## 5 Results and Discussion
However, the MAE and RMSE of MIUKF-FSRCKF-estimated SOC are only 0.54% and 0.65%, respectively, and the MAE and RMSE of voltage error are only 4.8 mV and 6.1 mV, respectively. This is basically the same as the situation in which the identified \(R_{0}\) is directly used as the initial \(R_{0}\) to estimate SOC under the FUDS condition. The results show that this algorithm has high precision, higher practicability and stronger  
Figure 7: Comparison of the results of the four algorithms under BJDST: (**a**) SOC estimation result; (**b**) SOC error; (**c**) voltage estimation result; (**d**) voltage error. \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 & 1.63 & 5.0 & 6.7 \\ FCKF & 0.82 & 0.99 & 3.9 & 5.0 \\ FSRCKF & 0.61 & 0.73 & 3.6 & 4.7 \\ MIUKF-FSRCKF & 0.58 & 0.72 & 3.5 & 4.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SOC error and voltage error of each algorithm under the US06 test. \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 & 2.53 & 2.83 & 16.9 & 24.1 \\ FCKF & 1.66 & 2.12 & 12.3 & 17.6 \\ FSRCKF & 1.32 & 1.63 & 12.2 & 17.5 \\ MIUKF-FSRCKF & 0.54 & 0.65 & 4.8 & 6.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: SOC error and voltage error of each algorithm under the FUDS test. (The identified R0 by AGA is increased by 20% as the initial value of R0.) Figure 10: Comparison of the results of the four algorithms under the FUDS test. The identified \(R_{0}\) is increased by 20% as the initial value of \(R_{0}\): (**a**) SOC estimation result; (**b**) SOC error; (**c**) voltage estimation result; (**d**) voltage error. \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 & 2.48 & 2.79 & 7.2 & 9.8 \\ FCKF & 1.77 & 2.25 & 5.3 & 7.1 \\ FSRCKF & 1.35 & 1.70 & 5.1 & 6.9 \\ MIUKF-FSRCKF & 0.62 & 0.83 & 3.5 & 4.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: SOC error and voltage error of each algorithm under BJDST. (The identified \(R_{0}\) by AGA is increased by 20% as the initial value of \(R_{0}\). )The graph of real-time estimation of \(R_{0}\) by MIUKF-FSRCKF under different tests is given in Figure 13.  
For SOC estimation of the four algorithms under FUDS, BJDST and US06 operating conditions, the identified \(R_{0}\) by AGA is increased by 20% as the initial value of \(R_{0}\). Among them, the SOC error of FSRCKF is smaller than SRCKF and FCKF, but the estimation error of these three algorithms is large. MIUKF-FSRCKF estimates and updates \(R_{0}\) in real time on the basis of FSRCKF, so that the estimation effect of SOC is significantly improved. Both SOC error and voltage error are significantly better than the other three algorithms, and the estimated SOC curve is still close to the reference SOC curve, which indicates that the algorithm is not only highly accurate but also highly practical. Figure 11: Comparison of the results of the four algorithms under BJDST. The identified R\({}_{0}\) is increased by 20% as the initial value of \(R_{0}\): (**a**) SOC estimation result; (**b**) SOC error; (**c**) voltage estimation result; (**d**) voltage error. \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 & 2.44 & 2.73 & 13.7 & 18.3 \\ FCKF & 1.79 & 2.26 & 9.7 & 13.0 \\ FSRCKF & 1.37 & 1.70 & 9.6 & 13.0 \\ MIUKF-FSRCKF & 0.53 & 0.68 & 3.5 & 4.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: SOC error and voltage error of each algorithm under the US06 test.