## 2 Lithium-Ion Battery Modeling and Experimental Setup
### Co-Estimation of SOC and Model Parameters Based on UKF
The numerical comparison of the estimated SOC error is shown in Table 3. It can be seen that compared with the other two methods, the RMSE of SOC estimation results of the proposed method is reduced by 1.20-1.67% and the MAE is reduced by 0.97-1.28% in the pulse constant current discharge test, the RMSE is reduced by 0.82-9.18%, and the MAE is reduced by 0.73-0.85% in the dynamic discharge test. Figure 8: Comparison of different OCV construction methods in dynamic current discharge test. (**a**) Terminal voltage and OCV estimation result. (**b**) Estimation error of terminal voltage. (**c**) Comparison of SOC estimation result. (**d**) Comparison of SOC estimation error. Based on the above results and analysis, it can be seen that the proposed method can achieve accurate SOC estimation. It can maintain a small SOC estimation error in both the discharge process and relaxation stage because of the accurate fusion OCV curve and the joint estimation of SOC and model parameters online. ## 5 Conclusions

OCV and time-varying model parameters are essential reference variables for the model-based observer SOC estimation method for lithium-ion batteries. In this paper, we propose an OCV curve fusion method based on the increment test and low-current test. The fusion OCV curve is obtained by using the neural network algorithm to fit the fusion data set. The fusion OCV curve retains the non-linear characteristics of the cell electrode while almost eliminating the polarization effect. By designing the state equation including SOC and model parameters, we use the UKF algorithm to achieve a joint online estimation of SOC and model parameters. The experimental results show that the proposed method can achieve accurate and robust SOC estimation. The SOC estimation RMSE \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Test** & **Evaluating Indicator** & **UKF 1** & **PF 2** & **RLS-EKF 3** \\ \hline \multirow{2}{*}{Pulse constant current discharge test} & RMSE & 0.9918\% & 2.1932\% & 2.6907\% \\ \cline{2-5}  & MAE & 0.5866\% & 1.5567\% & 1.8705\% \\ \hline \multirow{2}{*}{Dynamic current discharge test} & RMSE & 1.6663\% & 10.8486\% & 2.4914\% \\ \cline{2-5}  & MAE & 1.0303\% & 1.8835\% & 1.7650\% \\ \hline \hline \end{tabular}

* The method of unscented Kalman filter(UKF). 2 The Particle Filter(PF) Method proposed in reference [6]. 3 The Recursive least square-Extended Kalman Filter(RLS-EKF) method proposed in reference [28].

\end{table} 
Table 3: Comparison of SOC estimation error for different estimation methods. Figure 9: Comparison of different SOC estimation methods. (**a**) Comparison of SOC estimation results of the pulse constant current discharge test. (**b**) The SOC estimation errors of the pulse constant current discharge test. (**c**) Comparison of SOC estimation results of the dynamic discharge test. (**d**) The SOC estimation errors of the dynamic discharge test. and MAE of the fusion OCV curve reached 0.99% and 0.58%, respectively. Furthermore, compared with the RLS-EKF and PF method, the SOC estimation RMSE and MAE reduced by 0.82-9.18% and 0.73-1.28%, respectively. Since the temperature is a critical factor affecting the cell model parameters, more future works are needed to verify and improve the proposed method. In addition, the effect of the aging process of lithium-ion batteries on the accuracy of SOC estimation is also needed for further research. Conceptualization, Y.W. and J.C.; Data curation, Y.W. ; Funding acquisition, L.Z. ; Methodology, Y.W. ; Project administration, L.Z. ; Software, Y.W. ; Validation, Y.W., J.Z. and S.W. ; Visualization, Y.W. ; Writing--Original draft, Y.W. ; Writing--Review and editing, Y.W., L.Z., J.C., J.Z. and S.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (Nos. 61633008, 61773132 and 61803115). The authors declare no conflict of interest. ## References

* [PERSON] et al.