data assimilation: the ensemble kalman filter  (Verlag GmbH)

Journal: Scientific Reports

Article Title: A hybrid data assimilation method based on real-time Ensemble Kalman filtering and KNN for COVID-19 prediction

doi: 10.1038/s41598-025-85593-z

Figure Lengend Snippet: A Hybrid Data Assimilation Method Based on Real-Time EnKF and KNN. (The classified target data, obtained through the introduction of classification criteria, is updated via resampling. This process selects high-weight particles while ensuring coverage of low-weight particles, thereby improving the performance of the new ensemble. The updated ensemble is then used as the input for the filtering update, facilitating the prediction process.).

Article Snippet: The Ensemble Kalman Filter (EnKF) method has demonstrated superior performance in assimilating data for nonlinear systems .

Techniques:

Journal: Scientific Reports

Article Title: A hybrid data assimilation method based on real-time Ensemble Kalman filtering and KNN for COVID-19 prediction

doi: 10.1038/s41598-025-85593-z

Figure Lengend Snippet: Real-Time EnKF and KNN-Based Hybrid Data Assimilation Method for Xi’an (Dec 9, 2021–Jan 8, 2022) Achieving Improved Alignment Between Predicted and Observed COVID-19 Cases.

Article Snippet: The Ensemble Kalman Filter (EnKF) method has demonstrated superior performance in assimilating data for nonlinear systems .

Techniques:

Journal: Scientific Reports

Article Title: A hybrid data assimilation method based on real-time Ensemble Kalman filtering and KNN for COVID-19 prediction

doi: 10.1038/s41598-025-85593-z

Figure Lengend Snippet: The real-time EnKF data assimilation method for Xi’an (Dec 9, 2021–Jan 8, 2022) demonstrates a comparison of optimization performance, showing that the real-time EnKF method outperforms traditional EnKF but performs worse than the hybrid method.

Article Snippet: The Ensemble Kalman Filter (EnKF) method has demonstrated superior performance in assimilating data for nonlinear systems .

Techniques: Comparison

Journal: Scientific Reports

Article Title: A hybrid data assimilation method based on real-time Ensemble Kalman filtering and KNN for COVID-19 prediction

doi: 10.1038/s41598-025-85593-z

Figure Lengend Snippet: The EnKF data assimilation method for Xi’an (Dec 9, 2021–Jan 8, 2022) demonstrates a comparison of optimization performance, showing that the EnKF method underperforms relative to both the real-time EnKF and hybrid methods.

Article Snippet: The Ensemble Kalman Filter (EnKF) method has demonstrated superior performance in assimilating data for nonlinear systems .

Techniques: Comparison

Journal: Scientific Reports

Article Title: A hybrid data assimilation method based on real-time Ensemble Kalman filtering and KNN for COVID-19 prediction

doi: 10.1038/s41598-025-85593-z

Figure Lengend Snippet: Comparison of prediction results, demonstrating a 7.97% reduction in prediction error with the hybrid method compared to traditional EnKF. This hybrid approach improves predictive accuracy by integrating real-time adjustments with pattern recognition techniques, thereby outperforming other data assimilation methods.

Article Snippet: The Ensemble Kalman Filter (EnKF) method has demonstrated superior performance in assimilating data for nonlinear systems .

Techniques: Comparison

Journal: Physical review research

Article Title: Poisson Kalman filter for disease surveillance

doi: 10.1103/physrevresearch.2.043028

Figure Lengend Snippet: Comparison of the PKF (optimal variable gain) and the Kalman filter (optimal fixed gain) for the SIRH model with Poisson observations of the infected and hydrocephalic populations. The true (a) susceptible S , (b) recovered R , (c) infected I , and (d) hydrocephalic H values (black) are compared to the PKF (red dashed curve) and Kalman filter (blue dotted curve) estimates. (c) and (d) also show the observations (green circles) rescaled by dividing by the constants c I and c H , respectively. (e) and (f) Expanded versions of (d), enlarged to show detail. When the number of cases is large, the KF estimate of H is very close to the observations, whereas the PKF adjusts to the larger observation variance and produces better estimates. Also shown are the Poisson rates (black) of (g) I and (h) H and the observed case numbers (red circles) from the Poisson distribution.

Article Snippet: Finally, we note that two closely related alternative approaches to applying the Kalman filter to nonlinear dynamics are the ensemble Kalman filter (EnKF) [ ] and ensemble adjustment Kalman filter (EAKF) [ ].

Techniques: Comparison, Infection

Journal: Physical review research

Article Title: Poisson Kalman filter for disease surveillance

doi: 10.1103/physrevresearch.2.043028

Figure Lengend Snippet: Comparison of the RMSE for the (a) infected and (b) hydrocephalic populations of the PKF (red solid curve, optimal variable gain) and the Kalman filter (blue solid curve, optimal fixed gain) as function of the system noise. We also compare to an oracle PKF (black dashed curve) which is given the optimal choice of V k = diag ( B x → k ) . System noise is quantified as a multiple of the base noise level W . The RMSE is averaged over 10 6 filter steps.

Article Snippet: Finally, we note that two closely related alternative approaches to applying the Kalman filter to nonlinear dynamics are the ensemble Kalman filter (EnKF) [ ] and ensemble adjustment Kalman filter (EAKF) [ ].

Techniques: Comparison, Infection

Journal: Physical review research

Article Title: Poisson Kalman filter for disease surveillance

doi: 10.1103/physrevresearch.2.043028

Figure Lengend Snippet: Comparison of the extended PKF (optimal variable gain) and the extended Kalman filter (optimal fixed gain for the noncontagious equilibrium) for the contagious SIRH model with Poisson observations of the infected and hydrocephalic populations. We compare the true S , I , R , and H values (black solid curve) to the PKF (red dashed curve) and Kalman filter (blue dotted curve) estimates. We show (a)–(d) a standard observation rate c I = 0.2 / T S and c H = 0.6 / T R and (e)–(h) a low observation rate c I = 0.0002 / T S and c H = 0.0006 / T R . The infected and hydrocephalic plots also show the observations (green circles) rescaled by dividing by the constants c I and c H , respectively. The system is initialized at the noncontagious equilibrium and run forward with β = 10 − 6 simulating the introduction of a contagious source of infection which moves the system to a new equilibrium.

Article Snippet: Finally, we note that two closely related alternative approaches to applying the Kalman filter to nonlinear dynamics are the ensemble Kalman filter (EnKF) [ ] and ensemble adjustment Kalman filter (EAKF) [ ].

Techniques: Comparison, Infection