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

无源雷达试图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发射信号。相反，无源雷达依赖于环境中已经存在的电磁辐射来照射目标，通常来自无线电，蜂窝和电视发射机等来源。为了使系统确定是否有目标在给定的角度和范围内以特定的速度移动，目标和噪声信号的复杂模型被用来构建最佳的测试统计量。本研究旨在使用分析和几何方法，使多个接收器的无源雷达系统中的噪声模型的计算与沃恩克拉克森教授在昆士兰州，谁在检测和估计理论的领域具有重要的经验。昆士兰州大学还提供了一个独特的机会，用从单频网络中提取的数据来测试这些模型，在该领域，克拉克森教授的团队具有特殊的专业知识。在多通道无源雷达系统中，在每个接收器处测量数据向量。当没有信号存在时，假设数据是相同分布的零均值复白色高斯噪声;在存在信号的情况下，该噪声被认为是相加的。它已被证明，在这样的系统中的秩一信号的存在的最佳测试统计量是从测量数据构造的Grammian矩阵的最大特征值。该Grammian矩阵具有复杂的Wishart分布，并且对于最大特征值分布存在封闭形式的表达式。然而，CDF的表达式涉及采用矩阵的行列式，其中项采用具有大整数参数的伽马函数的比率的形式，这压倒了实际感兴趣的情况下的浮点表示。本计画将利用结果的部分内积与正交多项式展开，以产生此矩阵的因式分解，使计算容易处理。在完成理论部分的工作后，昆士兰州大学收集的单频网络数据将用于实验测试。该奖项属于东亚和太平洋夏季研究所计划，支持美国研究生的夏季研究，由NSF和澳大利亚科学院共同资助。

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.