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

无源雷达寻求执行与有源雷达相同的目标检测和表征，关键区别在于无源系统不传输信号。相反，被动雷达依靠环境中已经存在的电磁辐射来照亮目标，通常来自无线电、蜂窝和电视发射机等来源。为了使系统能够判断是否有目标以给定的角度和距离以特定的速度移动，目标和噪声信号的复杂模型被用来构造最优检验统计量。这项研究试图与昆士兰大学在探测和估计理论领域具有丰富经验的沃恩·克拉克森教授合作，使用解析和几何方法来计算多接收器无源雷达系统中的噪声模型。昆士兰大学还提供了一个独特的机会，用来自单一频率网络的数据来测试这些模型，克拉克森教授的团队在这一领域拥有特殊的专业知识。在多通道无源雷达系统中，数据向量是在每个接收器上测量的。当不存在信号时，假设数据是相同分布的零均值复白高斯噪声；在存在信号的情况下，该噪声被考虑相加。结果表明，在这种系统中，存在一阶信号的最优检验统计量是由测量数据构造的Grammian矩阵的最大特征值。这个Grammian矩阵具有复杂的Wishart分布，并且对于最大本征值分布存在闭合形式的表达式。然而，CDF的表达式涉及采用具有大整数参数的伽马函数的比率的形式的矩阵的行列式，这在实际感兴趣的情况下压倒了浮点表示。这个项目将利用部分内积和正交多项式的结果展开来产生这个矩阵的因式分解，以使计算变得容易。在这项工作的理论部分完成后，昆士兰大学收集的单频网络数据将用于实验测试。东亚和太平洋夏季学院计划下的这个奖项支持一名美国研究生的夏季研究，由NSF和澳大利亚科学院联合资助。

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.