CIF: Small: Adaptive Spectral Estimation and Error Bounding

CIF：小：自适应频谱估计和误差界限

• 批准号: 1218388
• 负责人: Jian Li
• 金额: $ 30.47万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1218388&HistoricalAwards=false
• 关键词: CIF; Small; Adaptive; Spectral; Estimation

This research focuses on the development of data-adaptive algorithms and error bounds for spectral estimation, which is a stealth technology in diverse application fields. Spectral estimation plays a critical role in many applications, civil as well as military. Strengthening the theoretical underpinnings and the quality and robustness of spectral estimation algorithms enables the discovery of new technologies for information acquisition which would not have been possible using traditional methods. The results of this study can provide new opportunities in a wide range of studies ranging from building on the fundamentals of inverse problems for signal processing to devising practically applicable and reliable spectral estimation algorithms.This research leverages the recent advances in compressive sensing and is aimed at addressing the underlying technical challenges associated with the development of large scale spectral estimation algorithms. Moreover, quantifying uncertainty and assessing error bounds for current and new methods is also of significant importance. A metric needs to be well defined and naturally is a key element in any quantitative scientific theory. This research seeks to advance fundamental knowledge in novel data-adaptive spectral estimation algorithm design and to apply mathematical and engineering principles to address error bounding, while advancing mathematical and engineering knowledge on multiple fronts through the objectives listed below: 1) development of data-adaptive high resolution spectral estimation methods, 2) computationally efficient implementations of the algorithms for large scale problems, 3) theoretical quantitative assessment of the methods by deriving error bounds in suitable metrics, and 4) application of the methods to diverse real-world problems.

这项研究重点是用于光谱估计的数据自适应算法和错误界限的开发，这是多种应用领域的隐身技术。频谱估计在许多应用中，民事和军事都起着至关重要的作用。加强理论基础以及光谱估计算法的质量和鲁棒性，可以发现新技术用于信息获取，而传统方法是不可能的。这项研究的结果可以在广泛的研究中提供新的机会，这些研究包括基于信号处理的基础知识的基础，到设计实际适用且可靠的光谱估计算法算法。这项研究利用了压缩感应的最新进展，旨在解决与大规模频谱估计算法相关的基本技术挑战。此外，量化不确定性并评估当前和新方法的误差范围也很重要。指标需要得到充分的定义，并且自然是任何定量科学理论中的关键要素。这项研究试图在新型的数据自适应光谱估计算法设计中提高基本知识，并应用数学和工程原理来解决误差界限，同时通过列出的多个目标上的数学和工程知识在多个方面推进了数学和工程知识：1）数据适应性高分辨率频谱方法的开发，计算有效的量表，2）计算量规定的量表，2）计算量规定的量表，2）Algortiatients量的规模量表，2）Algortiatiation Algortiations，2）Algortiatients Algortiatients量级，2）Algortiatients量的规模量表，2）通过在合适的指标中得出误差界限，以及4）将方法应用于各种现实世界中的问题。