State of charge estimation of lithium-ion batteries with unknown parameters using an adaptive fractional-order center difference Kalman filter

An adaptive fractional-order central differential Kalman filter (AFCDKF) with an initial value compensation (IVC) algorithm is proposed in this paper for the estimation of the state of charge of lithium-ion batteries. In the adaptive estimation, the fractional-order is initially mapped to a reasonable range by using the hyperbolic tangent function, which prevents the proposed algorithm from failing due to the fractional-order being out of range (0, 1) during the parameter estimation, and further improves the stability and adaptability of the AFCDKF with IVC algorithm under different working conditions. Subsequently, the co-estimation of the state of charge and all parameters in the fractional-order model is achieved via the integration of linear Kalman filter and AFCDKF with IVC, which overcomes the problem on the difficult identification of model parameters under some complex working conditions, and also effectively suppresses the perturbation of model parameters caused by the sudden change of external temperature and discharging rates. Furthermore, the impact of the initial state is weakened by incorporating the IVC algorithm to prevent the fractional-order from becoming excessively small during the adaptive estimation, and the proposed algorithm is better applied to the working conditions where the initial values are unknown. Finally, the proposed algorithm is compared with several adaptive Kalman filtering algorithms and applied to various working conditions to demonstrate its superiority.