## 2 Lithium-Ion Battery Modeling and Experimental Setup
### Co-Estimation of SOC and Model Parameters Based on UKF
Figure 8 shows the experimental results of the dynamic current discharge test. It can be seen from Figure 8a,b that the estimated terminal voltage errors are 0.001-0.023 V during the dynamic discharge process. The OCV estimation results change with the DOD. Furthermore, the OCV estimation results slowly converge to the measurement of the terminal voltage in the relaxation stage. They are in line with expectations. From Figure 8c, it can be seen that the SOC estimation results based on the fusion OCV curve have the best tracking performance, and can converge to the reference value in the relaxation stage. Figure 8d is the SOC estimation absolute error. It is similar to the pulse constant current discharge test, and the SOC estimation error based on the fusion OCV curve is least. The SOC estimation error based on the low-current test OCV curve will accumulate with the increase of the discharge time. The SOC estimation error based on the increment test OCV curve is significant, and the convergence result of the relaxation stage is biased. From Table 2, it can be seen that the RMSE of SOC estimation results based on the fusion OCV curve is reduced by 0.26-1.69%, and the MAE is reduced by 0.17-0.76% compared with the other two methods. The above two test results show that the fusion OCV curve has the highest OCV description accuracy, which almost eliminates the polarization effect on the measurement results and preserves the non-linear characteristics of the electrode. The low-current test is affected by the polarization effect, and the deviation between the OCV measurement and the actual value increases continuously with the DOD, resulting in the steady-state error of the SOC estimation results. The poor accuracy of the incremental test-based OCV curve results in a significant error in the SOC estimation results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Test** & **Evaluating** & **Fusion OCV** & **Low Current** & **Increment Test** \\  & **Indicator** & **Curve** & **Test OCV Curve** & **OCV Curve** \\ \hline \multirow{2}{*}{Pulse constant current discharge test} & RMSE & 0.9918\% & 3.9525\% & 2.0772\% \\ \cline{2-5}  & MAE & 0.5866\% & 3.6636\% & 1.5856\% \\ \hline \multirow{2}{*}{Dynamic current discharge test} & RMSE & 1.6663\% & 1.9236\% & 2.3598\% \\ \cline{2-5}  & MAE & 1.0303\% & 1.2070\% & 1.7902\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of SOC estimation error for different OCV Curves. ### Comparison of Different SOC Estimation Methods

Figure 9 shows the comparison results between the proposed method with the RLS-EKF [6] and PF [28] SOC estimation method. Note that those estimation methods are all based on the fusion OCV curve. Figure 9a,c are the SOC estimation results of the pulse constant current discharge test and the dynamic discharge test, respectively. It can be seen from the zoom view of Figure 9a,c that the proposed method has higher accuracy of SOC estimation in the discharge process, and can converge to the SOC reference value in the relaxation stage. The SOC estimation accuracy of the RLS-EKF method and the PF method in the discharge process is poor, and there is a sizeable steady-state error between the SOC estimation results and the reference values in the relaxation stage. Figure 9b,d are the SOC estimation absolute errors of the two tests. It can be seen that the proposed method can maintain a small SOC estimation error in the whole discharge and relaxation process, while the SOC estimation error of the RLS-EKF and PF methods is bigger. This is because the cell internal resistance, the polarization internal resistance as well as the polarization capacitance change greatly when SOC is at 40-50% and below 10%, the PF method cannot adapt to the time-varying model parameters, and the RLS-EKF method cannot accurately estimate the model parameters due to the effect of the environmental noise and measurement noise.