Design Of Adaptive Fractional-order Unscented Kalman Filters And Its Application In State Of Charge For Lithium-ion Batteries

The Kalman filter is the most commonly used estimator for estimating and tracking the target state.In contrast,the unscented Kalman filter（UKF）has a high estimation accuracy of state.The fractional-order calculus has the memory properties,which can well describe the dynamic characteristics of the actual physical systems with the memory properties.Applying fractional-order calculus to the UKF algorithm has a high state estimation accuracy.Therefore,using the fractional-order UKF algorithm to estimate the state of charge（SOC）of lithium-ion batteries has a high estimation accuracy,and can effectively enhance the algorithm’s adaptive ability to actual working conditions.This paper mainly studies the following aspects:（1）In this paper,an UKF for a nonlinear fractional-order system with the unknown order is proposed.The continuous-time nonlinear fractional-order system is discretized by Grünwald-Letnikov（G-L）difference,and the corresponding difference equation is obtained.Besides,the augmented vector is presented to establish the augmented equation with respect to the state and fractional-order,and the nonlinear functions in the nonlinear augmented equation are performed by the unscented transform（U-T）.The state and unknown order are estimated by the proposed adaptive UKF to improve the accuracy of state and order estimations compare with the extended Kalman filter（EKF）.（2）In this paper,the G-L difference method is used to discretize a continuous-time nonlinear fractional-order system with unknown parameters and fractional-order,and the discrete difference equation of the system is obtained.Taking the unknown fractionalorder and parameters as the augmented states,the augmented state equation is established to solve the problem on the unknown fractional-order and parameters.In order to improve the accuracy of state estimation,an adaptive fractional-order UKF is designed to deal with the nonlinear functions by using the U-T.Meanwhile,the problem on state estimation for the estimated system with non-differentiable nonlinear functions is also solved.（3）To deal with the changes of internal characteristics in lithium-ion battery at different temperatures and different charge and discharge rates,a design method of adaptive UKF in this paper is proposed to improve the adaptive ability of the algorithm in the complex environment.To solve the problem on the estimations of unknown parameters and order in the lithium-ion battery model effectively,the fractional-order and the SOC are mapped to the effective value ranges via the Sigmoid function to prevent the failure of SOC estimation.Using the augmented vector method,the augmented state equations in terms of system states including SOC,order and parameters are established.Based on the method of U-T,the nonlinear function of the lithium-ion battery described by a fractional-order model is processed,and the SOC estimation with a high estimation accuracy is obtained.In addition,the adaptive estimation algorithms for noise covariance matrices are discussed to further increase the adaptive ability of the proposed algorithms in complex environment.