### Abstract

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598-631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

Original language | English (US) |
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Pages (from-to) | A1251-A1279 |

Journal | SIAM Journal on Scientific Computing |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2016 |

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### Keywords

- EnKF
- Filtering
- Fokker-planck

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Scientific Computing*,

*38*(3), A1251-A1279. https://doi.org/10.1137/140984415