## 1 Introduction
The model-based methods are dominated by Kalman filter and its derivatives. [PERSON] et al. [12] used an extended Kalman filter (EKF) along with a nonlinear battery model to estimate the SOC of the lithium-ion battery. In order to further improve the accuracy, adaptive extended Kalman filter (AEKF), unscented Kalman filter (UKF), and adaptive unscented Kalman filter (AUKF) are proposed. [PERSON] et al. [13] identified the parameters of an improved Thevenin battery model using EKF, and then adopted an AEKF for obtaining correct and robust SOC of the lithium-ion batteries. In [14], a UKF-based method was used to self-adjust the model parameters and provide state of charge estimation of the battery. References [15; 16] adopted AUKF to realize SOC estimation. In addition, an adaptive cubature Kalman filter (CKF) was proposed in [17] to improve the convergence rate and SOC estimation accuracy. To overcome the accuracy degradation caused by non-Gaussian noise, particle filters were utilized to estimate the SOC of batteries in [18; 19]. To compensate for the time-variability of battery parameters due to variational operating conditions and battery aging, a dual EKF and a dual UKF were employed in [20; 21] for simultaneous SOC and parameters estimation, respectively. The model-based methods eliminate the need for correct initial SOC values and accurate measurement, which are requisite for the CC method, and have no demand for a large amount of train data, so it is widely applied and is studied extensively. However, the estimation accuracy is strongly affected by the battery model and parameters. Once there is a model mismatch, the estimation performance will rapidly decline. In practical applications, the battery model parameters will change with SOC, temperature, and the degree of battery aging. Moreover, the statistic information of the process noise and sensor noise may be unknown or time-varying. Under these situations, the traditional KF-based methods will have low estimation accuracy and poor robustness. To address this issue, some researchers [22; 23; 24] resort to a Heo filter, which takes the time-varying battery parameter into account and has no need to know the statistics of the process noise and the measurement noise. It has strong robustness under uncertain conditions. However, the Hoo filter is a tradeoff between robustness and accuracy, so the SOC estimation accuracy is sacrificed to some extent for the robustness. [PERSON] et al. [25] combined the idea of square root filter and adaptive unscented Kalman filter (ASRUKF) algorithm based on improved Sage-Husa estimation to estimate the SOC of a lithium-ion battery. This method adaptively adjusted the values of the process and measurement covariances in the estimation process to improve the accuracy of SOC estimation. However, it does not consider the uncertainties brought by varying battery model parameters. [PERSON] et al. [26] proposed a multiple-model EKF (MM-EKF) and an autocovariance least squares (ALS) method for estimating the SOC of lithium-ion battery cells. MM-EKF reduced the dependence of the EKF algorithm on the correct assumptions of the measurement noise statistics by weighted summation of the estimates of multiple hypothesized EKFs. The ALS method extracted the possible correlation in the innovation sequence to estimate the measurement noise covariance. However, both methods leave out consideration of the time-varying battery parameters. Furthermore, the computation load is larger compared with the conventional EKF algorithm. In fact, the Bayesian approach is the most general approach of solving the problem with uncertain parameters. But it is hard to get the analytical solution for most Bayesian approaches due to complex probability density function or high dimension of integration.