# Lithium Battery SoC Estimation Based on Improved Iterated Extended Kalman Filter
## 1 Introduction
[16] proposed a thermoelectrochemical coupling model for the EKF algorithm, which helps to solve the SoC estimation problem when there is a certain error in the initial voltage measurement, through which the estimated SoC value of the EKF algorithm can quickly reduce the estimation error within 200 s after starting. [PERSON] et al. [17] used the PNGV equivalent circuit model combined with the adaptive fading unscented Kalman filter algorithm to estimate the battery SoC, which improved the accuracy and convergence speed of the filter. However, the complexity of the PNGV model is high, which increases the computational requirements. Through the exploration of the current research status of SoC prediction, it is not difficult to find that the various filtering algorithms based on the Kalman filter algorithm are the most promising directions. However, the shortcomings of the Kalman filter method, such as its slow convergence speed, still need to be further improved. Researchers must strive to avoid its shortcomings while giving full play to the characteristics of the Kalman filter estimation effect and low calculation difficulty. The characteristics of various common SoC estimation methods are shown in Table 1.  
In order to solve the problems in the estimation process of the above algorithms, this paper takes the INR 18650-20R lithium battery (the manufacturer is South Korea Samsung Company, sourced from Seoul, South Korea, purchased in Shenzhen, China) as \begin{table}
\begin{tabular}{c c c} \hline \hline
**Estimation Methodology** & **Estimation Accuracy** & **Estimation of the Level of Complexity** \\ \hline Ampere-hour integration method & Poor & Easy \\ Open-circuit voltage method & Poor & Complex \\ Neural network method & High & Very complex \\ Kalman filter and its derivative & High & Generally complex \\ algorithms & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of various estimation methods. the research object, establishes a second-order Thevenin equivalent circuit model to simulate the characteristics of lithium batteries, identifies the equivalent parameters of the battery through HPPC testing, and plots the OCV-SoC curve according to the parameters obtained by HPPC testing. Finally, it constructs the expression of the battery equivalent model. Then, different simulation conditions are set up to estimate the SoC of the battery, and the LM-IEKF algorithm is innovatively proposed, which fuses the LM (Levenberg-Marquardt) method with the IKEF algorithm [18]. A multi-step iteration strategy based on the LM algorithm is used to estimate the state and error covariance of the update stage, and the iteration process is optimized. Finally, in order to verify the LM-IEKF algorithm proposed in this paper, the EKF and IEKF algorithms are used to estimate the value of the SoC under the same working conditions, and the error of the three algorithms is compared. It is proved that the LM-IEKF algorithm proposed in this paper has the characteristics of a high accuracy, fast convergence speed, and strong robustness, and it can be well adapted to the situation of large current fluctuations. The LM-IEKF algorithm proposed in this paper gives full play to the characteristics of the high prediction accuracy of the Kalman filter method, obtains good SoC estimation results, and also overcomes the problems of slow convergence speed and high computational complexity, which has good practical significance. Currently, with the increasing development of new energy technology, it is important not only for the field of electric vehicles but also for the scientific and technological development of unmanned robots and energy storage tools.