Mathematical Sciences: Non-Linear Filtering and Estimation

该项目将从长期依赖和高变异性的角度研究线性和非线性滤波。在石英晶体振荡器和半导体器件的频率波动数据中，存在长距离依赖关系。在降雨数据和固态材料弛豫时间等大概率值的情况下，无限方差是一个合理的模型。筛选器的选择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取决于所使用的滤波器的类型。首席研究员，连同博士后助理，将研究估计器的鲁棒性，以及探索长期依赖。当输入具有高可变性时，将研究非线性滤波器的行为。

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.