# A Data-Driven Battery Degradation Estimation Method for Low-Earth-Orbit (LEO) Satellites
## 4 Experiments and Results
The battery's aging and charge states, which experts analyzed, were selected as reference data, and the results were then compared with other predicted values. The estimation results obtained using the proposed method are represented in red, while the reference values, determined by experts using all available mission data from the ground, are shown in green. Additionally, the results of SOC estimation obtained using the aging estimation with various mission condition data with the UKF are depicted in blue. In the graph on the left, depicting the data from 10 November 2013, all SOC estimation results are similar, indicating that during the initial phase of satellite operation, battery performance degradation was negligible; thus, accounting for aging has minimal impact on SOC estimation accuracy. Conversely, the graph on the right, illustrating the data from 10 November 2017, shows that as time progresses and battery aging advances, the discrepancy between the SOC estimates with and without considering aging becomes increasingly noticeable. Without accounting for aging, the SOC may be overestimated or underestimated, so the condition of the battery will not be accurately reflected. This indicates that mission planning based on uncorrected SOC values may result in the use of stored energy beyond the permissible range, potentially compromising a satellite's ability to perform continuous missions. As seen in the figure, the results obtained using the proposed method are closer to the reference values than those derived from the UKF algorithm, which utilized all mission data. This outcome is attributed to the proposed method's ability to estimate battery degradation states even when using data that are not generated under uniform conditions. A quantitative summary of these results over an extended period is presented in Table 3. To evaluate the performance of the model and its predictions, the maximum error of the voltage estimation results was calculated. This quantitative analysis was performed specifically for mission intervals, where the maximum error is particularly important for battery fault management and mission modeling. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Season**} & \multirow{2}{*}{\
\begin{tabular}{c} **Maximum DOD Error with SOH** \\ **(Proposed Technique)** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Maximum DOD Error with SOH** \\ **(Using Real Mission Data Along with a** \\ **UKF Algorithm)** \\ \end{tabular} } \\ \hline \multirow{4}{*}{2014} & Sunlight duration & \multirow{4}{*}{1.5} & \multirow{4}{*}{2.7} \\  & (10 July 2014) & & & \\ \cline{1-1}  & Eclipse duration & & & \\  & (10 December 2014) & & & \\ \hline \multirow{4}{*}{2016} & Sunlight duration & \multirow{4}{*}{1.4} & \multirow{4}{*}{2.8} \\  & (10 July 2016) & & & \\ \cline{1-1}  & Eclipse duration & & & \\ \cline{1-1}  & (10 December 2016) & & & \\ \hline \multirow{4}{*}{2018} & Sunlight duration & \multirow{4}{*}{1.6} & \multirow{4}{*}{3.0} \\  & (10 July 2018) & & & \\ \cline{1-1}  & Eclipse duration & & & \\ \cline{1-1}  & (10 December 2018) & & & \\ \hline \multirow{4}{*}{2020} & Sunlight duration & \multirow{4}{*}{1.6} & \multirow{4}{*}{2.9} \\  & (10 July 2020) & & & \\ \cline{1-1}  & Eclipse duration & & & \\ \cline{1-1}  & (10 December 2020) & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum DOD error results for mission duration with an increasing operational period after one year of launch. For the analysis, the errors between the reference values and each estimated value were summarized from 2014, one year after launch, to 2020. Given that aging does not occur over a short period, analyses using data covering at least 12 months are expected to provide meaningful insights and be useful. As shown in the table, the proposed method consistently demonstrated superior accuracy across all operational periods, even under varying satellite degradation and operational conditions.