Bootstrap方法在阵列信号处理方面的应用

Direction of arrival (DOA) estimation by array is an important research branch in the field of modern signal processing. It has a great variety of applications in many fields, such as communications, radar and sonar, etc. In order to make passive detection system have the ability of measuring multiple radiant signals arrived simultaneously and improve the angle resolution of DOA estimation, application of super-resolution DOA estimation algorithm by array to passive detection system is reseached deeply .. According to the problems faced to DOA estimation,such as signal pulse is time constraints or the process is nonstationary and only small portions of stationary data are considered, the new novel path to be applied in array signal proceesing. Here the bootstrap method is going to introduce into DOA estimation. in simple word,the bootstrap does with a computer what the experimenter would do in proctice.With the bootstrap, the obervations are randomly ressigned ,and the estimatees recomputed, there assignements and recomputions are done thousnads of times and treated as reperted experiments .Bootstrap is an extremely attractive tool in that it requires very little in the way of modeling,assumptions, or analysis. an it canbe applied in an automatic way. the bootstrap is a computer-based method that substitutes considerable amounts of computation in place of theoretical analysis.in an eraof exponentially declining comoputions are done thousands of times and treated as repeated experiments..Use the suitable bootstrap can sovle some of problems in array signal processing.firstly,theoretical and practical work have shown that bootstrap methods are potentially superior to conventional parameter estimation method ,such as least square and MLE in small-sample condition. in some circumstances where standar approaches that invoke strong assumptions are judge inappropriate,the bootstrap may be appliced.so in the circumstances where sample impluse is narrow or signals are.non-stationary ,the bootstrap methods have great research value

波达角(Direction of Arrival，DOA)估计是现代阵列信号处理领域中的重要研究内容，它在通信、雷达、声纳等领域有着非常广泛的应用。为了使探测系统具有对同时到达雷达信号DOA进行估计的能力，本申请主要针对阵列探测系统面临的复杂电磁环境，围绕阵列天线DOA估计在应用所面临的关键问题展开研究。提出以Bootstrap 方法解决DOA估计所面临的众多重点问题，如接收目标脉冲较窄，采样数据较少；接收目标信号长时不平稳等。Bootstrap方法是一种以计算机仿真代替实际实验采样的方法，通过对接收的实际少量数据样本重新组合，重新计算实现对大样本数据的替代，从而实现对参数的估计。该方法在小样本情况下，比传统的最小方差法和最大似然方法更有吸引力，估计精度更高。该类方法正在被国外广大学者应用到各个参数估计领域，国内该方法应用较少，在阵列信号处理领域应用更少，因此研究该方法在DOA估计中的应用

阵列信号处理中的空间谱估计在许多领域中有着重要的作用，在近年来取得了快速发展。为了到达高精度和高分辨率，通常需要足够的采样数据完成渐进估计，但在实际系统中，实时处理中待测信号的观测窗长有限，导致获得的可靠采样数据不够，降低了一些渐进估计方法的性能下降或失效。为了使得在采样样本较小情况下，使基于阵列信号处理的信源估计和波达方向估计（DOA）难以达到理想的估计效果，本课题将Bootstrap方法引入阵列信号处理当中。Bootstrap方法作为一种统计方法，可以应用在样本数量较少或者分布未知的情况下。Bootstrap方法应用在空间谱估计的信源数估计和波达方向估计中，研究内容主要包括均匀噪声、非均匀噪声和相干信号源下的信源数估计以及DOA估计精度和分辨力的提高。.信源数检测是辐射信号参数估计的先决条件。在实际中，由于接收辐射源强度不同、各阵列各个阵元增益差异等因素导致的噪声非均匀性，使得传统的算法无法精确的估计出信源数。课题研究了基于Bootstrap方法的非均匀噪声背景下的两类信源数估计算法：一是根据特征子空间的特征投影，形成一系列检测统计量，进行信源的多元假设检验；另一类则是根据阵列流型矢量和特征矢量的内积形成检测统计量进行多元假设检验。在接收数据的分布未知情况下，两类算法在零假设下的检测统计量分布都是应用Bootstrap方法进行估计，以获得可靠的统计量。由于环境因素，辐射源在传播当中，会在接收端产生相干信号，相干信号源个数估计也是信源数检测问题中的难点问题。本课题同时研究了在相关源存在情况下，信源数检测的算法。采用空间平滑技术结合基于Bootstrap非相关信源检测方法，实现了对相关信源存在下的信源数检测问题。..在样本数量较少或者分布未知情况下，波达方向估计难以到达理想性能。为此，将Bootstrap方法与多重信号分类(MUSIC)或旋转不变子空间（ESPRIT）等算法结合，相当于增大了样本数量，从而提高了估计精度。对原样本重采样，形成新的样本集;求出每一个新样本的阵列数据协方差矩阵,进行波达方向估计;将DOA估计结果进行统计分析，将估计中出现次数最多的估计方向作为最终估计的波达方向。或者采用参数化DOA估计方法，先将数据协方差分解成信号协方差与噪声协方差阵，对进行的噪声协方差阵采用bootstrap抽取。重新构造多个数据协方差进行估计，最终的DOA估计结果。