### 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) |
---|---|

Pages (from-to) | A1251-A1279 |

Journal | SIAM Journal on Scientific Computing |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2016 |

### Fingerprint

### 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

**Deterministic mean-field ensemble Kalman filtering.** / Law, Kody J.H.; Hamidou, Tembine; Tempone, Raul.

Research output: Contribution to journal › Article

*SIAM Journal on Scientific Computing*, vol. 38, no. 3, pp. A1251-A1279. https://doi.org/10.1137/140984415

}

TY - JOUR

T1 - Deterministic mean-field ensemble Kalman filtering

AU - Law, Kody J.H.

AU - Hamidou, Tembine

AU - Tempone, Raul

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - EnKF

KW - Filtering

KW - Fokker-planck

UR - http://www.scopus.com/inward/record.url?scp=84976902222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976902222&partnerID=8YFLogxK

U2 - 10.1137/140984415

DO - 10.1137/140984415

M3 - Article

AN - SCOPUS:84976902222

VL - 38

SP - A1251-A1279

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 3

ER -