Dynamic Mode Decomposition based on Bootstrapping Extended Kalman Filter Application to Noisy data

In this study, dynamic mode decomposition (DMD) based on bootstrapping extended Kalman filter is proposed for time-series data. In this framework, state variables ($x$ and $y$) are filtered as well as the parameter estimation ($a_{ij}$) which is conducted in the conventional DMD and the standard Kalman-filter-based DMD. The filtering process of state variables enables us to obtain highly accurate eigenvalue of the system with strong noise. In the presentation, formulation, advantages and disadvantages are discussed.