Geodesic
Comparison of data assimilation methods based on the classical, ensemble and local Kalman filter by the example of the advection equation and Lorenz system
Numerical methods and programming, Tome 19 (2018) no. 4, pp. 507-515.

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The paper is devoted to the comparison of three data assimilation methods: the Kalman Filter (Kalman Filter, KF), the ensemble Kalman Filter (EnKF), and the local Kalman Filter (LKF). A number of numerical experiments on data assimilation by these methods are performed on two different models described by systems of differential equations. The first one is a simple one-dimensional linear equation of advection and the second one is the Lorenz system. The mean errors and the execution time of these assimilation methods are compared for different model sizes. The numerical results are consistent with the theoretical estimates. It is shown that the computational complexity of local and ensemble Kalman filters grows linearly with the size of the model, whereas in the classical Kalman Filter this complexity increases according to the cubic law. The efficiency of parallel implementation of the local Kalman filter is considered.
Keywords: Kalman Filter, Local Kalman Filter
Mots-clés : Ensemble Kalman Filter, Lorenz equations, advection equation, data assimilation. 
@article{VMP_2018_19_4_a16,
     author = {D. A. Rostilov and M. N. Kaurkin and R. A. Ibrayev},
     title = {Comparison of data assimilation methods based on the classical, ensemble and local {Kalman} filter by the example of the advection equation and {Lorenz} system},
     journal = {Numerical methods and programming},
     pages = {507--515},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a16/}
}
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D. A. Rostilov; M. N. Kaurkin; R. A. Ibrayev. Comparison of data assimilation methods based on the classical, ensemble and local Kalman filter by the example of the advection equation and Lorenz system. Numerical methods and programming, Tome 19 (2018) no. 4, pp. 507-515. http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a16/