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.

线性滤波理论在很大程度上是由高斯随机过程的特性所推动的。同样，无数过滤理论的研究是由阿尔法稳定过程的统计性质推动的，该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能是物理原理的结果。无数滤波算法的基础在于将样本无数定义为一类α稳定分布的位置估计。本研究的主要目标是：(1)研究样本Myriad的理论性质，并利用其几何结构来开发高效的计算算法。(2)解决最优“加权无数”滤波问题--类似于最优FIR(Wiener)滤波器和最优加权中值滤波器的设计问题。(3)为基础信号的统计特性可能未知或变化的应用，开发用于简单设计加权无数滤波器的自适应滤波算法。(4)将滤波公式推广到信号复杂或多变量的情况，为设计稳健的码分多址检测器提供了必要的工具。这项工作可能对需要稳健估计和过滤的应用程序产生重大影响。即将在不久的将来部署的移动和个人通信系统尤其如此，其中噪声和干扰的基本统计数据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。这项研究的成果还可广泛应用于环境的遥感成像和材料的无损评价等问题。