Based on the fractional-order model (FOM), this paper proposes an adaptive fractional-order cubature Kalman filter (AFCKF) method for state of charge (SOC) estimation of a lithium-ion battery (LIB). Firstly, a FOM with two constant phase elements is built, which can accurately represent the dynamic features of a LIB with a higher accuracy. Secondly, the adaptive estimations of the coefficients in the measurement equation are achieved by a linear Kalman filter algorithm, which avoids the calculation of the relationship between the open-circuit voltage and SOC. Thirdly, an augmented state equation including the SOC, the fractional-orders and parameters in the FOM is investigated by introducing the augmented vector method, and the state information is estimated online via the AFCKF algorithm. The algorithm requires a little computational burden while ensuring the estimation accuracy and is well adapted to complex working conditions. Besides, this study fully considers the impact of noises on the estimation effect. To better overcome the disturbances caused by unknown noises and further improve the precision and stability of the algorithm, an adaptive estimation method of the noise covariance matrices is achieved. Finally, the experimental findings are given to reveal that the proposed method can be effectively used to different working conditions and the estimation accuracy is better than the adaptive integer-order cubature Kalman filter.

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