# Online SoC Estimation of Lithium-Ion Batteries Using a New Sigma Points Kalman Filter
## 4 Experimental Results
### The Experimental Validation  
The battery test platform established in Section 4.1 was used to verify the ECM established in Section 2 of this article and the algorithm proposed in Section 3. We first charged the battery sample at constant current and constant voltage to the cut-off voltage of 4.2 V and let it stand for 1 h, discharged at 20% at constant current, and let it stand for another 1 h. At this moment, the initial value of the true SoC of the battery was 0.8. To verify the effectiveness of the proposed estimation method in the presence of initial SoC error, different hypothetical initial SoC values of 0.7 and 0.9 were set. The four algorithms, i.e., the proposed algorithm, UKF, CDKF and EKF, were used to estimate the SoC under FUDS and US06 charging and discharging conditions, respectively, and compare the initial error correction ability and robustness of the four algorithms. The charge and discharge test results of the battery are shown in Table 5.  
In order to verify the effectiveness of the proposed algorithm, the battery was tested under two dynamic conditions of US06 and FUDS. The US06 is a high acceleration aggressive driving schedule that is used by the United States Environmental Protection Agency for vehicle emissions and fuel economy testing [41]. The FUDS is an urban driving schedule based on an automobile industry standard [42]. The current of the battery constantly changes under dynamic working conditions, which can better simulate the actual operation of electric vehicles. Figure 7 show the current excitation of the battery under the US06 operating condition, and Figure 8 show the current excitation of the battery under the FUDS operating condition. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Serial Number** & **Condition** & **The Initial True SoC** & **The Initial SoC Guess** \\ \hline
1 & FUDS & 0.8 & 0.7 \\
2 & FUDS & 0.8 & 0.9 \\
3 & US06 & 0.8 & 0.7 \\
4 & US06 & 0.8 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Battery charge and discharge tests. Figure 6: Real-time SoC estimation platform based on dSPACE Rapid Prototyping Systems. (VAF) of the SoC is shown. The error results have been combined in Table 6. The time of initial error convergence is shown in Table 7.  
Figure 14: The four evaluation indexes of the initial SoC guess were 0.9 under the FUDS condition. Figure 13: The four evaluation indexes of the initial SoC guess were 0.7 under the FUDS condition. Figure 16: The four evaluation indexes of the initial SoC guess were 0.9 under the US06 condition. Figure 15: The four evaluation indexes of the initial SoC guess were 0.7 under the US06 condition. By analyzing Tables 6 and 7, we can see that in the four conditions of the experiment, three evaluation indicators (RMS Error-MAE and SI) of CDKF and EKF were higher than the other two algorithms because these two algorithms approximate the posterior mean and covariance of the state with first-order accuracy. Compared with CDKF, the RMS of the proposed algorithm was reduced from 2.01%, 1.22%, 1.92%, 1.29% to 0.65%, 0.61%, 0.46%, 0.47%, respectively. The newly proposed algorithm could use the Sigma points in the UT transformation to approximate the posterior mean and covariance of the state with third-order Taylor accuracy in all four conditions. The calculation convergence time was close to that obtained with the UKF algorithm, achieving the effect of quickly correcting the initial error. The MAPE was found to be less than 2%. The VAF of the proposed algorithm ranked first three times and ranked second once (the initial SoC guess was 0.9 under the FUDS condition). The proposed algorithm showed better robustness in three of the four working conditions.