EAPSI: Computation of Wishart Eigenvalue Distributions for Multi-Channel Passive Radar Detection

EAPSI：多通道无源雷达检测的 Wishart 特征值分布计算

• 批准号: 1614403
• 负责人: Scott Jones
• 金额: $ 0.54万
• 依托单位: Jones Scott
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1614403&HistoricalAwards=false
• 关键词: EAPSI; Computation; Wishart; Eigenvalue; Distributions

Passive radars seek to perform the same detection and characterization of targets as an active radar, with the key difference that passive systems do not transmit a signal. Instead, passive radars rely on electromagnetic radiation already present in the environment to illuminate targets, typically from sources such as radio, cellular, and television transmitters. In order for the system to decide if there is a target traveling at a particular velocity at a given angle and range, sophisticated models of the target and noise signals are employed to construct an optimal test statistic. This research seeks to use analytic and geometric methods to enable computation of noise models in multiple receiver passive radar systems in collaboration with Professor Vaughan Clarkson at the University of Queensland, who has significant experience in the areas of detection and estimation theory. The University of Queensland also offers the unique opportunity to test these models with data drawn from a single frequency network, in which area Professor Clarkson's group has particular expertise.In a multiple channel passive radar system, data vectors are measured at each receiver. When no signal is present, it is assumed that the data is identically distributed zero mean complex white Gaussian noise; this noise is considered additively in the case of a present signal. It has been shown that the optimal test statistic for presence of a rank one signal in such a system is the largest eigenvalue of the Grammian matrix constructed from the measured data. This Grammian matrix has a complex Wishart distribution, and closed form expressions exist for the largest eigenvalue distribution. However, expressions for the CDF involve taking the determinant of matrices with terms taking the form of ratios of gamma functions with large integer arguments, which overwhelm floating point representations for cases of practical interest. This project will utilize results expansions in terms of partial inner products with orthogonal polynomials to produce a factorization of this matrix to make computation tractable. Following completion of the theoretical portions of the work, single frequency network data gathered by the University of Queensland will be used for experimental tests.This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Australian Academy of Science.

被动雷达寻求对目标进行相同的检测和表征作为活动雷达，其关键差异是被动系统不会传输信号。取而代之的是，被动雷达依赖于环境中已经存在的电磁辐射来照亮目标，通常来自诸如无线电，蜂窝和电视发射机之类的来源。为了使系统确定是否存在特定速度的目标以给定角度和范围行驶，采用目标和噪声信号的复杂模型来构建最佳测试统计量。这项研究试图使用分析和几何方法来与昆士兰州大学的沃恩·克拉克森教授合作，在多个接收器被动雷达系统中计算噪声模型，后者在检测和估计理论领域具有重要的经验。昆士兰州大学还提供了独特的机会来通过从单个频率网络中绘制的数据来测试这些模型，在该网络中，克拉克森教授的组具有特殊的专业知识。在多个通道无源雷达系统中，每个接收器都测量了数据向量。当不存在信号时，假定数据是相同分布的零平均复杂白色高斯噪声。在当前信号的情况下，这种噪声被认为是加性的。已经表明，在这种系统中存在等级一信号的最佳测试统计量是根据测量数据构建的格莱美族矩阵的最大特征值。该格莱美族矩阵具有复杂的欲望分布，并且对于最大的特征值分布而存在封闭形式的表达式。但是，CDF的表达方式涉及采用矩阵的决定因素，术语采用具有大整数参数的伽马函数比率的形式，这使实际关注的情况淹没了浮点表示。该项目将以正交多项式的部分内部产品来利用结果扩展，以产生该矩阵的分解，以使计算可进行。完成工作的理论部分完成后，昆士兰大学收集的单频网数据将用于实验测试。根据东亚和太平洋夏季研究所计划，该奖项支持美国研究生的夏季研究，并由NSF和澳大利亚科学学院共同资助。