State of charge estimation of lithium-ion battery with an adaptive fractional-order cubature Kalman filter considering initial value problem

For the problem of the accurate estimation of the state of charge (SOC) in lithium-ion batteries, an adaptive fractional-order cubature Kalman filtering algorithm (AFCKF) considering the initial value problem is proposed in this paper. Firstly, we establish the state space equation describing the dynamic characteristics of lithium-ion batteries based on the relationship between the Caputo derivative and the Riemann–Liouville derivative. Secondly, an AFCKF algorithm considering the initial value problem is designed to achieve the SOC estimation for the case that the model parameters are uncertain. Then, the adaptive adjustment of multiple noise covariance matrices is implemented by using an iterative method. Finally, the simulation results indicate that the designed algorithm is superior to the AFCKF without the initial value compensation algorithm.