Unscented/ensemble transform-based variational filter

► The Unscented Transform (UT) approach is used to give an evolution to the prediction error covariance matrices. ► The Ensemble Transform (ET) is employed to implement the update of the covariance matrices. ► The variational minimization is chosen to get a state correction for a nonlinear dynamics. ► The rank reduction technique is modified to conduct the dimension diminishment with an adaptive manner.