Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering

Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering

Kody J.H. Law, Hamidou Tembine, Raul Tempone, Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering, submitted to arXiv:1409.0628v2, Nov. 2014
Kody J.H. Law, Hamidou Tembine, Raul Tempone
Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering
2014
‚ÄčThis paper provides a proof of convergence of the standard EnKF generalized to non-Gaussian state space models, based on induction following the proof of Legland 2011 [LGMT+11]. A density-based deterministic approximation of the mean-field EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d<2k. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.