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Robust Fractional Embedded Cubature Kalman Filter for Fractional Nonlinear Stochastic System

Jing Mu*, Feng Tian, Changyuan Wang, Wuqi Gao, and Jianlian Cheng
International Journal of Control, Automation, and Systems, vol. 20, no. 11, pp.3549-3560, 2022

Abstract : In this study, the fractional embedded cubature Kalman filter (FECKF) and robust fractional embedded cubature Kalman filter (RoFECKF) are proposed to design the estimate the states for fractional-order nonlinear discrete systems with Gaussian and non-Gaussian measurement noise, respectively. We develop FECKF algorith by extending embedded cubature Kalman filter to fractional nonlinear stochastic system with Gaussian noise. Meanwhile, RoFECKF is put forward to increase the estimation robustness under noisy measurements by applying the Huber method to FECKF. Simulation results on adaptive system identification and re-entry target tracking system demonstrate the effectiveness and robustness of the proposed approach.

Keyword : Embedded cubature rule, fractional calculus, fractional-order nonlinear stochastic systems, Kalman filter, state estimation.

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