Ensemble Kalman Filtering with One-Step-Ahead Smoothing
Ensemble Kalman filters (EKFs) sequentially assimilate the observations into the dynamical model to determine a better characterization of the model's state. At each assimilation cycle of an EnKF, an ensemble of states is first propagated in time with the model for forecasting. The forecasted ensemble is then updated with incoming observations based on a Kalman-like correction. The forecast-update cycle is however not the only pathway to compute the state analysis. This work explores the efficiency of the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem which reverses the order of the forecast and update steps to propose new OSA smoothing-based EnKF algorithms. Filtering with OSA smoothing introduces an extra Kalman-smoothing step, conditioning the ensemble sampling with more information. Exploiting future observations should be particularly beneficial in the context of the EnKF as it brings in more information that help mitigating for the suboptimal character of the EnKFs; being formulated under the linear Gaussian assumption, and usually implemented with limited ensembles and crude approximate noise statistics. Numerical results will be presented to demonstrate the efficiency of the proposed approach.
Prof. Ibrahim Hoteit Earth Science and Engineering