# Lithium Battery SoC Estimation Based on Improved Iterated Extended Kalman Filter
## 1 Introduction  
With the continuous development of new energy vehicles, lithium-ion batteries have been widely used in the field of electric vehicles due to their high energy density and long cycle life [1, 2]. In order to enable the battery to provide stable and reliable energy and avoid the phenomenon of over-charge or over-discharge, it is very important to accurately estimate the state of charge (SoC) of the battery. The SoC of the battery represents the ratio of the available power of the battery at this time to the total power that can be stored in it [3], reflecting the remaining capacity of the battery at this moment [4]. Since most of the energy in the battery is output to the outside world in the form of current, the charge-discharge current is a key clue for analyzing the SoC. In addition, during the charge-discharge cycle, the maximum usable capacity of the battery will gradually decay. This means that the maximum value of the SoC will change, but since the SoC is a real-time estimate, this weak attenuation phenomenon is insignificant for the real-time change caused by the SoC compared to the charge or discharge current. Combined with the performance requirements in the use of electric vehicles and the meaning of SoC, it is not difficult to see that it is important to accurately estimate theSoC, which is not only related to the range of electric vehicles but also directly affects the performance of the battery. Accurate estimation of SoC is related to the driving range and performance of electric vehicles, but SoC cannot be measured directly and can only be obtained through indirect estimation methods [5]. Therefore, researchers constantly try to improve and optimize SoC estimation algorithms to meet the needs of high accuracy, real-time performance, and high efficiency in the field of electric vehicles. Currently, common SoC estimation methods include the ampere-hour integration method, open-circuit voltage method, neural network method, Kalman filter (KF) method, etc. [6]. For the ampere-hour integration method, its accuracy is highly dependent on the accuracy of the current measurement and the accuracy of the initial SoC value [7]. With the increase in time, the error will be accumulated, and the estimation result will become worse [8]. The open-circuit voltage method can estimate the SoC according to the open-circuit voltage at this time, but this method is not suitable for real-time estimation [9] because the accurate measurement of the open-circuit voltage usually requires the battery to stand for a long time to reach a stable state [10,11]. The accuracy of battery SoC estimation using the neural network method is relatively high [12], but the high-precision estimation results depend on a large amount of sample data training, and the algorithm requires a large number of calculations [13]. For example, [PERSON] et al. [14] used the extended Kalman filter (EKF) to predict the lithium-ion battery SoC, and the prediction error was kept at about 3%, which avoided the shortcomings of the poor adaptability of the Kalman filter to the nonlinear model. Some scholars [15] use the unscented Kalman filtering (UKF) method to predict the battery SoC, which is based on the unscented transform. It obtains good prediction results in the early and late stages of battery charging and discharging, with a fast convergence speed. Some scholars have introduced the iterated extended Kalman filter (IEKF) algorithm in the process of computing SoCs to improve the estimation accuracy. However, that too many iterations of the IEKF method will lead to an increase in the computation time. Therefore, the improvement effect of the estimation accuracy of the SoC is not obvious within a limited number of iterations. More deeply, [PERSON] et al.