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The Ensemble Kalman filter (EnKF) was introduced for highly dimensional systems, but it has poor performance in the presence of strong nonlinearities. The Cubature Kalman filter (CKF) has outstanding performance in strongly nonlinear systems, however, it is limited by high dimensionality. In this work, we provide a comparison between the EnKF and the CKF to elaborate the problems of each scheme in highly dimensional strongly nonlinear systems. To address these problems, we introduce a Cubature Ensemble Kalman filter (CEnKF) that is a combination between both types of filters making it more suitable for highly dimensional strongly nonlinear systems. These algorithms are tested by extensive computer simulations on several models for chaotic dynamical systems. In addition, the computational complexity of the CKF/EnKF/CEnKF is analyzed. Simulation results show that the CEnKF, given a large enough ensemble size, can perform better than the EnKF and CKF for highly dimensional strongly nonlinear systems with high measurement noise intensity. The CEnKF also has better stability than the EnKF, and it performs as good as the CKF with a large enough ensemble size.

Cubature Ensemble Kalman Filter for Highly Dimensional Strongly Nonlinear Systems