## 4 Simulation and Results Analysis
### The Comparative Test under Constant Current Discharge Conditions  
The battery was discharged at 0.5 C with a simulation duration of 2000 s and a sampling interval of 20 s. The simulation results were shown in Figures 3 and 4. \"AKF\" stands for the adaptive Kalman filter method; \"KF\" stands for the Kalman filter SOC estimate. It could be seen from Figures 3 and 4 that the adaptive Kalman filter method was featured with an SOC estimation error of less than 2%, which was higher than the SOC estimation accuracy of the Kalman filter method. Additionally, as can be seen from the figures, the AKF method tends to be stable at about 300 s while the KF method needs about 1100 s. This proves that the AKF method converges quickly, which is very important in practical applications. Therefore, the adaptive Kalman filter method could effectively reduce the influence of unknown noise on SOC estimation. current working condition. Table 2 shows a detailed step for the entire complete BBDST condition. The total time from the start of the bus to the last stop was 300 seconds [39]. This article used the LANBTS battery test system platform for the BBDST experiments. The SOC interval selected the platform area of 0.1-0.9. Since the experimental equipment was a single battery, the power output from the lithium-ion battery should be adjusted in proportion according to the output power in the standard BBDST operating condition. After conversion, we finally set the ratio of the output power of the lithium-ion battery to the output power of the standard BBDST condition to 1:5000. The specific experimental methods were as follows [39]:  
1. Charged the battery to the cut-off voltage at a temperature of 25 \({}^{\circ}\)C.
2. After that, it was discharged with a constant current rate of 1 C to SOC = 0.9, and then allowed to stand for 1 h.
3. Performed a complete BBDST test on the lithium-ion battery, then stopped the loading power, and continued to test the lithium-ion battery for a complete BBDST condition after 10 min of static. The above test steps were repeated for achieving 15 complete BBDST condition test cycles. 4. Re-discharged the battery at the 1 C rate until the battery was discharged to the cut-off voltage, finally terminated the discharge, and recorded the experimental data. Superimposed random noise processing was performed on the current and voltage data obtained by the test. The SOC accurate value was obtained by the OCV method and the ampere-hour method before the superimposed noise was taken as a comparison value of the SOC estimation. The superimposed noise data was substituted into the SOC estimation program designed above for simulation calculation. Finally, the following two figures could be drawn. It can be seen from Figures 7 and 8 that although the SOC estimation error in the BBDST operating condition followed the pulse change sharply, the maximum error still did not exceed 4%. It could be considered that this design meets the requirements (error \(\leq\) 5%). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Condition** & **Step Time (s)** & **Cumulative Time (s)** & **Battery Output Power (kW)** \\ \hline Start & 21 & 21 & 37.5 \\ Accelerating & 12 & 33 & 72.5 \\ Coastdown & 16 & 49 & 4.5 \\ Brake & 6 & 55 & \(-\)15 \\ Accelerating & 21 & 76 & 37.5 \\ Coastdown & 16 & 92 & 4.5 \\ Brake & 6 & 98 & \(-\)15 \\ Accelerating & 9 & 107 & 72.5 \\ Rapid acceleration & 6 & 113 & 92.5 \\ Uniform speed & 21 & 134 & 37.5 \\ Coastdown & 16 & 150 & 4.5 \\ Brake & 6 & 156 & \(-\)15 \\ Accelerating & 9 & 165 & 72.5 \\ Rapid acceleration & 6 & 171 & 92.5 \\ Uniform speed & 21 & 192 & 37.5 \\ Coastdown & 16 & 208 & 4.5 \\ Brake & 9 & 217 & \(-\)35 \\ Brake & 12 & 229 & \(-\)15 \\ Parking & 71 & 300 & 4.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The BBDST working condition. In actual use, computation time and calculation accuracy are equally important.