标题： 基于卡尔曼滤波的参数估计动态模态分解 显示英文标题

标题： Dynamic mode decomposition using a Kalman filter for parameter estimation

摘要： 一种基于卡尔曼滤波器的新型动态模态分解（DMD）方法被提出。 本文解释了所提出的卡尔曼滤波器DMD（KFDMD）与截断本征正交分解相结合的快速算法，用于多自由度问题。 数值实验表明，当已知观测噪声的性质时，KFDMD在严重噪声条件下比标准DMD或总最小二乘DMD（tlsDMD）方法更能精确估计特征模态，尽管在低和中等噪声水平下tlsDMD优于KFDMD。 此外，KFDMD即使在系统矩阵随时间变化的情况下也能精确跟踪特征模态，类似于在线DMD，由于卡尔曼滤波器的特性，这种扩展是自然进行的。 总之，KFDMD是一种具有强抗噪特性的有前途的工具，可用于分析顺序数据集。 显示英文摘要

摘要： A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for many-degree-of-freedom problems. Numerical experiments reveal that KFDMD can estimate eigenmodes more precisely compared with standard DMD or total least-squares DMD (tlsDMD) methods for the severe noise condition if the nature of the observation noise is known, though tlsDMD works better than KFDMD in the low and medium noise level. Moreover, KFDMD can track the eigenmodes precisely even when the system matrix varies with time similar to online DMD, and this extension is naturally conducted owing to the characteristics of the Kalman filter. In summary, the KFDMD is a promising tool with strong antinoise characteristics for analyzing sequential datasets.