SOME STATISTICAL TOPICS ON SEQUENTIAL DATA ASSIMILATION Submitted by

Among many techniques in sequential data assimilation, the ensemble Kalman lter (EnKF), proposed by Geir Evensen in 1994, had become popular in recent years. Nevertheless, EnKF still faces a number of pitfalls in some applications. In this study, two new variants of EnKF are proposed. The \u85rst one is initiated by the Goldberger-Theils mixed estimation and the updating equation of the con-ventional EnKF under this estimation becomes no longer linear. This variant of the EnKF is called the ensemble Goldberger-Theil Kalman \u85lter (EnGTKF). Due to the possible deviation of prediction and \u85ltering densities from Gaussianity, the multivariate Gram-Charlier densities were suggested for the estimation of the error statistics on both measurements and states. As a by-product, an ensemble Goldberger-Theil Kalman smoother (EnGTKS) was derived in which only infor-mation of the prediction density and the likelihood of measurement conditional on the states are required. The second variant of the EnKF was motivated by the Markov switching of regimes in the nonlinear state space model. Under the switching between hidde