## 3 Results and Discussion
### Model Validation and ANOVA Results
From the ANOVA, it can be said that rest time has the most pronounced effect on the signal-to-noise ratio, with 180 s offering the best performance. Lower C-rates and moderate discharge pulse times (between 100 and 150 s) are also beneficial. Overall, adjusting the rest time and C-rate can substantially improve the accuracy of battery parameter identification based on the \"Smaller is better\" criterion. Figure 7: The effect of input parameters (pulse time gap, discharge pulse time, discharge pulse C-rate, and rest time) on RMSE values for different ambient temperatures, (**a**) \(-10\)\({}^{\circ}\)C, (**b**) 25 \({}^{\circ}\)C, (**c**) 40 \({}^{\circ}\)C.  
At an ambient temperature of 25 \({}^{\circ}\)C (Figure 7b), the S/N ratio increases significantly from 50 to 200 s, indicating that increasing the pulse time gap improves the system's performance. The discharge pulse time has a marked effect on the S/N ratio, as shown by the peak at 125 s. There is a significant rise from 50 to 125 s, followed by a sharp decrease at 200 s. This suggests that the optimal discharge pulse time for achieving better signal-to-noise performance is around 125 s. Any further increase in discharge time might introduce negative effects, such as thermal instability, which degrade the precision of parameter estimation. The C-rate parameter has a relatively flat trend, but there is a slight decline in the S/N ratio as the C-rate increases. In terms of rest time, there is an increase in the S/N ratio from 60 to 120 s, followed by a slight decrease at 180 s.  
At an ambient temperature of 40 \({}^{\circ}\)C (Figure 7c), there is a sharp increase in the S/N ratio from 50 s to 125 s, indicating that increasing the pulse time gap significantly improves the precision of the parameter identification. However, after this peak at 125 s, the S/N ratio decreases sharply at 200 s. This suggests that while a pulse time gap of 125 s yields the best performance, extending the pulse time gap to 200 s may introduce detrimental effects, such as reduced accuracy or increased variability. The discharge pulse time exhibits a fluctuating trend. The S/N ratio increases slightly at 125 s, then drops at 200 s. The C-rate shows a relatively flat trend, with only minor variations in the S/N ratio. A slight increase can be observed between 2.9 and 5.8, followed by a decrease at 8.7. The rest time has a similar trend to the previous graphs, showing a drop in the S/N ratio at 120 s and a recovery at 180 s.  
Figure 8 presents the voltage and current profiles of a battery under varying ambient temperatures (\(-\)10 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 40 \({}^{\circ}\)C), highlighting the optimal experimental parameters under these conditions. At an ambient temperature of \(-\)10 \({}^{\circ}\)C, both voltage and current experience fluctuations, indicating a performance degradation at low temperatures. At 25 \({}^{\circ}\)C, the voltage remains relatively stable, but current fluctuations are more pronounced, with sharp peaks and troughs that may correspond to the optimal operation range under standard conditions. At 40 \({}^{\circ}\)C, there is a steady decline in voltage over time, while the current oscillates periodically. Figure 9 illustrates the regression analysis of the root mean square error (RMSE) for different SOC values at an ambient temperature of \(-\)10 \({}^{\circ}\)C. The regression lines, along with the 95% confidence intervals (CIs) and 95% prediction intervals (PIs), provide the relationship between the predicted and observed RMSE values for SOC at various stages of the battery's discharge cycle: SOC90, SOC50, and SOC30. All three issues demonstrate a positive correlation between the predicted and observed RMSE, with the data points generally clustering along the regression lines. The regression model results demonstrated that the SOC estimation method is most reliable in the early stages of discharge at \(-\)10 \({}^{\circ}\)C but faces challenges in the later stages, where estimation errors increase.