论文标题
在存在高斯噪声的情况下，使用时间延迟的时间来同化数据
Data Assimilation using Time-Delay Nudging in the Presence of Gaussian Noise
论文作者
论文摘要
我们研究了一种基于时间延迟的反馈控制的淡化时间的分散数据征服算法，在该反馈控制中，观察性测量已被高斯噪声过程污染。在二维不可压缩的Navier-Stokes方程的上下文中，我们证明了近似解决方案和参考解决方案之间的正方形误差的预期值，随时间时间与对数校正的噪声方差成正比。数值模拟进一步说明了我们分析的定性行为和物理相关性。
We study a discrete-in-time data-assimilation algorithm based on nudging through a time-delayed feedback control in which the observational measurements have been contaminated by a Gaussian noise process. In the context of the two-dimensional incompressible Navier-Stokes equations we prove the expected value of the square-error between the approximating solution and the reference solution over time is proportional to the variance of the noise up to a logarithmic correction. The qualitative behavior and physical relevance of our analysis is further illustrated by numerical simulation.
