studied. Manifold ambiguity does not necessarily implynonidentifiability. Association and model-fitting(Deconvolution) method for ambiguityresolution are derived from pattern recognition theory. Spatial under-sampling is theradical reason to manifold ambiguity. From Caratheodory theorem and Pisarenkoharmonic retrival theory, the manifold ambiguity resolution is automaticallyincorporated if a positive-definite and Toeplitz covariance matrix of a virtual uniformlinear array with the same aperture as the sparse array could be attained. Then manifoldambiguity resolution is translated into a pure math problem. The condition under whichthe various matrix completion method is applicable and the performance are analyzedand compared. For the particularity of an interferometric array configuration andinstability of the existing matrix completion methods, a novel ambiguity resolutionmethod with the combination of auxiliary elements and Toeplitz matrix completion isproposed， which improves stability.Simulation and real data demonstrate theeffectiveness and validity of the proposed method.
4. Low elevation angle with high accuracy is studied for an interferometric-likearray VHF radar. Limited by aperture, VHF radar generally has a wider beam. When thetarget is at low grazing angle or lies below about one-third of the beamwidth above thehorizon, multipath signal reflected from ground(sea) surface come into the mainlobe aswell as the direct echo, in which case the performance of low elevation estimation ofVHF radar is highly affected. The interferometric-like array extends the verticalaperture with small pieces of hardware. The interferometric Forward/Backward spatialsmoothing(IFBSS) technique is proposed from the conventional spatial smoothingalgorithm for uniform linear array, being used to decorrelate the multipath and directsignal. Then high accurate elevation angle estimation with dual-size unitary ESPRIT algorithm is achieved. As the surface roughness increases or the target approaches thehorizon, there is a huge mismatch between two-target model and actual multipath. Acomplete theoretical model of multipath is nearly impossible at present. From theperspective of wavenumber spectrum estimation, the nonparametric Multi-taper Method(MTM) is utilized for the feature of adaptive wavenumber of multipath. It isdemonstrated that the diffuse component is characteristic of colored-noise by real dataresult.
因此，结合某米波雷达课题，本文围绕分布式阵列米波雷达的高精度测角问题展开，对分布式阵列的稳健自适应波束形成、高精度方向估计、流形解模糊和低仰角估计等方面进行深入研究，具体工作概括如下：
1.研究分布式阵列米波雷达的稳健自适应波束形成技术。首先针对分布式阵列的结构特征，提出分散式与集中式两种数字波束形成的实现结构；再分析波束指向误差、阵元幅相误差等对分布式阵列的各种稳健自适应波束形成算法的性能影响，为分布式阵列的波束形成选择合理算法提供理论指导；最后，针对子阵相位中心未知或存在扰动的部分校正的分布式阵列，提出其导向矢量的结构化不确定集模型，将其波束形成问题转换成非凸的伪半正定优化(SDP)问题，由于非凸优化问题的难以求解，本文采用优化理论中的松弛方法求解，从而提出了部分校正的分布式阵列的半正定松弛(SDR)波束形成器，并通过计算机仿真验证其正确性与有效性。
2.提出三种分布式阵列结构及其高精度DOA估计方法。为了实现二维的高精度角度估计，本文依次提出干涉式L形阵、分布式相参阵列及斜线型分布式阵列三种分布式阵列结构及其高精度DOA估计方法。针对干涉式L形阵的结构特点，本文提出采用一维双尺度酉ESPRIT算法及基于子空间正交特性的配对算法实现无模糊高精度的方向估计，并简要地分析基线阵列基线长度对其DOA估计性能的影响。为了提高天线的增益、孔径，本文以干涉式L形阵为基础，将其一维线阵扩展为二维面阵，提出了分布式相参阵列。根据分布式相参阵列的面阵特征，本文采用二维双尺度ESPRIT算法及配对算法实现高精度的DOA估计。针对以上两种阵列的方向估计性能的明显门限效应，本文利用分段误差法(MIE)法分析分布式阵列的门限性能，并给出了SNR门限与基线门限的近似计算方法。最后，本文提出了斜线型分布式阵列，由于存在孔径耦合，斜线型分布式阵列的二维方向余弦精估计耦合并形成直线簇，因此本文提出基于点线间垂线距离最短准则的解模糊算法，且孔径耦合使斜线型阵列的方向估计性能存在明显的方位角与俯仰角分辨力得益区，并由分辨力得益区说明斜线型阵列仅能在方位维或俯仰维获得高精度性能，而无法同时获得二维方向的高精度估计性能。
3.研究阵列流形模糊及干涉阵列的矩阵完型解模糊算法。流形模糊并不表示不可识别，本文从模式识别理论分析流形解模糊的两种基本方法，即关联法与模型拟合法或解卷积法。分布式阵列对空间场的欠采样是产生流形模糊的根本原因。由Caratheodory定理及Pisarenko谐波分解理论可知，若能得到与稀疏阵列同孔径的虚拟均匀线阵的正定厄密Toeplitz协方差矩阵，则可自动解模糊，即将解模糊问题转换成正定Toeplitz矩阵完型的纯数学问题。因此本文先简要地分析并比较已有正定Toeplitz矩阵完型算法的性能及适用条件。针对干涉阵列米波雷达的阵列结构的特殊性及已有完型算法的不稳定性，本文提出辅助阵元与Toeplitz矩阵完型相结合的矩阵完型解模糊算法，实现软件算法的硬件化，提高解模糊算法的稳定性，仿真与实测数据证明了算法的有效性与正确性。
4.研究干涉式阵列米波雷达的高精度低仰角估计。由于地(海)面反射的多径反射信号严重影响了米波雷达的仰角估计性能，本文利用干涉式阵列扩展俯仰孔径，并提出了干涉式阵列的前后向空间平滑(IFBSS)解相干方法，以实现多径信号与直达信号的解相干，再采用ESPRIT算法提高米波雷达的仰角估计精度。仿真与实测数据验证了该阵列结构及IFBSS算法的有效性与正确性。针对常用的两目标近似模型与实际的多径信号的失配问题，本文研究了基于非参数化的MTM法的米波雷达多径信号自适应波数谱特征，实测数据分析结果表明了多径信号的色噪声特性及近似模型的不合理性。
VHF radar has the prominent advantages over the microwave radar of anti-stealth,anti-ARM and long detection range, while some distinct disadvantages such asnarrower bandwidth, wider beamwidth, lower angular resolution and lower localizationprecision are also severe. How to enhance the angular resolution and localizationprecision is indispensable for the development of VHF radar. An increase in the antennaaperture is an effective measurement for the problems mentioned above, but the stealthrequirement of radar or radar platforms, transportability, and battlefield survivingcapacity are adversely affected. As a solution to these problems, an array system withdistributed subarrays for VHF radar is proposed, consisting of a main transmit subarrayand distributed receive subarrays. Coherently Combination of the signals received bythe individual subarray can achieve high angular resolution of equivalent large antenna.
This dissertation addresses some issues of distributed subarrays array VHF radarwith the research task of given VHF radar. The research concentrates on the robustadaptive beamforming, high accuracy DOA estimation, manifold ambiguity resolutionand low elevation angle estimation.
The main content of this dissertation is summarized as follows.
1. The techniques of robust adaptive beamforming for distributed subarrays arrayVHF radar are studied. Firstly, In terms of the configuration of distributed subarrays,centralized and distributed structures for digital beamforming are proposed. Secondly,An analysis of effects of mismatches caused by look direction/pointing error, sensorsgains and phase errors on the performance of robust adaptive beamformers is made, ascould be used to provide theoretical guidance for selecting appropriate beamformeralgorithem.Lastly, A structured uncertainty model of steering vector is proposed fordistributed array composed of partly calibrated subarrays in which cases the phasecenters of the subarrays are unknown or disturbed. Then, the robust adaptivebeamforming is converted into a non-convex Pseudo-SDP problem, and a Semi-DefiniteRelaxation(SDR)-based beamformer is proposed.
2. High accuracy2-Dimensional DOA estimation methods for threeconfiguarations of distributed array are presented. Firstly, direction finding for aninterfermetric-like L shaped array and the effect of the baseline on accuracy of DOA areinvestigated. According to the array structure and the ambiguity caused by grating lobes, one-dimensional unitary ESPRIT algorithm is utilized to achieve lower variance andnon-ambiguous DOA estimates. Secondly,2-Dimensional unitary ESPRIT algorithm isused to estimate DOA for distributed coherent array. Threshold effect in DOAestimation is analyzed by Method of Interval Error(MIE), and the methods toapproximately compute threshold baseline and threshold SNR are presented. Lastly,aperture coupling between azimuthal and elevational aperture of slanting array leads tofine direction cosine estimate standing at a family of straight lines. Then, the directioncosine ambiguity can be resolved by the rule that the vectical distance between a dotand a line is the shortest. Simultaneously, aperture coupling causes the presence ofazimuthal and elevational resolution gain regions for slanting array.
3.Manifold ambiguity and matrix completion-based ambiguity resolution algorithmof an interferometric array are studied. Manifold ambiguity does not necessarily implynonidentifiability. Association and model-fitting(Deconvolution) method for ambiguityresolution are derived from pattern recognition theory. Spatial under-sampling is theradical reason to manifold ambiguity. From Caratheodory theorem and Pisarenkoharmonic retrival theory, the manifold ambiguity resolution is automaticallyincorporated if a positive-definite and Toeplitz covariance matrix of a virtual uniformlinear array with the same aperture as the sparse array could be attained. Then manifoldambiguity resolution is translated into a pure math problem. The condition under whichthe various matrix completion method is applicable and the performance are analyzedand compared. For the particularity of an interferometric array configuration andinstability of the existing matrix completion methods, a novel ambiguity resolutionmethod with the combination of auxiliary elements and Toeplitz matrix completion isproposed， which improves stability.Simulation and real data demonstrate theeffectiveness and validity of the proposed method.
4. Low elevation angle with high accuracy is studied for an interferometric-likearray VHF radar. Limited by aperture, VHF radar generally has a wider beam. When thetarget is at low grazing angle or lies below about one-third of the beamwidth above thehorizon, multipath signal reflected from ground(sea) surface come into the mainlobe aswell as the direct echo, in which case the performance of low elevation estimation ofVHF radar is highly affected. The interferometric-like array extends the verticalaperture with small pieces of hardware. The interferometric Forward/Backward spatialsmoothing(IFBSS) technique is proposed from the conventional spatial smoothingalgorithm for uniform linear array, being used to decorrelate the multipath and directsignal. Then high accurate elevation angle estimation with dual-size unitary ESPRIT algorithm is achieved. As the surface roughness increases or the target approaches thehorizon, there is a huge mismatch between two-target model and actual multipath. Acomplete theoretical model of multipath is nearly impossible at present. From theperspective of wavenumber spectrum estimation, the nonparametric Multi-taper Method(MTM) is utilized for the feature of adaptive wavenumber of multipath. It isdemonstrated that the diffuse component is characteristic of colored-noise by real dataresult.
引文
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