## 4 Conclusions  
This study demonstrated that using the Taguchi method and ANOVA for optimizing the HPPC profile significantly improves the accuracy of SOC estimation for lithium-ion batteries. In this context, the impact of four HPPC parameters (pulse time gap, discharge pulse time, discharge pulse C-rate, and rest time) on ECM performance at different operating temperatures (\(-10\)\({}^{\circ}\)C, \(25\)\({}^{\circ}\)C, \(40\)\({}^{\circ}\)C) was examined. The main findings showed the following:  
* All four parameters have an impact on the accuracy of the parameters' identification. * Lower temperatures (i.e., \(-10\)\({}^{\circ}\)C) lead to higher internal resistance and more significant voltage drops, particularly in cases with higher current pulses. The battery is more stable at \(25\)\({}^{\circ}\)C, with less voltage degradation compared to extreme temperatures (cold or hot). * Certain cases (e.g., Case 3 and Case 7) consistently show larger voltage drops across all temperatures, indicating that high current amplitudes and rapid cycling are more detrimental to battery health under extreme conditions. * Conversely, cases with lower current profiles (e.g., Case 1 and Case 2) are less affected by temperature changes. * Higher currents correlate with sharper voltage declines, particularly at colder temperatures. This is critical for battery management strategies, as it highlights the need for controlled current profiles in sub-optimal temperature environments. * When evaluation is made for different SOC values (SOC90, SOC50, SOC30), key findings include the significant impact of pulse time gap and discharge pulse time on model accuracy, with optimal values reducing RMSE between experimental and simulated data. * The application of EKF further enhances SOC estimation, allowing for real-time adjustments based on varying battery conditions. * The genetic algorithm-based multi-objective approach proves effective in selecting the optimal ECM parameters, especially under different temperature conditions. * The validation results indicate that the proposed methodology achieves high precision across a wide range of SOC and operating temperatures, confirming its robustness. * It was found that there is a significant reduction in RMSE, indicating improved performance under optimized conditions. The findings of this study offer significant potential for various practical applications. The optimized SOC estimation model can be integrated into EV battery management systems to enhance real-time monitoring, extend driving range, and improve energy management across diverse temperatures and SOC levels. This will prevent over-discharge, increase charging efficiency, and ensure safer operation, leading to more reliable electric vehicles with longer battery life. Furthermore, the model can be applied to lithium-ion energy storage systems in renewable energy grids to optimize charge/discharge cycles and improve grid stability. Additionally, it has applications in consumer electronics, improving battery life predictions and performance. The model's versatility also makes it suitable for industrial, military, and aerospace applications, where reliable energy management is crucial, especially in extreme conditions. For highly nonlinear operating conditions, such as low SOC or high C-rate at extreme temperatures, more advanced filtering techniques such as the Unscented Kalman Filter (UKF) or Particle Filters may be more appropriate. These methods are designed to handle nonlinearities more accurately but come at the cost of increased computational complexity. In future work, exploring nonlinear estimation techniques like the UKF or machine learning-based SOC estimation could further improve model accuracy, especially in dynamic or extreme environments. While this study focuses on NMC-based lithium-ion batteries, future research should validate the proposed methodology across a wider range of battery chemistries (e.g., LFP, NCA) and form factors (e.g., pouch cells, prismatic cells).