## 5 Results and Discussion  
In this paper, real-time current and voltage values of the Federal Urban Driving Plan (FUDS), Beijing Dynamic Stress Test (BJDST) and US06 Highway Driving Plan were used to verify and analyze the algorithm. Since the open source data used only provided data with SOC ranging from 0 to 0.8, and considering that the battery life will be seriously damaged if the battery level is lower than 10% in practical applications, the SOC in this paper is kept between 0.1 and 0.8 [31]. Figure 6 shows the SOC estimation by the four methods under the FUDS condition. Table 3 shows the SOC error and prediction voltage error of each method under the FUDS test. From the data comparison in the figure and table, it can be seen that the SOC estimation error and the voltage error of FSRCKF are smaller than those of FCKF and SRCKF. However, the accuracy of MIUKF-FSRCKF is slightly better than that of FSRCKF. BJDST and US06 are also used to compare and verify the four algorithms in this paper, and the corresponding outcomes are shown in Figures 7 and 8. The graphs of real-time estimation of \(R_{0}\) by MIUKF-FSRCKF under different tests are given in Figure 9. Tables 4 and 5 show the SOC error and prediction voltage error of each method under the BJDST and US06 tests, respectively. In summary, the accuracy of FSRCKF in estimating battery SOC is better than that of SRCKF and FCKF. The accuracy of MIUKF-FSRCKF is similar to that of FSRCKF, but the advantage is not obvious. This is because the DST  
Figure 5: The schematic diagram of MIUKF-FSRCKF. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**SOC Error (\%)**} & \multicolumn{2}{c}{**Voltage Error (mV)**} \\  & **MAE** & **RMSE** & **MAE** & **RMSE** \\ \hline SRCKF & 1.35 & 1.65 & 7.1 & 9.6 \\ FCKF & 0.91 & 1.05 & 5.3 & 6.8 \\ FSRCKF & 0.62 & 0.71 & 5.1 & 6.5 \\ MIUKF-FSRCKF & 0.56 & 0.66 & 4.7 & 6.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SOC error and voltage error of each algorithm under the FUDS test. used for identifying the parameters and the other three tests for verifying the algorithm are conducted successively; that is, the battery aging condition under these four tests has not changed significantly. Hence, the \(R_{0}\) identified offline is accurate, and the advantages of online estimation of \(R_{0}\) and updating \(R_{0}\) of MIUKF-FSRCKF cannot be reflected. In practice, \(R_{0}\) will gradually increase with the aging of the battery, so the initial \(R_{0}\) may not be accurate. In order to simulate the actual application, the identified \(R_{0}\) is increased by 20% as the initial \(R_{0}\). The SOC estimation accuracy of each algorithm is verified. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**SOC Error (\%)**} & \multicolumn{2}{c}{**Voltage Error (mV)**} \\  & **MAE** & **RMSE** & **MAE** & **RMSE** \\ \hline SRCKF & 1.27 & 1.62 & 3.3 & 4.2 \\ FCKF & 0.84 & 1.03 & 4.4 & 5.2 \\ FSRCKF & 0.64 & 0.76 & 4.1 & 4.8 \\ MIUKF-FSRCKF & 0.69 & 0.85 & 3.5 & 4.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SOC error and voltage error of each algorithm under BJDST. Figure 6: Comparison of the results of the four algorithms under the FUDS test: (**a**) SOC estimation result; (**b**) SOC error; (**c**) voltage estimation result; (**d**) voltage error. SOC estimation of the four algorithms is carried out under the FUDS test by taking 1.2 times the identified \(R_{0}\) as the initial value of \(R_{0}\), and the results are shown in Figure 10 and Table 6. The MAE and RMSE of SOC estimated by SRCKF, FCKF and FSRCKF are all more than 1%, and the MAE and RMSE of voltage error are all more than 10 mV. This is much worse than under the FUDS test, when the identified \(R_{0}\) is directly used as the initial \(R_{0}\) to estimate SOC (namely, the data in Table 1), indicating that the practicability of these three algorithms is not high.