Real-time SOC co-estimation algorithm for Li-ion batteries based on fast square-root unscented Kalman filters

The Li-ion battery is an important energy source for electric vehicles (EVs), and the accurate estimation of the battery power state provides a reliable reference for balancing the battery packing and battery management system (BMS). It also has great practical significance for making full and reasonable utilization of batteries, and improving the battery life cycle and vehicle operation efficiency. Practical issues that must be addressed include the filtering divergence caused by the non-positive definite error covariance matrix in the standard unscented Kalman filter (UKF) and the state estimation errors that accumulate from the simplified mathematical modeling of the Li-ion battery, with its inherently strong non-linearity, time variation, and uncertainty. To resolve these issues, in this article, a real-time state co-estimation algorithm was proposed based on a fast square-root unscented Kalman filter (SR-UKF) framework. First, during the iteration process, the non-linear measurement function, which describes the propagation of each sigma point, is called by an unscented transform. A reduction in computational complexity can be achieved if the non-linear measurement function is quasi-linearized. Second, instead of a state error covariance matrix, the square root of the state error covariance matrix is used, which is obtained by QR decomposition and first-order updating of the Cholesky factor. This step deals with the problem that arises if the state error covariance matrix is negative definite due to the computational errors accumulated while performing recursive estimation with the standard UKF. This guarantees the numerical stability of the battery’s estimated state of charge (SOC) in real time. Third, the inner ohmic resistance and nominal capacity that indirectly characterize the state of health can be estimated online, and a highly precise SOC estimation can be realized due to the accuracy and efficiency of the battery model. Comparative experimental results confirm and validate the feasibility and robustness of the proposed fast SR-UKF algorithm and co-estimation strategy.