论文标题
合奏Kalman过滤器具有扰动的观察结果，天气预报和数据同化
Ensemble Kalman Filter with perturbed observations in weather forecasting and data assimilation
论文作者
论文摘要
数据同化为各个领域的广泛应用提供了算法。处理复杂系统中很难估算的大量信息是实际的。天气预报是一种应用之一，鉴于观察结果，纠正了气象数据的预测。数据同化中包含许多方法。一种特定的顺序方法是卡尔曼滤波器。核心是通过测量的新数据和预测的先前数据来估算未知信息。实际上，卡尔曼过滤器中有不同的改进方法。在此项目中，考虑了带有扰动观察的合奏卡尔曼滤波器。它是通过蒙特卡洛模拟实现的。在这种方法中，集合参与计算而不是状态向量。另外，用扰动的测量被视为合适的观察。与线性Kalman滤波器相比，这些变化使其更有优势，因为当计算机计算数据时，在线性系统中不限于在线性系统中限制。论文试图逐渐通过扰动观察来开发集成的卡尔曼滤波器。通过数学初步，包括动态系统的引入，构建了线性卡尔曼滤波器。同时，得出了预测和分析过程。之后，我们使用类比的思想来引导非线性的集合卡尔曼过滤器，并具有扰动的观测值。最后，Matlab说明了经典的Lorenz 63模型。在示例中，我们实验集合成员的数量，并寻求研究方差误差与集成成员数量之间的关系。我们得出的结论是，在有限的规模上，大量的合奏成员表示预测的误差较小。
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the applications, where the prediction of meteorological data are corrected given the observations. Numerous approaches are contained in data assimilation. One specific sequential method is the Kalman Filter. The core is to estimate unknown information with the new data that is measured and the prior data that is predicted. As a matter of fact, there are different improved methods in the Kalman Filter. In this project, the Ensemble Kalman Filter with perturbed observations is considered. It is achieved by Monte Carlo simulation. In this method, the ensemble is involved in the calculation instead of the state vectors. In addition, the measurement with perturbation is viewed as the suitable observation. These changes compared with the Linear Kalman Filter make it more advantageous in that applications are not restricted in linear systems any more and less time is taken when the data are calculated by computers. The thesis seeks to develop the Ensemble Kalman Filter with perturbed observation gradually. With the Mathematical preliminaries including the introduction of dynamical systems, the Linear Kalman Filter is built. Meanwhile, the prediction and analysis processes are derived. After that, we use the analogy thoughts to lead in the non-linear Ensemble Kalman Filter with perturbed observations. Lastly, a classic Lorenz 63 model is illustrated by MATLAB. In the example, we experiment on the number of ensemble members and seek to investigate the relationships between the error of variance and the number of ensemble members. We reach the conclusion that on a limited scale the larger number of ensemble members indicates the smaller error of prediction.
