A two-stage variable-separation Kalman filter for data assimilation. (English) Zbl 07508537
Summary: This work presents a two-stage variable-separation Kalman filter (T-VSKF) to the combined parameters and state estimation in Bayesian data assimilation. The variable-separation method is used to construct a surrogate model for the forward problem and is able to significantly reduces the online computation for assimilation update. The stochastic basis functions from the variable-separation method are used to approximately express the unknowns of estimation. Then a sampling-free method and the variable-separation method are integrated to obtain an approximation of the posterior distribution in the Bayesian exploration. In T-VSKF, we update the coefficients of the stochastic basis functions for the unknowns. The proposed T-VSKF method has two stages. The first stage is to only update the coefficient corresponding to the constant basis function by the Kalman filter. Then all the coefficients are dynamically updated by the proposed method in the second stage. The first stage is to locate an approximate mean and the second stage is to improve the mean and reduce the uncertainty of the unknown parameters and state. T-VSKF significantly mitigates the underestimation for the variance of the posterior often occurred in ensemble Kalman filters. Moreover, the computation efficiency of T-VSKF is slightly impacted as the dimension of parameter and state increases. A few numerical data assimilation examples are presented in heterogenous porous media applications and nonlocal diffusion. The numerical results show the advantages of T-VSKF over some classical filter methods in the data assimilation.
MSC:
| 65Cxx | Probabilistic methods, stochastic differential equations |
| 62Fxx | Parametric inference |
| 60Hxx | Stochastic analysis |
Keywords:
ensemble square root filter; two-stage variable-separation Kalman filter; data assimilation; porous media applicationsReferences:
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