Dynamic mode decomposition using a Kalman filter for parameter estimation

Taku Nonomura, Hisaichi Shibata, Ryoji Takaki

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


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.

Original languageEnglish
Article number105106
JournalAIP Advances
Issue number10
Publication statusPublished - 2018 Oct 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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