## 2 Materials and Methods  
### Experimental Setup  
The selected battery cell in this research is a 2.9 Ah, cylindrical 18650 lithium-ion battery cell (Aspilsan INR18650A28), incorporating a nickel manganese cobalt oxide (NMC) cathode and a graphite anode. The detailed specifications of the cell are provided in Table 1.  
In this study, the charge and discharge tests were conducted using a QPY 1200 SP programmable DC power supply and a PRODIGIT 3117 programmable DC electronic load device and the control of these devices, and the data acquisition process were carried out with the LabVIEW 2020 SP1 software. To maintain the consistency of experimental data and to provide several different temperatures, all tests were carried out within a climate chamber, depicted in Figure 1.  
To ensure the battery's capacity is accurately measured and validated, it is essential to test the maximum available capacity. The testing process is conducted at three different ambient temperatures of \(-10\)\({}^{\circ}\)C, \(25\)\({}^{\circ}\)C, and \(40\)\({}^{\circ}\)C, beginning with charging the battery using a constant current. The temperatures \(-10\)\({}^{\circ}\)C, \(25\)\({}^{\circ}\)C, and \(40\)\({}^{\circ}\)C were selected to represent a wide range of environmental conditions that lithium-ion batteries commonly experience in real-world applications. Each temperature is chosen to simulate different operational scenarios, enabling a comprehensive understanding of how temperature impacts battery performance, model accuracy, and SOC estimation. At low temperatures, such as \(-10\)\({}^{\circ}\)C, lithium-ion batteries experience significant increases in internal resistance and decreases \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Value** \\ \hline Diameter (mm) & 18.30 + 0.1/\(-\)0.2 \\ Height (mm) & 65 \(\pm\) 0.2 \\ Weight (g) & 44.5 \(\pm\) 0.7 \\  & 2950 (Maximum) \\ Discharge Capacity (mAh) & 2900 (Typical) \\  & 2850 (Minimum) \\ Nominal Voltage (V) & 3.68 \\ Energy Density (Wh/kg) & 244 \\ Standard Charge Current (mA) & 1450 \\ Max. Continuous Charge Current (mA) & 4000 (10–50\({}^{\circ}\)C) \\ Charge Cutoff Current (mA) & 140 \\ Charge End Voltage (V) & 4.25 \\ Standard Discharge Current (mA) & 580 \\ Max. Continuous Discharge Current (mA) & 25,000 \\ Discharge End Voltage (V) & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the lithium-ion cell used in the experiments. in ionic conductivity, leading to voltage drops and reduced capacity. This condition was chosen to represent extreme cold environments, which are commonly encountered in regions with cold climates or during winter operations. The impact of low temperatures on battery performance is critical for applications like electric vehicles in cold weather, where reduced battery efficiency and energy loss can affect driving range and power availability. Studying the model's performance under these conditions helps improve SOC estimation and overall battery management in low-temperature environments. A temperature of 25 \({}^{\circ}\)C was chosen as the reference temperature because it represents standard laboratory conditions and is generally considered the optimal operating temperature for lithium-ion batteries. Under this temperature, the battery's electrochemical reactions are stable, internal resistance is minimal, and overall performance is predictable. Testing at this temperature provides a baseline for comparing battery performance and SOC estimation under more extreme conditions. Additionally, many industrial and consumer battery applications (e.g., electronics, stationary energy storage systems) operate at or near room temperature, making this an essential condition for model validation. High temperatures, such as 40 \({}^{\circ}\)C, were selected to simulate hot environments where lithium-ion batteries may experience thermal stress due to accelerated electrochemical reactions and increased thermal degradation.