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.

中文翻译：

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基于自适应分数阶容积卡尔曼滤波器的锂离子电池充电状态估计

基于分数阶模型（FOM），本文提出了一种用于锂离子电池（LIB）充电状态（SOC）估计的自适应分数阶立方卡尔曼滤波器（AFCKF）方法。首先，构建了具有两个恒定相位单元的FOM，该FOM能够以更高的精度准确地表示LIB的动态特征。其次，通过线性卡尔曼滤波算法实现了测量方程中系数的自适应估计，避免了开路电压与SOC之间关系的计算。再次，引入增广向量方法研究了包括SOC、分数阶和FOM中参数的增广状态方程，并通过AFCKF算法在线估计状态信息。该算法在保证估计精度的同时，计算负担小，能够很好地适应复杂的工况。此外，本研究充分考虑了噪声对估计效果的影响。为了更好地克服未知噪声带来的干扰，进一步提高算法的精度和稳定性，提出了一种噪声协方差矩阵的自适应估计方法。最后的实验结果表明，该方法能够有效地应用于不同的工况，且估计精度优于自适应整数阶体积卡尔曼滤波器。为了更好地克服未知噪声带来的干扰，进一步提高算法的精度和稳定性，提出了一种噪声协方差矩阵的自适应估计方法。最后的实验结果表明，该方法能够有效地应用于不同的工况，且估计精度优于自适应整数阶体积卡尔曼滤波器。为了更好地克服未知噪声带来的干扰，进一步提高算法的精度和稳定性，提出了一种噪声协方差矩阵的自适应估计方法。最后的实验结果表明，该方法能够有效地应用于不同的工况，且估计精度优于自适应整数阶体积卡尔曼滤波器。