## 5 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**MAE**} \\ \hline  & \(-20\)\({}^{\circ}\)C & \(-10\)\({}^{\circ}\)C & \(0\)\({}^{\circ}\)C & \(10\)\({}^{\circ}\)C & \(20\)\({}^{\circ}\)C & \(30\)\({}^{\circ}\)C & \(40\)\({}^{\circ}\)C & \(50\)\({}^{\circ}\)C \\ EKF & 4.2556 & 2.8469 & 2.4179 & 2.1860 & 2.1458 & 1.7587 & 1.3136 & 1.2558 \\ UKF & 3.9459 & 2.6408 & 1.8307 & 2.0419 & 2.1688 & 1.7202 & 1.1985 & 1.1593 \\ STF & 3.2692 & 2.2711 & 1.6102 & 1.9618 & 1.9292 & 1.5580 & 1.0925 & 1.1274 \\ \hline  & \multicolumn{8}{c}{**RMSE**} \\ \hline  & \(-20\)\({}^{\circ}\)C & \(-10\)\({}^{\circ}\)C & \(0\)\({}^{\circ}\)C & \(10\)\({}^{\circ}\)C & \(20\)\({}^{\circ}\)C & \(30\)\({}^{\circ}\)C & \(40\)\({}^{\circ}\)C & \(50\)\({}^{\circ}\)C \\ EKF & 5.7263 & 3.1847 & 2.8112 & 2.3636 & 2.2978 & 1.9360 & 1.5081 & 1.4964 \\ UKF & 4.6393 & 2.6023 & 2.0419 & 2.1297 & 2.2687 & 1.8886 & 1.3736 & 1.3426 \\ STF & 4.0924 & 2.5410 & 1.8461 & 2.1017 & 2.0763 & 1.7240 & 1.2160 & 1.2795 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The statistical data of MAE and RMSE for EKF, UKF, and STF. Figure 13: The MAE and RMSE of EKF, UKF, and STF at different temperatures. Figure 14: Robustness performance results with a SOC guess of 80% at a temperature of 0 \({}^{\circ}\)C: (**a**) SOC estimation results; (**b**) the enlarged window from 0 to 1500 \(\mathrm{s}\); (**c**) SOC estimation error. To further discuss this topic, the initial SOC guess was set to 80%, 50%, and 30%, respectively. Figure 15 shows the part of the estimation results, and all the cases were summarized in Table 5 for comparison. There was an interesting point that could be noted in Figure 15. Regardless of the initial SOC guess values, all the curves converged at a specific point. After that point, the estimated curves present overlapped. We called this occurrence the convergence point, because it represented the convergence time of the algorithm. Judging from the position of the convergence point, the convergence times of UKF and STF were almost the same but a bit less than that of EKF. All the three algorithms were less than 2.5% of the whole operation time. This result is satisfactory for BMS applications. Figure 15: _Cont._  
Finally, we were also interested in the robustness against the voltage measurement signal of the three algorithms. The quality of the acquired voltage signals was always a challenge for BMS, especially when the BMS was exposed to the vehicle's high electromagnetic interference environment. Hence, a constant \(-5\) mV voltage measurement offset is designed to simulated the real-world voltage sensor drift in the BMS. We used the test datasheet of 30 \({}^{\circ}\)C for validation. The voltage offset data was embedded in the validation test datasheet of 30 \({}^{\circ}\)C with the initial SOC at 100%. As shown in Figure 16, the STF had minimum error and the fastest convergence rate. Moreover, the MAE and RMSE of the three algorithms were tabulated in Table 6. With the same initial SOC, the MAE and RMSE of three algorithms were arranged from large to small by EKF, UKF, and STF sequence, thereby suggesting that STF was the most robust. Figure 15: The robustness results for three algorithms: (**a**) EKF; (**b**) UKF; (**c**) STF. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**MAE**} \\ \hline Initial SOC Guess (\%) & EKF & UKF & STF \\
80 & 2.431 & 1.906 & 1.603 \\
50 & 2.632 & 2.043 & 1.732 \\
30 & 2.761 & 2.122 & 1.826 \\ \hline \multicolumn{4}{c}{**RMSE**} \\ \hline Initial SOC Guess (\%) & EKF & UKF & STF \\
80 & 2.936 & 2.260 & 1.980 \\
50 & 4.045 & 3.173 & 2.967 \\
30 & 5.032 & 3.884 & 3.805 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The MAE and RMSE by EKF, UKF, and STF at 0 \({}^{\circ}\)C.