Mathematical Sciences: Non-Linear Filtering and Estimation

数学科学：非线性过滤和估计

• 批准号: 8805627
• 负责人: Murad Taqqu
• 金额: $ 5.2万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-08-01 至 1991-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805627&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Non; Linear; Filtering

The project will study both linear and non-linear filtering from the point of view of long term dependence and high variability. Long range dependence occurs in data on frequency fluctuations of quartz crystal oscillators, and on semi-conductor devices. Infinite variance is a reasonable model in situations where large values are taken with high probability such as in rain data and in relaxation times of solid state materials. The choice of the filters is made to get appropriate output processes that serve as good models. The statistical estimators of the parameters of interest thus depend on the types of filters used. The principal investigator, along with the post doctoral associate, will investigate the robustness properties of the estimators as well as explore the long range dependence. The behavior of the non-linear filters will be investigated when the input has high variability.

该项目将从长期依赖性和高可变性的角度研究线性和非线性滤波。 石英晶体振荡器和半导体器件的频率波动数据存在长范围依赖性。 在以高概率取大值的情况下（例如降雨数据和固态材料的弛豫时间），无限方差是一个合理的模型。 选择滤波器是为了获得适当的输出过程，作为良好的模型。 因此，感兴趣的参数的统计估计器取决于所使用的滤波器的类型。 首席研究员与博士后助理将研究估计量的稳健性并探索长期依赖性。 当输入具有高可变性时，将研究非线性滤波器的行为。