UWB雷达目标频率响应和极点的求解
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摘要
超宽带(UWB)雷达是现代雷达系统发展的重要方向之一,在频域上的大幅度扩展使其能够获取更为丰富的目标和环境波谱信息,特别地,UWB雷达可以激励仅与目标本质物理属性有关的谐振特征(极点),有利于提高精导武器和战场侦察系统的目标识别能力。从理论上分析UWB雷达目标频率响应与极点的数值求解技术,对UWB雷达系统下目标特性和目标识别的研究有着实际意义。本文针对这一应用背景,围绕UWB雷达目标的频率响应和极点两个重要特性,展开了四个方面的研究工作:首先是电磁场积分方程的高效矩量法求解技术,这是分析目标特性的数值工具;其次是UWB雷达目标的频率响应求解;然后研究任意复杂形状及不同材质目标的极点计算;最后利用频率响应数据及极点特征对白、色噪声环境下任意复杂形状及不同材质目标进行识别研究。
本文首先从电磁场基本理论出发,利用等效原理和边界条件,归纳了用于分析金属、介质、金属与介质混合结构的边界积分方程表示式;概述了矩量法的一般过程。针对高阶基函数可以用较少的未知量数目满足较高求解精度的优点,论文研究了两类常用高阶叠层基函数:修正Legendre基函数和幂基函数。在矩量法阻抗矩阵填充方面,提出了以矩阵向量积求解多维数值积分的方法,积分节点及部分被积函数预先计算并存储,每次矩阵元素的填充只需要重新计算格林函数和一次低维矩阵向量积,从而实现了阻抗矩阵的快速填充。推导了数值积分中奇异处理的奇异提取解析法公式。讨论了Schwarz预处理和带阈值的不完全LU分解(ILUT)预处理在迭代求解矩阵方程中的应用。
在目标超宽带频率响应的求解方面,传统的方法多采用渐近波形估计(AWE)和模基参数估计(MBPE)技术。鉴于AWE和MBPE的精度对采样频点和频段范围选择的敏感性,本文在目标低频区和谐振区低端,提出了积分核的Chebyshev多项式逼近方法,从积分方程核函数中分离出频率因子,只有Chebyshev多项式系数与频率有关,其它与空间参数有关的数据项预先计算并存储,不同频率下只需重新计算多项式系数,从而实现多频点散射响应的快速计算。当频率比较高时,则需采用逐点计算的方法,按照积分节点而不是基函数分组的原则,在高阶叠层基函数矩量法中引入了快速多极算法,并给出了求解步骤,加速了在迭代求解矩阵方程时矩阵矢量积的计算。
在复杂雷达目标极点特征的数值求解方面,分析了常用的围线积分法在求解复杂目标极点时失效的原因。根据高阶矩量法未知量少的特点,对阻抗矩阵的性质做了分析,证明了极点相对于积分方程的独立性。提出了复频平面上搜索极点的区域差分、SVD技术,并求解了几类金属、金属介质混合结构等复杂目标模型的极点分布。为了进行数值验证,对从散射场提取极点的矩阵束法进行了改进,利用目标频率响应经逆傅立叶变换后得到的时域响应提取主极点,通过结果对比证明了理论方法的正确性。
在极点特征于目标识别中的应用方面,分析了已有目标识别方案对白噪声环境下复杂目标模型的识别性能,研究了高阶统计量方法在色噪声环境下对复杂目标模型的识别性能,结果表明,色噪声环境下,采用高阶统计量的识别方法利用极点特征对复杂目标的识别是可行的。
The ultra wide-band (UWB) radar is an important development direction of modern radar system. Because of the widely expansion in frequency domain in the new radar system, much richer spectrum information of targets and environment can be obtained. Specially, features of resonance region (poles), which are only relative to physical attributes of objects, can be excited in UWB radar system. That will improve the target identification performance in the precise guidance weapon and battlefield surveillance system. So, it has importantly academic and actual significance to study on numerical calculation techniques of frequency responses and poles of UWB radar targets. Under that application background, on topics of two important features of frequency responses and poles, four parts of contents are investigated. Firstly, we study high efficient method of moments (MoM) to solve electromagnetic field integral equations, which is the numerical implement to analyze target features. Secondly, computing techniques of scattering responses in frequency domain for UWB radar targets are proposed. Then, calculation of poles of complex shaped and different material objects is analyzed. Lastly, the identification of complex targets in white or colour noise using poles' feature is studied through numerical results of frequency responses and poles.
Above all, the boundary integral equations for metallic structures, dielectric structures, composite metallic and dielectric structures are elaborated uniformly based on the surface equivalence principle and boundary conditions. The solving procedures of MoM are also summarized. The higher order basis functions in MoM have many advantages to low order ones, such as fewer unknowns. So, we analyze two kinds of higher order hierachical basis functions including modified Legendre functions and power functions. On impedance-matrix filling, it is proposed that multi-dimension integrations are replaced by matrices products. The quadrature nodes and some integrated functions are calculated and stored in advance. Only Green's functions and one time low dimension matrix-vector product are to be computed each time when impedance matrix is filled. So, the matrix is fast filled. What's more, near singular process procedure is presented to increase the precision of results for irregular shaped scatterers. It is also discussed for the Schwarz preconditioner and incomplete LU decomposition with threshold preconditioner used in higher order MoM.
On the aspect of calculation techniques of scattering response in frequency domain, the asymptotic waveform evaluation (AWE) and model-based parametric evaluation (MBPE) are usually used. Considering that the precision of AWE and MBPE is sensitive to sampling frequencies and the choice of frequency range, we propose Chebyshev polynomial approximation of integral nucleus in low frequency domain or resonance domain. Then, the frequency factor can be separated from integration, and only the coefficients of polynomials are relative to frequency. Other terms relative to space parameters are computed and stored. At different frequency, only the coefficients need be computed. That will largely speed up the calculation of scattering responses in a wide frequency domain. When frequency is high, the method of point-by-point should be adopted. The fast multipole method (FMM) is applied in higher order MoM on the basis of point-to-point interactions, and the particular procedure is presented. That largely accelerates the matrix-vector product in iterative process.
On the aspect of calculation of poles of complex shaped and mixture objects, it is firstly reasoned that traditional contour integration is invalid for complex objects. Then, using the character of fewer unknowns in higher order MoM, the property of impedance matrix is analyzed, and the domain difference method and SVD technique to search poles are proposed. Poles of several metallic and composite metallic/dielectric target models are computed. For validate numerical results, the matrix pencil method is modified to extract dominant poles from scattering responses using frequency responses and inverse fast Fourier transformation (IFFT). The relative errors between two approaches testify the proposed methods.
Lastly, the application of poles in target identification is studied. The performance of existent discrimination schemes to complex targets in white noise is analyzed. The performance of higher-order statistics for complex targets identification in the presence of colour noise is studied. The numerical results show that it is doable using the higher-order statistics to identify targets in complex background.
本文首先从电磁场基本理论出发,利用等效原理和边界条件,归纳了用于分析金属、介质、金属与介质混合结构的边界积分方程表示式;概述了矩量法的一般过程。针对高阶基函数可以用较少的未知量数目满足较高求解精度的优点,论文研究了两类常用高阶叠层基函数:修正Legendre基函数和幂基函数。在矩量法阻抗矩阵填充方面,提出了以矩阵向量积求解多维数值积分的方法,积分节点及部分被积函数预先计算并存储,每次矩阵元素的填充只需要重新计算格林函数和一次低维矩阵向量积,从而实现了阻抗矩阵的快速填充。推导了数值积分中奇异处理的奇异提取解析法公式。讨论了Schwarz预处理和带阈值的不完全LU分解(ILUT)预处理在迭代求解矩阵方程中的应用。
在目标超宽带频率响应的求解方面,传统的方法多采用渐近波形估计(AWE)和模基参数估计(MBPE)技术。鉴于AWE和MBPE的精度对采样频点和频段范围选择的敏感性,本文在目标低频区和谐振区低端,提出了积分核的Chebyshev多项式逼近方法,从积分方程核函数中分离出频率因子,只有Chebyshev多项式系数与频率有关,其它与空间参数有关的数据项预先计算并存储,不同频率下只需重新计算多项式系数,从而实现多频点散射响应的快速计算。当频率比较高时,则需采用逐点计算的方法,按照积分节点而不是基函数分组的原则,在高阶叠层基函数矩量法中引入了快速多极算法,并给出了求解步骤,加速了在迭代求解矩阵方程时矩阵矢量积的计算。
在复杂雷达目标极点特征的数值求解方面,分析了常用的围线积分法在求解复杂目标极点时失效的原因。根据高阶矩量法未知量少的特点,对阻抗矩阵的性质做了分析,证明了极点相对于积分方程的独立性。提出了复频平面上搜索极点的区域差分、SVD技术,并求解了几类金属、金属介质混合结构等复杂目标模型的极点分布。为了进行数值验证,对从散射场提取极点的矩阵束法进行了改进,利用目标频率响应经逆傅立叶变换后得到的时域响应提取主极点,通过结果对比证明了理论方法的正确性。
在极点特征于目标识别中的应用方面,分析了已有目标识别方案对白噪声环境下复杂目标模型的识别性能,研究了高阶统计量方法在色噪声环境下对复杂目标模型的识别性能,结果表明,色噪声环境下,采用高阶统计量的识别方法利用极点特征对复杂目标的识别是可行的。
The ultra wide-band (UWB) radar is an important development direction of modern radar system. Because of the widely expansion in frequency domain in the new radar system, much richer spectrum information of targets and environment can be obtained. Specially, features of resonance region (poles), which are only relative to physical attributes of objects, can be excited in UWB radar system. That will improve the target identification performance in the precise guidance weapon and battlefield surveillance system. So, it has importantly academic and actual significance to study on numerical calculation techniques of frequency responses and poles of UWB radar targets. Under that application background, on topics of two important features of frequency responses and poles, four parts of contents are investigated. Firstly, we study high efficient method of moments (MoM) to solve electromagnetic field integral equations, which is the numerical implement to analyze target features. Secondly, computing techniques of scattering responses in frequency domain for UWB radar targets are proposed. Then, calculation of poles of complex shaped and different material objects is analyzed. Lastly, the identification of complex targets in white or colour noise using poles' feature is studied through numerical results of frequency responses and poles.
Above all, the boundary integral equations for metallic structures, dielectric structures, composite metallic and dielectric structures are elaborated uniformly based on the surface equivalence principle and boundary conditions. The solving procedures of MoM are also summarized. The higher order basis functions in MoM have many advantages to low order ones, such as fewer unknowns. So, we analyze two kinds of higher order hierachical basis functions including modified Legendre functions and power functions. On impedance-matrix filling, it is proposed that multi-dimension integrations are replaced by matrices products. The quadrature nodes and some integrated functions are calculated and stored in advance. Only Green's functions and one time low dimension matrix-vector product are to be computed each time when impedance matrix is filled. So, the matrix is fast filled. What's more, near singular process procedure is presented to increase the precision of results for irregular shaped scatterers. It is also discussed for the Schwarz preconditioner and incomplete LU decomposition with threshold preconditioner used in higher order MoM.
On the aspect of calculation techniques of scattering response in frequency domain, the asymptotic waveform evaluation (AWE) and model-based parametric evaluation (MBPE) are usually used. Considering that the precision of AWE and MBPE is sensitive to sampling frequencies and the choice of frequency range, we propose Chebyshev polynomial approximation of integral nucleus in low frequency domain or resonance domain. Then, the frequency factor can be separated from integration, and only the coefficients of polynomials are relative to frequency. Other terms relative to space parameters are computed and stored. At different frequency, only the coefficients need be computed. That will largely speed up the calculation of scattering responses in a wide frequency domain. When frequency is high, the method of point-by-point should be adopted. The fast multipole method (FMM) is applied in higher order MoM on the basis of point-to-point interactions, and the particular procedure is presented. That largely accelerates the matrix-vector product in iterative process.
On the aspect of calculation of poles of complex shaped and mixture objects, it is firstly reasoned that traditional contour integration is invalid for complex objects. Then, using the character of fewer unknowns in higher order MoM, the property of impedance matrix is analyzed, and the domain difference method and SVD technique to search poles are proposed. Poles of several metallic and composite metallic/dielectric target models are computed. For validate numerical results, the matrix pencil method is modified to extract dominant poles from scattering responses using frequency responses and inverse fast Fourier transformation (IFFT). The relative errors between two approaches testify the proposed methods.
Lastly, the application of poles in target identification is studied. The performance of existent discrimination schemes to complex targets in white noise is analyzed. The performance of higher-order statistics for complex targets identification in the presence of colour noise is studied. The numerical results show that it is doable using the higher-order statistics to identify targets in complex background.
引文
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