| This dissertation discusses about mathematical properties of ensemble Kalman filter (EnKF). On one hand, it gives a rigorous statement and proof for asymptotic convergence of (EnkF) to the full Kalman filter for linear dynamics. On the other hand, it investigates drawbacks of the EnKF when a small ensemble size is used. Inefficient covariance approximation and non-smooth model states paths are found and explained using random matrix theory and random field theory respectively. An improved sampling method based on singular value decomposition and Gaussian cubature rule is proposed and shown to outperform the EnKF in numerical experiments. |
