# Dynamic mode decomposition using a Kalman filter for parameter estimation

@article{Nonomura2018DynamicMD, title={Dynamic mode decomposition using a Kalman filter for parameter estimation}, author={Taku Nonomura and Hisaichi Shibata and Ryoji Takaki}, journal={AIP Advances}, year={2018} }

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…

## 33 Citations

Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising

- Computer Science, EngineeringPloS one
- 2019

EKFDMD performs better than existing algorithms for the case in which system noise is present and requires significant numerical resources for many-degree-of-freedom (many-DoF) problems and the combination with truncated proper orthogonal decomposition (trPOD) helps the algorithm to apply to many- doF problems, though it prevents the algorithm from being fully online.

Kalman Filter Dynamic Mode Decomposition for Data Assimilation

- EngineeringInternational Conference on Computational & Experimental Engineering and Sciences
- 2019

In this presentation, a family of Kalman filter dynamic mode decomposition, which consists of algorithms of the linear Kalman filter DMD method which identify the linear system and the extended…

Challenges in dynamic mode decomposition

- Computer ScienceJournal of the Royal Society Interface
- 2021

The results show that even for very mildly nonlinear conditions, DMD methods often fail to recover the spectrum and can have poor predictive ability, and this work is motivated by the experience modelling multilegged robot data.

Consistent Dynamic Mode Decomposition

- Computer ScienceSIAM J. Appl. Dyn. Syst.
- 2019

A new method for computing Dynamic Mode Decomposition (DMD) evolution matrices based on a variational formulation consisting of data alignment penalty terms and constitutive orthogonality constraints, which is applicable to a wide range of problems including non-linear scenarios or extremely small observation sets.

Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter

- EngineeringSensors
- 2021

The results demonstrate that the highly non-linear unknown characteristic curves can be estimated by using the proposed parameter estimation algorithm, and it is demonstrated that the root mean square error associated with the estimation of the characteristic curve is 0.08% with respect to the real model.

Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data

- Computer ScienceAIAA Journal
- 2021

By adding truncation regularization to the TLS D MD algorithm, T-TLS DMD improves the stability of the computation while maintaining the accuracy of TLS DMD, and shows the importance of regularization in the DMD algorithm.

Dynamic mode decomposition for compressive system identification

- Computer ScienceArXiv
- 2017

This work integrates and unify two recent innovations that extend DMD to systems with actuation and systems with heavily subsampled measurements, yielding a novel framework for compressive system identification.

Quantitative evaluation of predictability of linear reduced-order model based on particle-image-velocimetry data of separated flow field around airfoil

- Engineering
- 2021

A quantitative evaluation method for a reduced-order model of the flow field around an NACA0015 airfoil based on particle image velocimetry (PIV) data is proposed in the present paper. The velocity…

Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations

- Computer ScienceAIAA SCITECH 2022 Forum
- 2022

The proposed sketching-based framework can accelerate various portions of the DMD algorithm, compared to classical methods that operate directly on the raw input data, which eventually leads to substantial computational gains that are vital for digital twinning of high dimensional systems.

Mode Decomposition for Homogeneous Symmetric Operators

- MathematicsArXiv
- 2020

This work forms a closed form solution of DMD for dynamics, embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD), and forms a discrete decomposition, related to nonlinear eigenfunctions of $\gamma-homogeneous operator.

## References

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Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising

- Computer Science, EngineeringPloS one
- 2019

EKFDMD performs better than existing algorithms for the case in which system noise is present and requires significant numerical resources for many-degree-of-freedom (many-DoF) problems and the combination with truncated proper orthogonal decomposition (trPOD) helps the algorithm to apply to many- doF problems, though it prevents the algorithm from being fully online.

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