# A Data-Driven Battery Degradation Estimation Method for Low-Earth-Orbit (LEO) Satellites
## 4 Experiments and Results
As observed in the results of the analysis, the proposed voltage estimation method maintained stable mean and maximum errors even as the satellite's operational period increased, indicating convergence. Additionally, as shown in the waveform in Figure 10, the satellite's operating conditions, including current and voltage, vary significantly between the summer and winter periods. These external condition variations occur because eclipse periods are present in the winter but absent in the summer. Despite these external mission condition changes, the proposed model maintains a consistent error level while generating voltage profiles, demonstrating its robustness and reliability. On the other hand, the probability-based ARIMA model exhibited a significantly higher maximum error and did not achieve performance comparable to that of the proposed method in terms of mean error. This result is likely due to the inherent limitations of probability-based models in incorporating external environmental factors and other key influencing variables. Similarly, the Bi-LSTM model also yielded higher mean and maximum errors than the proposed technique. However, it required less processing time. Nonetheless, this difference in processing time is not significant when considering ground-based processing standards. It can be observed that the proposed technique accurately estimated battery voltage under different charge-discharge current conditions, mission conditions, and power generation environments, demonstrating that the changes in battery voltage estimated by the network can be a reliable tool for monitoring and predicting battery states. Therefore, the proposed voltage prediction model demonstrated minimal error despite variations in mission conditions and accurately estimated changes over the satellite's \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Year** & **Season** & & **RMSE (V)** & **Maximum Error (\%)** & **Processing Time (s)** \\ \hline \multirow{3}{*}{2013} & Eclipse duration & Proposed technique & 3.32 & 4.84 & 111 \\  & (10 November 2013) & ARIMA & 4.21 & 10.01 & 4 \\  & launch after 2 months & Bi-LSTM & 4.51 & 5.12 & 80 \\ \hline \multirow{3}{*}{2013} & Eclipse duration & Proposed technique & 2.52 & 3.83 & 110 \\  & (10 December 2013) & ARIMA & 4.34 & 9.99 & 4 \\  & launch after 4 months & Bi-LSTM & 3.95 & 4.98 & 82 \\ \hline \multirow{3}{*}{2014} & Sunlight duration & Proposed technique & 0.51 & 1.76 & 109 \\  & (10 July 2014) & ARIMA & 3.98 & 8.96 & 4 \\  & & Bi-LSTM & 0.99 & 3.11 & 82 \\ \cline{2-6}  & Eclipse duration & Proposed technique & 0.53 & 1.78 & 111 \\  & (10 December 2014) & ARIMA & 4.54 & 10.21 & 4 \\  & & Bi-LSTM & 0.98 & 3.29 & 80 \\ \hline \multirow{3}{*}{2016} & Sunlight duration & Proposed technique & 0.57 & 1.68 & 110 \\  & (10 July 2016) & ARIMA & 3.03 & 9.11 & 4 \\  & & Bi-LSTM & 0.99 & 3.26 & 82 \\ \cline{2-6}  & Eclipse duration & Proposed technique & 0.59 & 1.65 & 110 \\  & (10 December 2016) & ARIMA & 4.75 & 10.21 & 4 \\  & & Bi-LSTM & 0.93 & 3.21 & 81 \\ \hline \multirow{3}{*}{2018} & Sunlight duration & Proposed technique & 0.57 & 1.58 & 111 \\  & (10 July 2018) & ARIMA & 3.98 & 8.99 & 4 \\  & & Bi-LSTM & 0.98 & 3.10 & 82 \\ \cline{2-6}  & Eclipse duration & Proposed technique & 0.54 & 1.66 & 110 \\  & (10 December 2018) & ARIMA & 4.69 & 9.97 & 4 \\  & & Bi-LSTM & 1.03 & 2.98 & 82 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: One-day battery voltage prediction results during the mission. operational period. This confirms that the generated voltage prediction results can be utilized for estimating a battery's degradation state. Although this study focuses on developing a ground-based framework, future advancements may require real-time battery aging updates and charge-discharge state predictions directly on board the satellite. Thus, in future research, we will extend this work by developing techniques for model optimization, including lightweight, sampling time, and dimensionality reduction.