Dynamic mode decomposition using a Kalman filter for parameter estimation

TL;DR

This paper introduces a Kalman filter-based dynamic mode decomposition method that improves eigenmode estimation accuracy in noisy, time-varying systems, especially for sequential data analysis.

Contribution

It proposes the KFDMD algorithm combining Kalman filtering with truncated POD, enhancing eigenmode estimation under severe noise and dynamic conditions.

Findings

KFDMD outperforms standard DMD and tlsDMD in noisy environments.

KFDMD accurately tracks eigenmodes in time-varying systems.

KFDMD is effective for sequential data analysis with strong noise robustness.

Abstract

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.