Resolution, Coherence and Distance between Density Functions

密度函数之间的分辨率、相干性和距离

• 批准号: 0701248
• 负责人: Tryphon Georgiou
• 金额: $ 28.47万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0701248&HistoricalAwards=false
• 关键词: Resolution; Coherence; Distance; between; Density

Intellectual merit:The main thrust of the proposed research is to develop tools and quantitative measures for robust high resolution signal analysis. A range of tools is envisaged and outlined --from versions of a multivariable-periodogram applied to generalized statistics, to mathematical solutions of spectral inverse problems. Distance metrics for assessing spectral uncertainty are suggested which quantify differences in predictive qualities between two time-series. These metrics are sought to quantify the quality of estimation and to provide a means to tune estimation algorithms. Emphasis is placed on the analysis of vectorial processes in spacio-temporal domains. A concept of causal coherence is being proposed for use in control applications, as exemplified by problems of noise suppression and vibration isolation.Broader impact:Signal analysis is a critical technology behind a wide range of applications. Recent collaborative work of the principal investigator on non-invasive temperature sensing via ultrasound (for e.g., computer guided tumor ablation and therapy) and on vibration isolation experiments utilizing distributed sensor arrays, underscore the need for the proposed research and its potential to enhance pertinent technological advances. The research may impact an even greater range of technologies involving distributed sensor arrays, identification, modeling and data mining. An experimental set up to demonstrate relevant concepts of estimation and control for educational purposes will be developed and, in coordination with the Science Museum of Minnesota, it will be planned as an exhibit in the physical sciences and technology section of the museum

智力优势：提出的研究的主要推力是为鲁棒高分辨率信号分析开发工具和定量措施。设想并概述了一系列工具——从应用于广义统计的多变量周期图的版本，到谱逆问题的数学解决方案。提出了评估光谱不确定度的距离度量，量化了两个时间序列之间预测质量的差异。寻求这些度量来量化估计的质量，并提供一种调整估计算法的方法。重点放在矢量过程的分析在时空域。正在提出一个因果相干的概念，用于控制应用，例如噪声抑制和隔振问题。更广泛的影响：信号分析是广泛应用背后的关键技术。首席研究员最近在超声非侵入性温度传感（例如，计算机引导的肿瘤消融和治疗）和利用分布式传感器阵列的隔振实验方面的合作工作，强调了拟议研究的必要性及其促进相关技术进步的潜力。这项研究可能会影响更广泛的技术，包括分布式传感器阵列、识别、建模和数据挖掘。将为教育目的发展一种实验装置，以展示有关的估计和控制概念，并与明尼苏达科学博物馆协调，计划在博物馆的自然科学和技术部分展出