Ensemble Kalman filter with the unscented transform

Abstract

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.

References in corpus (1)

• Morphing Ensemble Kalman Filters

Cited by in corpus (13)

• The Ensemble Kalman Filter: A Signal Processing Perspective
• Efficient big data assimilation through sparse representation: A 3D benchmark case study in seismic history matching
• An Ensemble 4D Seismic History Matching Framework with Sparse Representation Based on Wavelet Multiresolution Analysis
• Robust ensemble filtering and its relation to covariance inflation in the ensemble Kalman filter
• Scaled unscented transform Gaussian sum filter: theory and application
• Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications
• A two-stage ensemble Kalman filter based on multiscale model reduction for inverse problems in time fractional diffusion-wave equations
• Ensemble Kalman filtering with a divided state-space strategy for coupled data assimilation problems
• Ensemble Kalman filtering with residual nudging: an extension to state estimation problems with nonlinear observation operators
• Toward an enhanced Bayesian estimation framework for multiphase flow soft-sensing
• Recursive Bayesian Filters for Data Assimilation
• Reply to "Comment on 'Ensemble Kalman filter with the unscented transform'"
• A Generalized Unscented Transformation for Probability Distributions