Dynamic mode decomposition using a Kalman filter for parameter estimation
arXiv:1804.00143 · doi:10.1063/1.5031816
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.
References in corpus (8)
- On Dynamic Mode Decomposition: Theory and Applications
- Sparsity-promoting dynamic mode decomposition
- Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
- Dynamic Mode Decomposition for Large and Streaming Datasets
- Principal Component Analysis with Noisy and/or Missing Data
- Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising
- Preconditioned dynamic mode decomposition and mode selection algorithms for large datasets using incremental proper orthogonal decomposition
- Online dynamic mode decomposition for time-varying systems
Cited by in corpus (12)
- Determinant-based Fast Greedy Sensor Selection Algorithm
- Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising
- Data-Driven Approach for Noise Reduction in Pressure-Sensitive Paint Data Based on Modal Expansion and Time-Series Data at Optimally Placed Points
- Quantitative Evaluation of a Linear Reduced-order Model based on Particle-image-velocimetry Data of Separated Flow Field around Airfoil
- Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model
- Data-Driven Selection of Actuators for Optimal Control of Airfoil Separation
- Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data
- Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
- Combining Dynamic Mode Decomposition with Ensemble Kalman Filtering for Tracking and Forecasting
- A physics-informed machine learning model for reconstruction of dynamic loads
- Modes of Homogeneous Gradient Flows
- Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations