Ensemble Kalman filter with the unscented transform

A modification scheme to the ensemble Kalman filter (EnKF) is introduced
based on the concept of the unscented transform (Julier et al., 2000; Julier
and Uhlmann, 2004), which therefore will be called the ensemble unscented
Kalman filter (EnUKF) in this work. When the error distribution of the analysis
is symmetric (not necessarily Gaussian), it can be shown that, compared to the
ordinary EnKF, the EnUKF has more accurate estimations of the ensemble mean and
covariance of the background by examining the multidimensional Taylor series
expansion term by term. This implies that, the EnUKF may have better
performance in state estimation than the ordinary EnKF in the sense that the
deviations from the true states are smaller. For verification, some numerical
experiments are conducted on a 40-dimensional system due to Lorenz and Emanuel
(Lorenz and Emanuel, 1998). Simulation results support our argument.