Ensemble Kalman filter with the unscented transform

TL;DR

This paper introduces the ensemble unscented Kalman filter (EnUKF), a modification of the ensemble Kalman filter that uses the unscented transform to improve estimation accuracy in symmetric error distributions.

Contribution

The paper proposes the EnUKF, which enhances the ensemble Kalman filter by incorporating the unscented transform for better mean and covariance estimation.

Findings

EnUKF provides more accurate ensemble mean and covariance estimates.

Simulation results show improved state estimation performance.

EnUKF outperforms the ordinary EnKF in numerical experiments.

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.