Weighted Myriad Filters and Their Applications in Communications

加权无数滤波器及其在通信中的应用

• 批准号: 9530923
• 负责人: Gonzalo Arce
• 金额: $ 30.5万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9530923&HistoricalAwards=false
• 关键词: Weighted; Myriad; Filters; Their; Applications

Linear Filtering theory has been largely motivated by the characteristics of Gaussian random processes. In the same manner, research in myriad filtering theory is motivated by the statistical properties of alpha-stable processes which describe an important class of processes, impulsive in nature, that obey a Generalized Central Limit Theorem; thus these processes can arise in practice as a result of physical principles. The foundation of myriad filtering algorithms lies in the definition of the sample myriad as the location estimate of a class of alpha-stable distributions. The main goals of this research are: (1) To study the theoretical properties of the sample myriad and to exploit its geometrical structure for the development of efficient computational algorithms. (2) To solve the optimal "weighted myriad" filtering problem - the problem analogous to the design of the optimal FIR (Wiener) filter and the optimal weighted median filter. (3) To develop adaptive filtering algorithms for the simple design of weighted myriad filters for applications where the statistical characteristics of the underlying signals may be unknown or varying. (4) To extend the filter formulation to the case where the signals are complex or multivariate, providing us with the tools needed to develop robust CDMA multiple access detectors. This work can have a significant impact on applications requiring robust estimation and filtering. This is particularly the case in mobile and personal communication systems, to be deployed in the near future, where the underlying statistics of the noise and interferences closely follow the models used in this research rather that the traditional models used in practice today. The results of this research can also be applied to a wide range of problems including remote sensing imaging of the environment and non-destructive evaluation of materials.

高斯随机过程的特性极大地激发了线性滤波理论的发展。 同样，无数过滤理论的研究也是由α稳定过程的统计特性所激发的，α稳定过程描述了一类重要的过程，本质上是脉冲的，服从广义中心极限定理;因此这些过程在实践中可以作为物理原理的结果出现。 Myriad滤波算法的基础在于将样本Myriad定义为一类α稳定分布的位置估计。 本研究的主要目的是：（1）研究样本数的理论性质，并利用其几何结构来发展有效的计算算法。 (2)为了解决最优“加权无数”滤波问题--这个问题类似于最优FIR（维纳）滤波器和最优加权中值滤波器的设计。 (3)开发自适应滤波算法，用于基础信号的统计特性可能未知或变化的应用中的加权无数滤波器的简单设计。 (4)将滤波器公式扩展到信号复杂或多变量的情况，为我们提供了开发鲁棒CDMA多址检测器所需的工具。 这项工作可以对需要鲁棒估计和滤波的应用产生重大影响。 在不久的将来部署的移动的和个人通信系统中尤其是这种情况，其中噪声和干扰的基本统计密切遵循本研究中使用的模型，而不是今天实践中使用的传统模型。 这项研究的结果也可以应用于广泛的问题，包括遥感成像的环境和非破坏性评估的材料。