scholarly journals An Ensemble Kalman Filter Implementation Based on Modified Cholesky Decomposition for Inverse Covariance Matrix Estimation

2018 ◽  
Vol 40 (2) ◽  
pp. A867-A886 ◽  
Author(s):  
Elias D. Nino-Ruiz ◽  
Adrian Sandu ◽  
Xinwei Deng
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Cholesky Decomposition ◽  
Covariance Matrix Estimation ◽  
Matrix Estimation ◽  
Modified Cholesky Decomposition ◽  
Inverse Covariance Matrix

scholarly journals An efficient ensemble Kalman Filter implementation via shrinkage covariance matrix estimation: exploiting prior knowledge

2021 ◽  
Vol 25 (3) ◽  
pp. 985-1003
Author(s):  
Santiago Lopez-Restrepo ◽  
Elias D. Nino-Ruiz ◽  
Luis G. Guzman-Reyes ◽  
Andres Yarce ◽  
O. L. Quintero ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Prior Knowledge ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
General Circulation ◽  
Circulation Model ◽  
Covariance Matrix Estimation ◽  
Practical Implementation ◽  
Matrix Estimation ◽  
The Impact

AbstractIn this paper, we propose an efficient and practical implementation of the ensemble Kalman filter via shrinkage covariance matrix estimation. Our filter implementation combines information brought by an ensemble of model realizations, and that based on our prior knowledge about the dynamical system of interest. We perform the combination of both sources of information via optimal shrinkage factors. The method exploits the rank-deficiency of ensemble covariance matrices to provide an efficient and practical implementation of the analysis step in EnKF based formulations. Localization and inflation aspects are discussed, as well. Experimental tests are performed to assess the accuracy of our proposed filter implementation by employing an Advection Diffusion Model and an Atmospheric General Circulation Model. The experimental results reveal that the use of our proposed filter implementation can mitigate the impact of sampling noise, and even more, it can avoid the impact of spurious correlations during assimilation steps.

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