## 1 Introduction
These model-based estimators include the electrochemical model, the Equivalent Circuit Model (ECM), and the empirical model. The electrochemical model is the most precise model among the others, wherein it describes the electrochemical reaction processes of the battery by adopting a set of partial differential equations. However, it is also the most complicated model for the limited BMS computational resource. Meanwhile, the empirical model usually has a simple model structure with a low computation demand. However, a large number of experiments are required to build a database. Moreover, for most BMS applications, the ECM is used as a solution, because it meets the best compromise between the accuracy and model complexity. Currently, the combinations of ECM and system filtering theory have drawn continuous attention by scholars and industry developers. Among all the system filtering theories, the Kalman filter (KF) is the most frequently used [12]. Compared with other system filtering algorithms, the KF method does not need an accurate initial value of SOC because the result will gradually approach the optimal value and the current measurement error will be updated during the operational process of the algorithms. Meanwhile, it is a closed-loop observer, and it can achieve accurate and continuous estimation performance during the whole range of battery operations. The abovementioned advantages make KF a promising solution for BMS application implementation. Moreover, the ordinary KF is only suitable for linear systems, whereas the BMS applications require the use of more complex and nonlinear algorithms. Several advanced modifications have been proposed, such as an extended Kalman filter (EKF), unscented Kalman filter (UKF), and Central-Difference Kalman filter (CDKF). [PERSON] was the first to establish EKF for SOC estimation [13; 14; 15; 16]. Based on his pioneeringwork, a great variety of research concerning the applications of EKF to the non-linear system have been reported in several literatures [17; 18; 19; 20; 21; 22]. However, EKF is essentially a first-order Taylor series expansion of the state-space equations that have the theoretical limitation of estimation accuracy under the case of high dynamic current change. In addition, the EKF needs to calculate the Jacobi matrix, which leads to the algorithm being inefficient or even numerical instabilities in the implementation of a low-cost microcontroller. As an alternative system linear approach, the UKF was developed to improve the estimation accuracy and to compute reliability Theoretically, all KF variants require the knowledge of process and measurement noise covariance. Inappropriate tuning parameters may lead to low convergence and high oscillation. Therefore, adaptive technology has been introduced to combine with the KFs. [PERSON] et al. [23] presented an adaptive UKF to estimate the SOC of EV applications. The adaptive adjustment of the noise covariance was dealt by covariance matching methods. [PERSON] et al. [24] proposed a data-driven-based approach for SOC estimation by employing an adaptive EKF algorithm. Their methods achieved good accuracy and convergence for different types of lithium-ion batteries. To summarize, a modern smart algorithm for online SOC estimation in a BMS application requires the following characteristics: capable of describing the first- or second-order nonlinear behavior of battery system under dynamic excitation; adaptive adjustment for system noise matrices and high converge robustness against the drastic change of current; numerical stability; and ease of implementation in an embedded chip. To address the abovementioned problems, an optimized model-based algorithm combined with Strong Tracking Filter (STF) was put forward for online SOC monitoring. The one-state hysteresis model was applied to state-space function and the hysteresis voltage was considered in terms of temperature.