Micro Statistics in Signal Decomposition and the Optimal Filtering Problem

信号分解的微观统计与最优滤波问题

• 批准号: 9020667
• 负责人: Gonzalo Arce
• 金额: $ 12.58万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-02-15 至 1993-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9020667&HistoricalAwards=false
• 关键词: Micro; Statistics; Signal; Decomposition; Optimal

Optimal Filtering is a statistical signal processing problem of major engineering importance. Historically, the most frequently used signal processing tools have been linear in nature, but despite rich linear systems theories, many signal processing problems have not been satisfactorily addressed through the use of linear schemes. This research aims at the theoretical development of a large class of non-linear filters which are based in combination of either the observation vector, the sorted observation vector, or in general a non-linear transformation of the observation vector. Thus, we achieve non-linear filter response characteristics but with the machinery of linear systems theory available for their optimization and design. The optimal solution requires the statistical characterization of the set of decomposed signals (micro-statistics). The filtering problem reduces to a set of filters operating on the decomposed signals (micro-statistic filters) where the output is a weighted sum of the decomposed filtered signals. In this work, a theory will be developed for robust micro-statistic filters in which linear operations are executed in a sorted observation vector. For environments with unknown or non-stationary characteristics, we develop adaptive micro-statistic filters and address issues such as convergence, lattice structures, fast algorithms, and complexity.

最优滤波是一个具有重大工程意义的统计信号处理问题。从历史上看，最常用的信号处理工具本质上是线性的，但是尽管有丰富的线性系统理论，许多信号处理问题并没有通过使用线性方案得到满意的解决。本研究旨在理论发展一大类非线性滤波器，这些滤波器要么是基于观测向量，要么是基于排序的观测向量，要么是基于观测向量的非线性变换。因此，我们实现了非线性滤波器的响应特性，但与线性系统理论的机械可用于其优化和设计。最优解需要分解信号集合的统计特征（微观统计）。滤波问题简化为一组对分解后的信号进行滤波的滤波器（微统计滤波器），其中输出是分解后的滤波信号的加权和。在这项工作中，将开发一种理论，用于鲁棒微统计滤波器，其中线性操作在排序的观测向量中执行。对于具有未知或非平稳特征的环境，我们开发了自适应微统计滤波器，并解决了收敛性、晶格结构、快速算法和复杂性等问题。