摘要: 针对标准UKF 算法本身存在着因状态误差协方差矩阵无法实现Cholesky分解而导致滤波发散的隐患，以及在电池状态估计过程中由离线标定的电池等效模型参数而造成的累积误差的问题，本文发展了一种平方根无迹卡尔曼滤波(square-root unscented Kalman filter, SR-UKF)算法，并设计了一种电池状态联合估计策略。① 快速SR-UKF算法通过对观测方程进行准线性化处理，降低了每次无迹变换时的计算开销；② 在迭代过程中，用状态误差协方差矩阵的平方根代替状态误差协方差矩阵，该平方根是由QR分解与 Cholesky因子的一阶更新得到，解决了UKF 算法迭代过程中可能由计算累积误差引起状态误差协方差矩阵负定而导致滤波结果发散的问题，保证了电池荷电状态(state of charge，SOC)在线滚动估计的数值稳定性；③ 采用联合估计策略，对电池等效模型参数进行实时辨识，保证了电池等效模型的准确性与有效性，从而提高了电池SOC的估计精度。仿真对比结果验证了快速SR-UKF算法以及电池状态联合估计策略的可行性与鲁棒性。
Real-time States Co-Estimation Algorithm for Li-ion Power Batteries Based on Fast Square-Root Unscented Kalman Filters
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Abstract: Upon the practical issues such as filtering divergence caused by non-positive definite error covariance matrix in standard unscented Kalman filter (UKF) and accumulative state estimation errors due to the simplified mathematical modeling of li-ion power battery who has inherent features of strong non-linearity, time-variety as well as uncertainty, a real-time states co-estimation algorithm that is based on fast square-root unscented Kalman filter framework is thus proposed in this article. Firstly, during the iteration process, the non-linear measurement function which describes the propagation of each sigma point is called by unscented transform (UT) at iteration step. And the reduction of computational complexity could be achieved providing that the non-linear measurement function is quasi-linearized. Secondly, instead of state error covariance matrix, the square root of the state error covariance matrix, which can be obtained by QR decomposition and first-order updating of Cholesky factor is employed so as to deal with the problem that the state error covariance matrix may be negative definite caused by the accumulative computational errors while performing the recursive estimation in the standard UKF, and then the numerical stability of battery state of charge (SOC) estimation in real time can be well-guaranteed. Thirdly, the inner ohmic resistance as well as nominal capacity which could characterize the state of health (SOH) indirectly can be estimated online, and accordingly a high-precision estimation of SOC is able to be realized owing to the accuracy and efficiency of the battery model. The comparative experimental results confirmed and validated the feasibility and robustness of the fast SR-UKF algorithm as well as co-estimation strategy suggested.