Scaled unscented transform-based variational optimality filter

An efficient method based on the concept of the variational optimality and the ensemble transform (ET) as well as the scaled unscented transform (SUT), therefore called the scaled unscented transform-based variational optimality filter (SVOF), is introduced in this work. Based on the SUT Kalman filter (SUKF) [1], the SVOF suggests a new correction for the ensemble mean and covariance estimation, which incorporates the variational optimality as well as the ET-like covariance correction into the ordinary update scheme. Moreover for dealing high dimensionality of dynamics, the truncated singular value decomposition (TSVD) was applied to generate a size-diminished set of sigma points. For verification, numerical experiments were conducted on Lorenz-95 and the results confirm the outperforming and efficiency of the SVOF.