Abstract
Theoretical properties of the ensemble Kalman filter (EnKF) and smoother (EnKS) for nonlinear non-Gaussian state-space models are provided. I first show that the EnKF is an approximation algorithm for the linear optimal filter. I next define the moment-matching linearization (MML) and from this viewpoint, I prove that the EnKF is more accurate than the Gaussian filter for both discrete-time and continuous-time cases. I also define the linear optimal smoother (LOS) using the MML. Then, the EnKS algorithm that approximates the LOS is derived and its difference from the existing EnKS is clarified.
