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A novel dynamic mode decomposition (DMD) method based on a Kalman filter isproposed. This paper explains the fast algorithm of the proposed Kalman filterDMD (KFDMD) in combination with truncated proper orthogonal decomposition formany-degree-of-freedom problems. Numerical experiments reveal that KFDMD canestimate eigenmodes more precisely compared with standard DMD or totalleast-squares DMD (tlsDMD) methods for the severe noise condition if the natureof the observation noise is known, though tlsDMD works better than KFDMD in thelow and medium noise level. Moreover, KFDMD can track the eigenmodes preciselyeven when the system matrix varies with time similar to online DMD, and thisextension is naturally conducted owing to the characteristics of the Kalmanfilter. In summary, the KFDMD is a promising tool with strong antinoisecharacteristics for analyzing sequential datasets.

Dynamic mode decomposition using a Kalman filter for parameter estimation