# A Data-Driven Battery Degradation Estimation Method for Low-Earth-Orbit (LEO) Satellites
## 4 Experiments and Results
In this study, the proposed on-orbit battery aging estimation results were compared with those obtained from applying the DCIR-based state estimation algorithm. Battery aging is closely associated with an increase in internal resistance. The DCIR method evaluates a battery's condition by directly measuring its internal resistance, enabling quantitative modeling of the battery's aging state. Specifically, in the DCIR method, internal resistance is calculated by measuring the voltage drop (\(\Delta\)V) and current under specific charge-discharge conditions. The terminal voltage of the battery is modeled as shown in Equation (9). The differential voltage can be expressed as the product of the terminal current and the parallel impedance of the differential capacitance and differential resistance. Therefore, the terminal voltage can be formulated as the sum of the OCV, the product of the terminal current, and the total internal impedance of the battery. By expressing the differential voltage in Equation (9) in terms of the terminal current and transforming it into the frequency domain, it can be rewritten as Equation (13). Additionally, satellite batteries are typically subjected to a screening process to minimize internal impedance variations within the packaged units. Therefore, for a battery pack composed of m series and n parallel cells, the impedance, OCV, and terminal voltage can be simplified as shown in Figure 11.  
Furthermore, since OCV variations in the mission operating period of the satellite are minimal, assuming the OCV fluctuation is zero, the relationship between terminal voltage variations and terminal current variations can be formulated, as shown in Equation (14). Consequently, the voltage variations corresponding to input current changes can be computed using Equation (14). This approach allows battery aging to be estimated by directly linking observed voltage behavior with internal resistance, providing a robust framework for satellite battery health monitoring and performance assessment. \[V_{k}(\mathbf{s})=\text{OCV}(\mathbf{s})-\text{I}_{\text{T}(\mathbf{s})}. \left(\frac{R_{d}}{1+R_{d}\cdot C_{d}\cdot\mathbf{s}}+R_{I}\right) \tag{13}\]  
\[\frac{\Delta V}{\Delta I}(s)=\frac{\Delta V}{I_{mission}}(s)=\frac{m\cdot R_{d}} {(1+R_{d}\cdot C_{d}\cdot\mathbf{s})}+\frac{m}{n}R_{I} \tag{14}\]  
Figure 11: Battery pack electrical circuit diagram with m series and n parallel cell configuration. The advantages of the DCIR method include its ability to evaluate battery conditions in real time and quantify the degree of aging through relatively simple calculations. However, obtaining accurate results in battery circuit modeling and aging estimation using satellite discharge currents requires several constraints and conditions to be fulfilled and met, respectively, leading to significant complexity and time requirements in data processing and analysis. In particular, modeling aging based on discharge current and voltage changes relies on verifying data under identical SOC conditions to ensure reliable results are obtained. Because satellite battery environments are subject to multivariable conditions (e.g., satellite orbit, mission state, and seasonal factors), maintaining a consistent SOC and obtaining data under uniform initial conditions are challenging. Consequently, postprocessing and data selection are essential for ensuring data accuracy. During postprocessing, large quantities of raw data are analyzed to extract discharge data collected under identical SOC conditions. This process involves aligning the data along the temporal and SOC axes and correcting deviations caused by external environmental factors (e.g., temperature variations, mission loads, etc.). Although these tasks can be automated using algorithms and tools, accurately understanding the data and setting appropriate processing criteria still require the expertise of experienced users. Moreover, various factors must be considered in the data selection process.