## 1 Introduction  
The recent problems with energy and the degradation of the environment have posed significant difficulties for individuals. The current rapid development of electric vehicles (EVs) not only effectively reduces the pressure on oil resources but also reduces the harm noise and air pollution inflict on people. As the key component of an electric vehicle, a power battery is not only the energy source of an electric vehicle but also an important energy storage device, which enormously influences the safety as well as performance of electric vehicles. In accordance with formula (1), the state of charge (SoC) of a power battery is the proportion between the battery's remaining capacity and its maximum capacity under certain conditions. Accurate battery estimates are a vital factor in ensuring battery performance, enhancing service safety and extending service life according to the SoC [1, 2]. \[SoC=\frac{Q_{t}}{Q}\times 100\% \tag{1}\]  
In the equation above, \(Q_{t}\) denotes the capacity of a battery at time \(t\), and \(Q\) denotes a battery's maximum capacity. Based on relevant investigations, a variety of methods are frequently employed to estimate the SoC of power batteries. Some of these methods include the Ampere-Hourintegral method [3], the open circuit voltage (OCV) method [4], the model-based Kalman filter (KF) [5], and data-based neural networks [6]. Regarding the estimation of SoC, there is a cumulative error in the open-circuit voltage method, and the Ampere-Hour integral method cannot make estimates in real time. The model-based Kalman filter [7] is an optimal recursive estimation method for dynamic linear system state estimation. It is a recursive predictive filtering algorithm. This method has good path-tracking performance and high accuracy. It is an effective online SoC estimation method [8], but the observation equation required by this method must be linear. To solve the optimal estimation problem in non-linear systems, scholars have proposed an extended Kalman filter (EKF) [9] algorithm for nonlinear system models. [PERSON] [10; 11; 12] first proposed a series of EKF-based SoC estimation algorithms for electric vehicle power batteries, which laid a theoretical foundation for the development of the EKF algorithm. However, the EKF algorithm linearizes nonlinear systems through Taylor series expansion, omits the high-order term, and thus introduces high-order loss error. [PERSON] et al. [13] implemented the dual extended Kalman filter (DEKF) in an electrochemical model and proposed a battery SoC estimation method based on OCV-SoC. The obtained simulation results showed that the model method had good accuracy, and the initial error was less than \(\pm 5\%\). [PERSON] et al. [14] used EKF and DEKF methods to estimate the SoC of a LiFePO4 battery under different state models, and the results showed that the maximum error of the estimated SoC was \(4\%\). [PERSON] et al. [15; 16] proposed an online estimation method of battery open circuit voltage using an adaptive extended Kalman filter (AEKF) and evaluated four different types of lithium batteries' (LiB) SoC according to the improved Thevenin model and the OCV-SoC relationship. This method reduces the SoC estimation error by \(4\%\). With the rapid development of the field of machine learning, the authors of [17] obtained battery parameters such as current, voltage, and temperature through experiments and used the improved backpropagation neural network (BPNN) to estimate the SoC value of a battery. In order to further improve the SoC estimation accuracy of power batteries, the researchers combined a data-based neural network with a filtering algorithm to compensate for the inaccuracy of the model and the complexity of calculation. The authors of [18; 19] used a BP neural network to compensate for the error caused by the EKF linearization process to optimize SoC estimation accuracy.