瞬态极化统计理论及应用研究
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摘要
随着现代战场电磁环境的日趋复杂,用瞬态极化的观点研究时变电磁波的极化现象,揭示波极化变化的内在规律,挖掘蕴含其间的物理本质,探究雷达目标与环境极化散射的特征机理,建立雷达目标极化散射统计特性的有效表征方法,最大限度的发掘和利用雷达传感系统所获得的电磁信息,使之能够适应复杂多变的战场环境、具备智能化的探测识别能力,已经成为雷达极化信息处理技术领域所面临的基础课题和紧迫任务。
在此背景下,本文研究了随机电磁波和雷达目标电磁散射的时变极化统计特性,部分完善了瞬态极化统计学理论,为雷达系统削弱恶劣电磁环境的影响、对抗有源干扰、反隐身和识别真假目标等方面提供了具有潜力的理论支持。具体内容可分为以下两个层面:
在随机电磁波的极化统计特性上,首先导出了高斯随机场的标准Stokes参数的统计特征,得到了其均值、方差以及高阶矩特征,并定义了新的散度,起伏度,以及斜度、峰度等概念,可以更加精细的描述随机场的起伏特性。针对不同时刻Stokes参数的相干特性,引入了瞬态相干极化与极化谱的概念,充分挖掘了极化相干信息,丰富了瞬态极化相干性研究理论。
然后分析了在Weibull分布假设条件下电磁波瞬态极化的统计特性,给出了瞬时Stokes参数以及Stokes子矢量的联合概率密度函数表达式。并且将K-分布随机波的瞬态极化统计特性化归到高斯随机波的瞬态极化统计特性上,使K-分布随机波的统计特性与高斯分布特性取得了形式上的一致。
在雷达目标的极化特性上,首先研究了雷达目标电磁散射的瞬态极化统计特性与参数表征及估计问题。提出了一种可用来描述更为广泛的目标或杂波的起伏特性的分布函数,即扩展Weibull分布(E-Weibull)以及相应的L-分布函数,并且推导了该分布的高阶矩性质。同时简化了其特例-高斯分布散射矩阵的Stokes参数分布。在此基础上,推导了基于散射矩阵相干分解的SDH目标分解参数的统计特性。同时分析了基于目标方差矩阵的H/A极化分解中特征值、特征矢量等极化分解参数的统计特性,给出了特征值分解的各参数物理机理及其参数估计方法,为合理确定极化特征参数提供了有效的方法。
然后研究了雷达目标的空域瞬态极化特性,在此基础上分析了空间箔条云团的极化散射特性,给出了不同空间参数分布情形下相干和非相干极化散射矩阵和极化散射截面面积的统计特性,对研究箔条云的干扰和抗干扰都有一定的指导意义。最后提出了在箔条云等背景下目标全极化散射中心提取的新方法。以指数衰减和模型(DE)为基础将空域目标全极化散射中心的参数提取问题转化为全极化约束总体最小二乘(CTLS)问题,得到散射中心的距离参数和类型参数,然后利用最小二乘法求解全极化测量方程获得每一个散射中心的复幅度信息,并分析了参数估计的精度问题。
In modern warfare, the electromagnetic (EM) environments have been more and more complicated. In order to exploit and utilize the EM information utmost, that is, to let the radar sensing system can adapt adverse battleground environments with intelligent detection and recognition capability; some problems are becoming a groundwork and impendent mission in radar polarization information processing. These problems mainly include studying the polarization phenomena of time-varying EM waves from dynamic and statistical viewpoints, revealing the inherent rules of random EM waves, exploring polarization scattering characteristics of radar targets and environments, and founding effectual descriptive means of polarization statistics of radar targets.
The dissertation studies the polarization characteristics of time-varying EM waves and radar target scattering. The methods and conclusions in this thesis can proffer some novel and promising techniques for weakening the influences of adverse EM environments, confronting active jamming, detecting concealed targets and recognizing targets and other applications. The main contributions of the thesis are as follows:
Firstly the statistical properties of the normalized Stokes parameters in a Gaussian stochastic plane wave field are described in details. The new dispersion, normalized contrast of fluctuation, skewness and kurtosis are defined to describe the non-Gaussian distribution characteristics. The definitions of the instantaneous coherent polarization function (ICPF) and polarimetric spectrum (ICPS) are presented for the first time, which shows the coherences of the instantaneous Stokes parameters in both time and frequency domain, even in spatial coherence. The new formula of definition can be extended to spatial propagation coherence, both in free space or any linear medium.
Secondly Then the statistics of the stochastic plane electromagnetic (EM) wave fields that is Weibull distributed is examined. The polarimetric Weibull distributed wave is characterized by three parameters: the sum of the amplitudes of the two electric vector components, the angle which the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the covariance matrix. Then the statistical properties of the normalized Stokes parameters are described in details in Weibull distributed stochastic fields. The joint and marginal probability density functions (PDF) of the three components of the normalized Stokes parameters are presented. Results of some numerical calculation can be obtained. The description of the Weibull polarimetric wave filed may be useful to random medium scattering and speckle filtering.
Thirdly a new class of distribution, named Extended Weibull distribution, arising from target fluctuation, is presented in this paper, along with their mainly properties and relations. Classical distributions, such as Gamma, Square Root of Gamma and Weibull, are particular cases of this new class. The statistics of Stokes parameters in pol-S AR is given in a new and simple formula. At the same time, the statistics of decomposed parameters for H/A decomposition and SDH decomposition are given for suitable choices of the accurate parameters.
Finally the polarization characteristics of radar target in spatial domain are studied. And the statistics of chaff cloud is studied, and the statistics of scattering matrix and radar cross section are presented under different spatial distribution of chaff cloud. At last a new method of 1 -D feature extracting of scattering centers is presented and the precision is analyzed.
These conceptions and conclusions proffer theoretical foundations and avail tools for polarization characteristic analyzing of random EM waves or radar target scattering, feature extraction and other applications. And these are possessed of practical significance to engineering applications.
在此背景下,本文研究了随机电磁波和雷达目标电磁散射的时变极化统计特性,部分完善了瞬态极化统计学理论,为雷达系统削弱恶劣电磁环境的影响、对抗有源干扰、反隐身和识别真假目标等方面提供了具有潜力的理论支持。具体内容可分为以下两个层面:
在随机电磁波的极化统计特性上,首先导出了高斯随机场的标准Stokes参数的统计特征,得到了其均值、方差以及高阶矩特征,并定义了新的散度,起伏度,以及斜度、峰度等概念,可以更加精细的描述随机场的起伏特性。针对不同时刻Stokes参数的相干特性,引入了瞬态相干极化与极化谱的概念,充分挖掘了极化相干信息,丰富了瞬态极化相干性研究理论。
然后分析了在Weibull分布假设条件下电磁波瞬态极化的统计特性,给出了瞬时Stokes参数以及Stokes子矢量的联合概率密度函数表达式。并且将K-分布随机波的瞬态极化统计特性化归到高斯随机波的瞬态极化统计特性上,使K-分布随机波的统计特性与高斯分布特性取得了形式上的一致。
在雷达目标的极化特性上,首先研究了雷达目标电磁散射的瞬态极化统计特性与参数表征及估计问题。提出了一种可用来描述更为广泛的目标或杂波的起伏特性的分布函数,即扩展Weibull分布(E-Weibull)以及相应的L-分布函数,并且推导了该分布的高阶矩性质。同时简化了其特例-高斯分布散射矩阵的Stokes参数分布。在此基础上,推导了基于散射矩阵相干分解的SDH目标分解参数的统计特性。同时分析了基于目标方差矩阵的H/A极化分解中特征值、特征矢量等极化分解参数的统计特性,给出了特征值分解的各参数物理机理及其参数估计方法,为合理确定极化特征参数提供了有效的方法。
然后研究了雷达目标的空域瞬态极化特性,在此基础上分析了空间箔条云团的极化散射特性,给出了不同空间参数分布情形下相干和非相干极化散射矩阵和极化散射截面面积的统计特性,对研究箔条云的干扰和抗干扰都有一定的指导意义。最后提出了在箔条云等背景下目标全极化散射中心提取的新方法。以指数衰减和模型(DE)为基础将空域目标全极化散射中心的参数提取问题转化为全极化约束总体最小二乘(CTLS)问题,得到散射中心的距离参数和类型参数,然后利用最小二乘法求解全极化测量方程获得每一个散射中心的复幅度信息,并分析了参数估计的精度问题。
In modern warfare, the electromagnetic (EM) environments have been more and more complicated. In order to exploit and utilize the EM information utmost, that is, to let the radar sensing system can adapt adverse battleground environments with intelligent detection and recognition capability; some problems are becoming a groundwork and impendent mission in radar polarization information processing. These problems mainly include studying the polarization phenomena of time-varying EM waves from dynamic and statistical viewpoints, revealing the inherent rules of random EM waves, exploring polarization scattering characteristics of radar targets and environments, and founding effectual descriptive means of polarization statistics of radar targets.
The dissertation studies the polarization characteristics of time-varying EM waves and radar target scattering. The methods and conclusions in this thesis can proffer some novel and promising techniques for weakening the influences of adverse EM environments, confronting active jamming, detecting concealed targets and recognizing targets and other applications. The main contributions of the thesis are as follows:
Firstly the statistical properties of the normalized Stokes parameters in a Gaussian stochastic plane wave field are described in details. The new dispersion, normalized contrast of fluctuation, skewness and kurtosis are defined to describe the non-Gaussian distribution characteristics. The definitions of the instantaneous coherent polarization function (ICPF) and polarimetric spectrum (ICPS) are presented for the first time, which shows the coherences of the instantaneous Stokes parameters in both time and frequency domain, even in spatial coherence. The new formula of definition can be extended to spatial propagation coherence, both in free space or any linear medium.
Secondly Then the statistics of the stochastic plane electromagnetic (EM) wave fields that is Weibull distributed is examined. The polarimetric Weibull distributed wave is characterized by three parameters: the sum of the amplitudes of the two electric vector components, the angle which the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the covariance matrix. Then the statistical properties of the normalized Stokes parameters are described in details in Weibull distributed stochastic fields. The joint and marginal probability density functions (PDF) of the three components of the normalized Stokes parameters are presented. Results of some numerical calculation can be obtained. The description of the Weibull polarimetric wave filed may be useful to random medium scattering and speckle filtering.
Thirdly a new class of distribution, named Extended Weibull distribution, arising from target fluctuation, is presented in this paper, along with their mainly properties and relations. Classical distributions, such as Gamma, Square Root of Gamma and Weibull, are particular cases of this new class. The statistics of Stokes parameters in pol-S AR is given in a new and simple formula. At the same time, the statistics of decomposed parameters for H/A decomposition and SDH decomposition are given for suitable choices of the accurate parameters.
Finally the polarization characteristics of radar target in spatial domain are studied. And the statistics of chaff cloud is studied, and the statistics of scattering matrix and radar cross section are presented under different spatial distribution of chaff cloud. At last a new method of 1 -D feature extracting of scattering centers is presented and the precision is analyzed.
These conceptions and conclusions proffer theoretical foundations and avail tools for polarization characteristic analyzing of random EM waves or radar target scattering, feature extraction and other applications. And these are possessed of practical significance to engineering applications.
引文
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