ObsBattery: Position-Aware Federated Learning with Dueling DQN Clustering and Training Adaptation for Satellite Battery Prediction

Abstract

Satellite battery status prediction is crucial for ensuring the healthy operation of future satellite constellations. However, traditional telemetry-based methods, where satellite battery status is transmitted in real time to ground stations for processing, consume significant satellite bandwidth and introduce response delays. Advances in onboard computing and federated learning (FL) enable local model training and centralized parameter aggregation, reducing transmission overhead while leveraging distributed satellite data. Nevertheless, the unique orbital motion of satellites presents challenges for FL, primarily due to battery status heterogeneity arising from varying sunlight exposure. Limited onboard energy further necessitates balancing model performance with battery efficiency during local training. To tackle these issues, we propose ObsBattery—a position-aware FL framework that clusters satellites based on their orbital positions to improve model accuracy. ObsBattery employs a Dueling Deep Q-Network to dynamically determine satellite clustering and adapt local training rounds according to power availability, thereby reducing energy consumption during low-power phases. Evaluations on a real-world satellite battery dataset show that ObsBattery significantly improves both prediction accuracy and energy efficiency. Compared to a standard clustered FL approach, it reduces model MAE by 16% and energy consumption ratio by 6% under experimental conditions.

1. Introduction

With the development of 6G, various countries are actively launching satellite constellations. In the near future, tens of thousands of satellites will exist in space, interconnected to provide seamless network access for wide-area ground users. The satellite battery system, typically composed of solar panels, battery arrays, and power control units [1], is a critical subsystem that supplies power for all satellite functions. Monitoring the health of the battery systems (i.e., predicting battery status) is essential for ensuring the stable operation of large-scale constellations.

Currently, traditional battery monitoring for individual satellites primarily relies on ground gateways to collect and process satellite telemetry data (such as current and voltage) [2], where machine learning algorithms (e.g., SVM) [3,4] or deep learning algorithms (e.g., LSTM) [5,6,7] are employed to predict satellite battery status. However, such centralized data collection and processing pose two major drawbacks. First, transmitting massive telemetry data generated by a large number of satellites consumes a significant amount of satellite bandwidth, potentially overwhelming satellite communication channels [8]. Second, due to the long distance between satellites and the ground, high air interface latency can result in delayed transmission of abnormal warning messages, making satellite adjustments (e.g., activating backup battery systems) untimely [9].

With the development of edge computing, more satellites are being equipped with onboard processing capabilities. For instance, in 2021, Beijing University of Posts and Telecommunications launched the Baoyun satellite, which carries high-performance computing modules based on the KubeEdge framework with AI acceleration capabilities [10]. In 2024, ESA’s new Φsat-2 satellite pushes the boundaries of AI for Earth observation, enabling real-time data processing and intelligent analysis onboard. These onboard intelligences make real-time analysis of satellite battery parameters feasible, reducing the need for frequent satellite-to-ground interactions and minimizing abnormal response latency. In addition, to expand training datasets and enhance the accuracy of learning models, the role of Federated Learning (FL) in satellite constellations has been discussed [11]. FL leverages the satellite onboard computation resources and performs the model training in a decentralized manner. Applying FL for battery status prediction, only model weights are transmitted to the ground, ensuring access to sufficient training datasets while significantly reducing the volume and frequency of raw battery telemetry data transmissions.

However, satellites have unique orbital patterns, with their battery status exhibiting distinct heterogeneity, which makes it difficult for existing FL algorithms to handle effectively. First, satellite battery supply primarily relies on north-south solar arrays, and the parameters of photovoltaic panels are closely related to the intensity of sunlight they receive. As illustrated in Figure 1, the current values of satellite solar arrays in direct sunlight (Position B) are much higher than those in Earth or Lunar shadows (Positions A and C). Second, compared to devices on the ground, satellites have limited battery resources and therefore the energy consumption for the model training can not be ignored [12]. Addressing the balance between model performance and energy consumption remains a significant challenge in the local model training stage.

In this paper, we propose ObsBattery, a novel satellite battery status prediction framework that explicitly integrates satellite positional information into the FL process, enabling both improved accuracy and energy efficiency. Specifically, we cluster satellites based on their orbital positions to mitigate data heterogeneity arising from varying sunlight exposure, which significantly impacts battery behavior. Within each cluster, satellites train individual prediction models using historical battery variation data (e.g., current), which are subsequently aggregated at ground stations. Additionally, to optimize energy usage, ObsBattery adaptively adjusts the number of local training rounds based on each satellite’s real-time position. For instance, the number of training rounds will be increased when the satellite is in direct sunlight compared to when it is in Earth or Lunar shadows. By adaptively adjusting the number of training rounds, a balance between model accuracy and the satellite battery efficiency (i.e., the ratio of battery consumed for training to the battery’s capacity) can be achieved. Through extensive experiments on the real-world satellite battery parameter dataset, we illustrate that ObsBattery not only outperforms reference works with higher model accuracy but also achieves a higher battery efficiency. The contributions of our work are threefold:

• We consider the impact of satellite position on satellite battery parameter prediction and satellite energy supply and formulate the problem model.
• We propose a location-aware satellite battery parameter prediction method ObsBattery based on cluster FL. ObsBattery clusters satellites according to their positions and applies the position information to the training of prediction models. Compared with traditional methods, the model accuracy is improved by about 9%.
• We propose optimizing the energy consumption in the FL process based on location information, which sets different numbers of training rounds according to the location of the satellite. Compared with the traditional method, the energy efficiency is improved by 6.2%.

The rest of the paper is organized as follows. The related references are provided in Section 2. We describe the system overview of ObsBattery in Section 3. Section 4 elaborates on the system model and the optimization problem. Section 5 provides the details of the designed algorithm. Section 6 details the profiles of involved functions and shows the evaluation results. Section 7 concludes the paper.

2. Related Work

2.1. Satellite Battery Dynamics Prediction

Predicting satellite battery dynamics is essential for ensuring reliable operation. Accurate forecasting of the battery’s state-of-charge (SOC), state-of-health (SOH), and remaining useful life (RUL) forms the foundation of mission planning and optimization. Many studies have focused on developing models to predict battery performance under the unique conditions of space missions, considering factors such as temperature fluctuations and radiation exposure.

In terms of SOC prediction, Amiri et al. [13] proposed a hybrid model combining physics-based approaches with data-driven techniques for predicting satellite battery dynamics. Jondhle et al. [14] introduced a real-time battery management system using recurrent neural networks to predict SOC under varying conditions. Li et al. [12] proposed a battery-aware energy optimization method for satellite edge computing, addressing the challenges specific to satellite missions.

In terms of SOH prediction, Yun et al. [5] used bidirectional long short-term memory (Bi-LSTM) networks to predict battery current and voltage during non-contact periods with ground stations. Wang et al. [15] conducted a comprehensive review of battery modeling techniques, highlighting the combination of electrochemical models with data-driven methods to improve battery performance predictions. Rodrigues et al. [2] further emphasized the role of deep learning models in satellite battery health management, improving the reliability of battery performance forecasting.

In terms of RUL prediction, Luo et al. [7] developed a hybrid data preprocessing-based deep learning model for predicting spacecraft lithium-ion battery RUL, employing multiscale hierarchical attention BiLSTM networks. Nascimento et al. [16] proposed a hybrid model to predict satellite battery performance, considering aging and environmental perturbations.

2.2. Energy-Awared Federated Learning

As the use of mobile and IoT devices increases, the challenge of optimizing FL for energy efficiency in battery-powered devices becomes more pressing. Many studies focus on addressing this issue through energy-aware strategies for energy saving and communication cost minimization.

For energy saving, Arouj and Abdelmoniem [17] proposed an energy-efficient client selection strategy that balances the number of clients involved in training and their energy consumption. Albelaihi et al. [18] extended this concept by introducing a green FL approach, which ensures that selected clients have sufficient energy to complete model updates, reducing the risk of battery depletion during training. Zaw et al. [19] studied energy-aware resource management in edge computing environments, where the goal is to reduce the energy consumption of mobile devices while ensuring that the model training process remains efficient. Yu et al. [20] explored a similar challenge in the context of agricultural IoT networks, proposing energy-aware device scheduling to minimize energy use during model training.

For communication cost minimization, Aloqaily et al. [21] proposed methods to reduce energy consumption in vehicular networks, where device mobility adds complexity. Li et al. [22] addressed communication overheads in edge computing systems, where reducing the frequency of model updates and adapting learning rates help save energy.

Although there are a lot of studies on satellite battery parameter prediction and resource-efficient FL, many existing studies do not explicitly consider how orbital location (for example, eclipse/shadow periods and changing solar incidence) affects battery parameters and on-board power availability. First, satellites will enter special areas such as the Earth’s shadow and the Moon’s shadow during operation, and the satellite energy system will experience special parameter fluctuations. This will have a significant impact on both satellite energy parameter prediction and prediction model training. Second, as the satellite position changes, the power supply capacity of the satellite solar panels is different. Dynamically adjusting the training intensity and making full use of power are also issues worth considering.

To the best of our knowledge, this paper is among the first to explicitly integrate satellite orbital motion and its effect on time-varying power availability into the design of an energy-aware FL training framework. Specifically, we consider how the dynamic movement of satellites influences battery parameter changes over time and propose a clustering and local training strategy in FL that accounts for these variations. Our work not only enhances the accuracy of the predictions but also reduces the overall energy consumption of the prediction process.

3. System Overview

In this section, the related terms are defined, and an overview of the process of ObsBattery is presented.

3.1. Related Terms

• Client Satellites: Client Satellites (CSs) refer to satellites with battery parameter prediction requirements. These CSs are equipped with onboard processing capabilities, allowing them to locally run neural network models and perform real-time analysis of battery parameter changes. Based on their distance from the Earth’s surface, CSs can be categorized into three types: Low Earth Orbit (LEO), Medium Earth Orbit (MEO), and Geostationary Earth Orbit (GEO) CSs. This paper uses data from LEO satellites for scheme design and related experiments. LEO CSs positioned at altitudes between 200 and 2000 km form the primary components of satellite constellations, handling the majority of satellite-to-ground data transmission tasks [23]. LEO CS payloads are typically smaller, with relatively low onboard processing capabilities. Additionally, due to their proximity to Earth, LEO CSs travel at the highest orbital speeds, typically around 27,000 km/h.
• Satellite Battery System: The satellite energy system comprises two primary components: dual solar wings (north and south) and a backup battery management system. These components work in concert to support continuous and efficient energy harvesting, storage, and regulation throughout the satellite’s operation [24].

  –

  Dual Solar Wings (North and South): Mounted on opposite sides of the satellite, the solar wings collect solar energy depending on the satellite’s orientation relative to the sun. Their complementary positioning enables consistent power generation across orbital cycles, maximizing energy intake during sunlit phases regardless of attitude or orbital path.

  –

  Backup Battery Management System: While the solar wings serve as the primary power source, the backup battery system ensures uninterrupted operation during eclipse phases. It stores surplus energy generated during sunlight exposure and supplies power when solar input is unavailable, thus maintaining stable power delivery for critical functions.

• Battery Dynamics Prediction: The CS battery dynamics include current and voltage [25,26].

  –

  Current: The electrical current flowing through the north and south solar wings indicates the actual energy being generated by the solar arrays. By predicting current levels, it is possible to detect irregularities such as shading, degradation of solar cells, or connection issues, which could compromise energy collection and distribution.

  –

  Voltage: The voltage readings from the solar wings and backup battery system reflect the operational status of the power supply. Sudden drops or spikes in voltage can signify problems such as circuit malfunctions, overcharging, or energy distribution imbalances. Accurate voltage prediction ensures the system remains stable and prevents overloading or power outages.

• Satellite Position: The position of a CS is directly related to its orbital elements. As the CS moves and time progresses, it continuously transitions between three states: sunlight, Earth shadow, and Lunar shadow. The CS’s battery behavior also varies across these three states, exhibiting different characteristics in each [27].

  –

  Sunlight: When in direct sunlight, the CS can maximize solar energy collection, ensuring that its solar panels operate at peak efficiency. Typically, CSs spend the majority of their orbital time in sunlight.

  –

  Earth Shadow: When a CS moves to the far side of the Earth, sunlight is blocked by the Earth. The closer the CS is to the center of Earth’s shadow, the lower the energy generation capacity of its solar panels. Typically, a CS remains in Earth’s shadow for a relatively short period.

  –

  Lunar Shadow: Similar to Earth’s shadow, when a CS is blocked by the Moon, the energy generation capacity of its solar panels also decreases. However, due to the smaller size of the Moon, the CS spends a shorter time in Lunar shadow. As a result, the CS’s battery dynamics during this period is more unstable.

• Gateway Station: Gateway Station (GS) is a critical component in a satellite constellation, primarily responsible for orchestrating the CSs. It uplinks commands to CSs to adjust their operations, such as orbital maneuvers, attitude control, and system configuration. It downlinks telemetry data from satellites, providing real-time monitoring of their status. A typical GS can manage varying portions of the Earth’s surface depending on the satellite’s orbit. For LEO satellites, a single GS typically covers an area with a radius of 300–500 km, corresponding to approximately 0.5–1% of the Earth’s surface. In contrast, a GS for MEO satellites can cover a much broader region—typically 5–10% of the surface—while a GS serving GEO satellites may cover up to one-third of the Earth. Owing to the GS’s role as the central hub for coordinating CS activities, we designate it as the central controller in the ObsBattery system. Its primary responsibilities include synchronizing information across CSs, performing model aggregation, and managing model updates in FL framework.

3.2. Workflow of ObsBattery

Figure 2 illustrates the workflow of ObsBattery within the coverage of a single GS, comprising five key stages:

(1)

Initial Model Preparation: At the beginning of each communication cycle, the GS prepares a set of global models by initializing multiple cluster templates based on anticipated variations in sunlight intensity. These models are not yet bound to specific satellites, as the actual CS grouping has not been determined. This step serves as the foundation for subsequent assignment.

(2)

CS Identification: The GS broadcasts a query to all satellites within its coverage to detect available participants. Satellites that are willing to join the current training round respond with a beacon and register as CSs.

(3)

Dueling DQN-Based CS Clustering: Once the set of active CSs is identified, the GS uses their static attributes—such as battery capacity and orbital parameters (i.e., the Six Keplerian Elements)—along with the current timestamp to compute their real-time positions. A Dueling Deep Q-Network (Dueling DQN) then assigns each CS to the most appropriate cluster based on its current location and expected solar exposure.

(4)

Model Distribution and Training Round Decision: The GS distributes the newest global models to the CSs according to its assigned cluster (Process a in Figure 2). In addition, to balance energy usage and model performance, the Dueling DQN also determines the number of local training rounds for each CS. Satellites with higher solar input are allowed to train longer, while those under low sunlight operate fewer rounds to conserve power. After completing the assigned local training rounds, each CS uploads its locally updated model to the GS for aggregation (Process b in Figure 2).

(5)

Model Aggregation and Update: ObsBattery adopts an online FL paradigm: when a CS uploads its local model, the GS immediately updates the corresponding cluster’s global model and broadcasts the new version. Steps 4–5 are then repeated periodically to adapt to dynamic changes in satellite positions and energy states. These processes correspond to c and d in Figure 2.

Notably, when a CS moves out of a GS’s control region, it will no longer participate in the ongoing FL process and will remove the local model from onboard memory.

4. Problem Description and Formulation

This section provides a formal formulation of the ObsBattery framework, detailing how satellite positions, energy dynamics, and FL training rounds interact under energy constraints. Abbreviations summarize the key notations used.

4.1. Satellite Position and Battery Capacity

We consider N CSs operating within the coverage area of a GS. Let $s_i$ denote the i-th CS, and $S=\{s_1,s_2,\dots ,s_N\}$ the complete set of active CSs. Each $s_i$ collects real-time battery status data $d_i$—including current, voltage, and component temperature—and has a power supply capacity denoted by $p_i$.

The battery status of a satellite is closely linked to its orbital position. We represent each satellite’s orbit using the Six Keplerian Elements, denoted as $O_i$, which include semi-major axis, eccentricity, inclination, argument of perigee, longitude of ascending node, and true anomaly.

To model temporal changes, we discretize the 24-h orbital period into equal-length time slots (in seconds), indexed by $t\in {\mathbb{Z}}^{+}$. The real-time position at each t is computed using standard orbital mechanics.

4.2. Satellite Clustering

To effectively manage heterogeneous energy profiles among satellites, ObsBattery dynamically clusters client satellites based on their orbital positions and illumination conditions. This clustering enables satellites with similar battery behavior and environmental exposure to share a specialized global model, improving both prediction accuracy and energy efficiency.

Formally, each satellite $s_i$ is assigned to a cluster $C_j\in \{C_1,C_2,\dots ,C_M\}$ by the ground station (GS), based on its orbital state $O_i^t$ and illumination level $L_i^t$:

$$C_j=f_c(O_i^t,L_i^t),$$

(1)

where $f_c(·)$ is the clustering function executed at time step t.

Each cluster maintains a global model $G_j$, which is continuously updated by aggregating the local models of its members:

$$G_j={\displaystyle \frac{1}{|C_j|}}\sum _{i\in C_j}{g}_{i,j},$$

(2)

where $g_{i,j}$ is the local model trained by satellite $s_i$ using the cluster-initialized model $G_j^0$ and $R_i$ local training rounds:

$$g_{i,j}=f_t(G_j^0,R_i)·y_{i,j}.$$

(3)

Here, $y_{i,j}\in \{0,1\}$ is a binary indicator that specifies whether $s_i$ belongs to cluster $C_j$, subject to the following:

$$y_{i,j}=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}{s}_i\in C_j\hfill \\ 0,\hfill & \mathrm{otherwise},\hfill \end{array}\right.,$$

(4)

where $y_{i,j}$ ensures that each CS is assigned to one cluster:

$$\sum _{j=1}^M{y}_{i,j}=1.$$

(5)

This clustering mechanism serves as a foundation for localized modeling and prediction tasks. Once clustering is complete, each satellite proceeds to predict its battery status using the assigned cluster model, as described next.

4.3. Battery Parameter Prediction

After clustering, each satellite leverages its local model to forecast short-term battery behavior. Accurate prediction of battery parameters—such as current, voltage, and temperature—is crucial for maintaining power safety and dynamically allocating training resources under energy constraints.

Let $x_i^t$ denote the battery status vector of satellite $s_i$ at time t. Its recent historical sequence is represented as $X_{i,t}^T=(x_i^{t-T+1},\dots ,x_i^t)$, and its orbital state as $O_i^t$. During the c-th communication round, satellite $s_i$ uses its local model $g_{i,j}$ to forecast the battery status at the next timestamp:

$${\widehat{x}}_i^{t+1}=f_l(X_{i,t}^T,O_i^t;g_{i,j}),$$

(6)

where $f_l(·)$ denotes a learned time-series prediction function parameterized by $g_{i,j}$.

To evaluate the quality of battery predictions, we consider two levels of accuracy metrics: individual-level error and cluster-level model performance.

At the individual level, each satellite $s_i$ uses its local model $g_{i,j}$—adapted from the cluster-level global model $G_j$—to perform one-step prediction at time $t+1$. The accuracy of this local prediction is measured by the absolute error:

$$a_i^t=\left|{\widehat{x}}_i^{t+1}-x_i^{t+1}\right|,$$

(7)

where ${\widehat{x}}_i^{t+1}$ is the predicted battery status and $x_i^{t+1}$ is the observed value. This metric reflects the immediate performance of the local model $g_{i,j}$ under current conditions.

To evaluate the aggregated performance of the cluster-level global model $G_j$, we directly apply $G_j$ to the historical data of all satellites assigned to cluster $C_j$. Specifically, for each satellite $s_i\in C_j$, let $X_{i,t}^T=(x_i^{t-T+1},\dots ,x_i^t)$ denote its recent battery status sequence. The predicted sequence ${\overline{X}}_{i,t}^T=({\overline{x}}_i^{t-T+1},\dots ,{\overline{x}}_i^t)$ is then obtained by recursively applying the shared global model $G_j$ on $X_{i,t}^T$.

The Mean Absolute Error (MAE) of $G_j$ across the cluster is computed as follows:

$$A_j={\displaystyle \frac{1}{|C_j|}}\sum _{i\in C_j}\left({\displaystyle \frac{1}{T}}\sum _{t^{\prime }=t-T+1}^t\left|{\overline{x}}_i^{t^{\prime }}-x_i^{t^{\prime }}\right|\right),$$

(8)

where $|C_j|$ is the number of satellites in cluster $C_j$. This metric quantifies how well the shared model $G_j$ generalizes to all member satellites’ real battery dynamics, independent of their local adaptations.

In this formulation, the global model $G_j$ serves as the sole predictor, ensuring that $A_j$ reflects the intrinsic accuracy of the cluster-level model itself, rather than the performance of locally fine-tuned variants.

4.4. Training Cost and Battery Efficiency

Training incurs energy cost. The per-satellite battery consumption is modeled as follows:

$$e_i=\sum _{r=1}^{R_i}\left({\displaystyle \frac{\alpha d_i}{{\kappa }_i}}+\beta {\Theta }_{r,i}+{\displaystyle \frac{\gamma }{{\zeta }_i}}\right),$$

(9)

where ${\kappa }_i$ is computation capacity, ${\Theta }_{r,i}$ orbital impact, and ${\zeta }_i$ communication rate. Coefficients $\alpha ,\beta ,\gamma$ weigh each factor.

In most cases, the data generated during satellite operations and used per training round remains constant, making battery consumption approximately proportional to the number of training epochs. Thus, satellite battery consumption can be expressed as a function of training epochs:

$$e_i=f_e\left(R_i\right),$$

(10)

where $f_e(·)$ denotes the battery consumption model, which increases with the number of round and can be expressed as follows:

$$f_e\left(R_i\right)=a{R}_i+b,$$

(11)

In real-world scenarios, when a satellite’s battery supply is sufficient, the battery consumption for model training has a relatively minor impact compared to the negative effects caused by insufficient battery supply. Therefore, the battery consumption during model training should be adapted to the satellite’s power supply capacity. To assess whether the battery consumed for model training is consistent with the satellite’s available power, we define a battery efficiency ratio ${\epsilon }_i$:

$${\epsilon }_i={\displaystyle \frac{e_i}{c{e}_i-E}},$$

(12)

where E denotes the battery reserve required for satellite operation, which is a constant. To minimize battery consumption, ${\epsilon }_i$ needs to be controlled at a smaller value.

In addition, to ensure the continuity and timeliness of the training process, the GS will distribute the satellite’s clustering and training round number information to the CS when communicating for the aggregation of models.

In summary, the GS needs to dynamically adjust the number of local training rounds according to the satellite’s position and lighting conditions to ensure rationalization of the battery system’s battery power distribution.

4.5. Optimization Objective

This study aims to optimize the trade-off between battery consumption and model accuracy within the FL framework, striving to reduce battery consumption during the model training process while maintaining model accuracy.

This optimization problem can be formulated as minimizing each satellite’s total battery consumption ${\epsilon }_i$ while maintaining the model loss function $A_i$ within acceptable accuracy bounds. The exponential terms $e^{-A_i}$ and $e^{-{\epsilon }_i}$ effectively normalize $e^{-A_i}$ and $e^{-{\epsilon }_i}$ into the interval $[0,1]$, reducing the impact of extreme data on the problem.

The ultimate goal of ObsBattery is to balance prediction accuracy and energy efficiency across satellites. The optimization problem is formulated as follows:

$$\begin{array}{cc}\hfill \mathcal{P}:\underset{R_i}{min}& -\left({\lambda }_1{e}^{-A_i}+{\lambda }_2{e}^{-{\epsilon }_i}\right),\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill \mathrm{s}.\mathrm{t}.& A_i\le \varphi ,\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill & {\epsilon }_i\le \phi ,\hfill \end{array}$$

(15)

where ${\lambda }_1$ and ${\lambda }_2$ control the trade-off between accuracy and energy usage, with values depending on the requirements of different tasks for model accuracy, and the value of ${\lambda }_1$ is also larger for tasks with high accuracy requirements; $\varphi$ and $\phi$ are user-defined thresholds that constrain the model loss and energy efficiency ratio, respectively.

Equation (13) implements the accuracy–energy trade-off by minimizing the negative weighted sum of normalized accuracy and energy terms, $-\left({\lambda }_1{e}^{-A_i}+{\lambda }_2{e}^{-{\epsilon }_i}\right)$. In this formulation, increasing ${\lambda }_1$ places more emphasis on accuracy (reducing $A_i$), while increasing ${\lambda }_2$ favors energy savings (reducing ${\epsilon }_i$); the exponential mapping bounds each contribution to $(0,1]$ and provides diminishing returns, which stabilizes the balance during optimization.

5. ObsBattery Framework

In this section, we introduce the proposed battery parameter prediction algorithm, ObsBattery, designed to optimize satellite battery parameter prediction tasks. The primary objective of this algorithm is to minimize the energy consumption associated with training the prediction model while maintaining the accuracy of battery parameter forecasts. The CSs use the Gated Recurrent Unit (GRU) algorithm to train the battery parameter prediction model. The GS runs the model aggregation algorithm and uses the Dueling DQN to optimize the model training process.

5.1. GRU-Based FL Battery Parameter Prediction

During satellite operation, the satellite battery system continuously generates many parameters. To effectively monitor these parameters and predict potential failures, we use the GRU algorithm to train the battery system parameter prediction model because it particularly effectively captures temporal dependencies in the data.

The GRU model consists of a set of recurrent units designed to capture long-term dependencies in sequential data. Each GRU unit operates based on the following key equations:

(a)

Update Gate ($z_t$): Given that the current input includes both position data $O_t$ and battery parameters $X_t$, the update gate is calculated as follows:

$$z_t=\sigma (W_z·[h_{t-1},O_t,X_t]+b_z),$$

(16)

where $h_{t-1}$ is the previous hidden state, $O_t$ and $X_t$ are the satellite’s position and battery parameter at time t, $W_z$ and $b_z$ are the weight matrix and bias term, and $\sigma$ denotes the sigmoid activation function.

(b)

Reset Gate ($r_t$):

$$r_t=\sigma (W_r·[h_{t-1},O_t,X_t]+b_r),$$

(17)

where $W_r$ and $b_r$ are the weight matrix and bias term for the reset gate.

(c)

Candidate Hidden State (${\widehat{h}}_t$):

$${\widehat{h}}_t=tanh(W_h·[r_t·h_{t-1},O_t,X_t]+b_h),$$

(18)

where $W_h$ and $b_h$ are the weight matrix and bias term, and tanh is the hyperbolic tangent activation function.

(d)

Final Hidden State ($h_t$):

$$h_t=(1-z_t)·h_{t-1}+z_t·{\widehat{h}}_t,$$

(19)

The update gate $z_t$ controls how much of the candidate hidden state ${\widehat{h}}_t$ contributes to the final hidden state, allowing the model to adaptively decide how much to retain from the previous time step and how much to update based on the current input.

The process of local training can be expressed as follows:

$$g_i=f_{gru}(O_t,X_t),$$

(20)

Although the GRU-based model is effective in capturing the temporal dependencies in battery parameters and satellite position data, the satellite operating environment is inherently complex and dynamic. To enhance model accuracy and optimize energy utilization, the next section presents an approach for improving satellite clustering and dynamically adjusting the number of training rounds.

5.2. Dueling DQN-Based Joint Decision for Clustering and Training Rounds

To jointly manage satellite clustering and local training costs under dynamic orbital and energy conditions, we formulate the decision-making process as a Markov Decision Process (MDP), as illustrated in Figure 3. At each communication round, the GS observes the current state of each satellite and determines (1) the cluster to which the satellite belongs and (2) the number of local training rounds it should perform. This two-fold decision directly affects both prediction accuracy and battery efficiency.

5.2.1. MDP Formulation

We formulate the satellite-side control problem as a Markov Decision Process (MDP), defined by the tuple $\mathcal{M}=(\mathcal{S},\mathcal{A},\mathcal{P},\mathcal{R},\gamma )$:

• State ${\mathcal{S}}_i^t$: Represents the environment and model status of satellite $s_i$ at time t. It is defined as follows:

  $${\mathcal{S}}_i^t=\{O_i^t,g_i\},$$

  where $O_i^t$ is the satellite’s real-time orbital position, and $g_i$ denotes the current state of its battery prediction model. In implementation, $O_i^t$ expands to the six Keplerian elements (and derived illumination $L_i^t$ when available), while $g_i$ is a compact feature vector summarizing the current prediction model (e.g., recent loss statistics and hidden representation), giving a fixed-dimensional state input.
• Action ${\mathcal{A}}_i^t$: Consists of two parts:

  $${\mathcal{A}}_i^t=\{C_i^t,R_i^t\},$$

  where $C_i^t\in \{1,2,\dots ,M\}$ indicates the assigned cluster, and $R_i^t\in \{R_{min},\dots ,R_{max}\}$ specifies the number of local training rounds. Thus the discrete action space size is $M\times (R_{max}-R_{min}+1)$; each action index encodes a pair (cluster ID, local round count), enabling the agent to jointly pick grouping and computational intensity.
• Transition function $\mathcal{P}$: Captures the stochastic evolution of satellite states under orbital motion and model updates. Although not modeled explicitly, it is implicitly learned through exploration.
• Reward function $\mathcal{R}$: Balances prediction performance and battery cost. Following the objective in Equation (13), it is defined as follows:

  $${\mathcal{R}}_i^t={\lambda }_1{e}^{-A_i}+{\lambda }_2{e}^{-{\epsilon }_i},$$

  (21)

  where $A_i$ is the prediction error defined at Equation (8), ${\epsilon }_i$ is the battery efficiency ratio defined at Equation (12); ${\lambda }_1$, ${\lambda }_2$ are weights that control the trade-off between accuracy and energy, with values depending on the requirements of different tasks for model accuracy.
• Discount factor $\gamma$: A scalar $\gamma \in (0,1]$ that controls the relative importance of future rewards.

This MDP formulation provides a principled foundation for applying reinforcement learning to jointly optimize energy-aware clustering and training round allocation in dynamic satellite environments.

5.2.2. Dueling DQN Solution

To address the joint decision-making problem of satellite clustering and training round assignment, we adopt a Dueling Deep Q-Network (Dueling DQN). Unlike standard DQN, Dueling DQN decouples the estimation of the state value and the action advantage, allowing the model to learn which states are inherently valuable, regardless of the specific actions taken [28]. This separation reduces variance in Q-value estimates when many actions share similar outcomes (e.g., adjacent training round choices), improving sample efficiency and stabilizing learning under orbital non-stationarity.

This distinction is particularly beneficial in our scenario, where the orbital state of a satellite (e.g., its position and energy profile) often plays a more decisive role in long-term reward than minor variations in clustering or training assignments. By emphasizing the evaluation of state importance, Dueling DQN improves learning stability and convergence, especially in environments with sparse or noisy rewards—common in satellite systems with delayed performance feedback. Empirically, it converges faster to effective clustering and training round policies than a plain DQN in our setting because the value stream learns global orbital desirability while the advantage stream focuses on fine-grained per-action adjustments, reducing overfitting to transient reward spikes.

In Dueling DQN, the Q-value function is expressed as follows:

$$Q(\mathcal{S},\mathcal{A})=V(\mathcal{S};{\theta }_v)+A(\mathcal{S},\mathcal{A};{\theta }_a)-{\displaystyle \frac{1}{\left|\mathcal{A}\right|}}\sum _{{\mathcal{A}}^{\prime }}A(\mathcal{S},{\mathcal{A}}^{\prime };{\theta }_a),$$

where ${\theta }_v$ and ${\theta }_a$ are the parameters of the value and advantage streams, respectively. This decomposition enables better generalization, especially in environments where the choice of action has marginal impact on overall utility.

To stabilize learning, we normalize the model prediction error $A_i$ and battery efficiency ratio ${\epsilon }_i$ across episodes. The resulting reward function is expressed as follows:

$${\mathcal{R}}_i^t={\lambda }_1{e}^{-{\overline{A}}_i}+{\lambda }_2{e}^{-{\overline{\epsilon }}_i},$$

where ${\overline{A}}_i$ and ${\overline{\epsilon }}_i$ are standardized values, and ${\lambda }_1,{\lambda }_2$ are trade-off weights.

Dueling DQN together with normalized reward shaping allows the GS to learn more robust and energy-efficient control policies for FL under dynamic orbital conditions, the algorithm are shown in Algorithm 1.

Algorithm 1 Dueling DQN for Clustering and Training Decision.

Input: Satellite states $\{O_i^t,g_i\}$ Output: Cluster $C_i^t$, rounds $R_i^t$ 1: Initialize Dueling Q-network with parameters ${\theta }_v,{\theta }_a$; replay buffer $\mathcal{D}$ 2: for each round t do 3:    for each satellite $s_i$ do 4:      Observe state ${\mathcal{S}}_i^t=\{O_i^t,g_i\}$ 5:      Select action ${\mathcal{A}}_i^t=\{C_i^t,R_i^t\}$ using $ϵ$-greedy with: $Q(\mathcal{S},\mathcal{A})=V(\mathcal{S};{\theta }_v)+A(\mathcal{S},\mathcal{A};!{\theta }_a)-{\displaystyle \frac{1}{\left|\mathcal{A}\right|}}{\sum }_{{\mathcal{A}}^{\prime }}A(\mathcal{S},{\mathcal{A}}^{\prime };{\theta }_a)$ 6:      Execute ${\mathcal{A}}_i^t$, obtain accuracy $A_i$ and energy ratio ${\epsilon }_i$ 7:      Compute reward: $\mathcal{R}={\lambda }_1{e}^{-A_i}+{\lambda }_2{e}^{-{\epsilon }_i}$ 8:      Observe next state ${\mathcal{S}}_i^{t+1}$, store transition $({\mathcal{S}}_i^t,{\mathcal{A}}_i^t,{\mathcal{R}}_i^t,{\mathcal{S}}_i^{t+1})\in \mathcal{D}$ 9:    end for 10:    Sample batch $(\mathcal{S},\mathcal{A},\mathcal{R},{\mathcal{S}}^{\prime })\sim \mathcal{D}$ 11:    for each sample do 12:      Compute target: $y=\mathcal{R}+\gamma {max}_{{\mathcal{A}}^{\prime }}Q({\mathcal{S}}^{\prime },{\mathcal{A}}^{\prime })$ 13:      Compute loss: $\mathcal{L}={(Q(\mathcal{S},\mathcal{A})-y)}^2$ 14:      Update ${\theta }_v,{\theta }_a$ by gradient descent on $\mathcal{L}$ 15:    end for 16: end for

5.3. Integration Algorithm of FL and Dueling DQN

Integrating the above prediction and decision algorithms, the complete FL process includes the following important processes: model initialization, local model training, clustering model aggregation, Dueling DQN training optimization decision, and iterative convergence, as described in Section 3.

This iterative process ensures continuous refinement of the prediction models while optimizing energy efficiency and computational resources. The overall algorithm complexity can be simplified as $O(E\ast T_{train})$, where E is the epoch and $T_{train}$ is the amount of training data.

6. Simulation

In this section, we conduct experiments using satellite battery system data collected in real-world environments to evaluate the performance of the ObsBattery.

6.1. Experimental Environment and Dataset Setup

We conduct simulation experiments to evaluate the performance of ObsBattery using real-world satellite battery system data. All experiments were executed on a workstation equipped with an Intel Core i9-14900K processor running Windows 11. The codebase was implemented in Python 3.9 and executed within the Anaconda environment. The Dueling DQN training and FL modules were implemented using PyTorch 2.4.

The dataset used in this study consists of telemetry data collected from multiple LEO satellites. The collected data reflect typical characteristics of satellite energy behavior. Each record contains measurements such as the current and voltage of north and south solar panels, bus voltage and current, and component temperatures. The data were sampled every 2 s over periods ranging from 12 to 24 h and stored in CSV format following basic preprocessing. Moreover, we estimated each satellite’s orbital position using telemetry timestamps and propagation models derived from known orbital parameters, following a process similar to reconstructing position from the Six Keplerian Elements. Concretely, VN5 and VN8 denote north-facing and south-facing solar cell voltages in volts, while IN11 and IN21 are north and south power bus currents in amperes; each subset spans 12–24 h, around 21,600–43,200 samples at 2 s intervals.

6.2. Simulation Design

The ObsBattery includes two important networks. The first is a GRU network, which performs status prediction locally on the CSs, and the second is a Dueling DQN network, which optimizes the FL training process on the GS. Detailed implementation specifics can be found in Algorithms 1 and 2. The GRU network structure we used could be seen at

Table 1. GRU Network Architecture.

Layer	Input	Output	Parameters
GRU	(B, 15, 1)	(B, 15, 64)	12,480
Fully Connected	(B, 64)	(B, 1)	65

B represents the batch size.

. The GRU network takes the satellite position and battery status as input, and outputs the predicted battery status.

Algorithm 2 FL with Dueling DQN-Based Satellite Clustering and Training Optimization.

Input: Satellite local data, initial global model, clustering strategy, maximum number of iterations. Output: Converged global model. 1: Step 1: Initialization 2: Initialize global model $G_0$ 3: Initialize satellite local models $g_i=G_0$ for all CSs 4: Initialize satellite clustering $C_j$ and training rounds $R_i$ for each satellite 5: Set maximum number of iterations $R_{\max }$ 6: Initialize the Dueling DQN model with parameters ${\theta }_v$ and ${\theta }_a$ 7: Step 2: Local Model Training 8: for each satellite i do 9:      Train local model $g_i$ using local data 10:    Send local model $g_i$ to the GS 11: end for 12: Step 3: Model Aggregation 13: for each cluster j do 14:    Aggregate local models in $C_j$ to update global model $G_j$ 15: end for 16: Step 4: Dueling DQN-Based Decision Making 17: For each satellite, compute current state ${\mathcal{S}}_i=\{O_{t,i},g_i\}$ 18: Apply Dueling DQN to determine cluster assignment $C_j$ and training rounds $R_{t,i}$ for each satellite, where $R_{t,i}<R_{\max }$ 19: Distribute updated global models and new assignments back to the satellites 20: Step 5: Repeat 21: if The model has not converged then 22:    Repeat Steps 2–4 23: else 24:    Output final model group $G=\{G_1,\dots ,G_j,\dots ,G_M\}$ 25: end if

In ObsBattery, we use clustering methods to improve the model’s prediction accuracy and use Dueling DQN to optimize the FL training process to optimize energy consumption. We designed three experiments to test ObsBattery’s performance in clustering model accuracy, training energy consumption ratio, and comprehensive performance, and we set up a comparison with other solutions for each group of experiments as follows:

• To investigate the effect of clustering on model accuracy, we compare the performance of a non-clustering approach (i.e., a single global model shared by all satellites) with scenarios involving varying numbers of clusters. To ensure a fair comparison, the same number of training rounds is applied across all clusters.
• To evaluate the energy consumption efficiency of the FL training process, we measure the training parameters of the satellite model under different public health strategies, as shown in Equation (12). The purpose is to investigate the impact of adjusting the number of training rounds on the model convergence effect and the energy efficiency of the training process.
• The comprehensive performance simulation combines the previous two experiments and evaluates the system’s overall performance, considering both model accuracy and energy consumption. We compare ObsBattery’s approach with other FL solutions regarding the balance between training efficiency, energy usage, and model prediction accuracy. In this context, we compare ObsBattery against baseline schemes with no clustering or dynamic training control, referred to as the Standard Group.

6.3. Clustering Accuracy Evaluation

To assess the effect of satellite clustering on model prediction accuracy, we designed a series of experiments with varying numbers of clusters. Five configurations were evaluated:

• Cluster_1 (Standard Group): No clustering; all satellites share a single global model.
• Cluste_3: Satellites are grouped into 3 clusters.
• Cluster_6: Satellites are grouped into 6 clusters.
• Cluster_9: Satellites are grouped into 9 clusters.
• Cluster_12: Satellites are grouped into 12 clusters.

All experimental groups underwent 20 global communication rounds with the same number of local training epochs to ensure a fair comparison. The objective is to evaluate how model accuracy responds to different levels of granularity in clustering. We tested on four datasets reflecting different telemetry signals: VN5 (north-facing solar cell voltage), VN8 (south-facing solar cell voltage), IN11 (north bus current), and IN21 (south bus current).

The results are shown in Figure 4. We observe that increasing the number of clusters generally leads to a reduction in prediction error. For instance, on the VN8 dataset, compared to Cluster_1 (no clustering), the MAE values for Cluster_3, Cluster_6, Cluster_9, and Cluster_12 decreased by 9.5%, 16.7%, 23.5%, and 17.0%, respectively. Among all groups, Cluster_9 achieved the lowest average MAE, suggesting that moderately fine-grained clustering can yield significant performance gains.

However, increasing the number of clusters to 12 slightly degrades performance. This indicates that while clustering helps to specialize models for distinct satellite groups, excessive fragmentation may reduce the statistical robustness within each group, leading to overfitting or insufficient learning.

To further assess the spatial effectiveness of the clustering strategy, we conducted a location-wise comparison between the Cluster_1 (no clustering) and Cluster_6 (six clusters) configurations. After 20 communication rounds of training, one representative satellite was selected from each of the six clusters in Cluster_6, denoted as $L_1$ through $L_6$. These locations span diverse orbital positions and battery usage patterns, offering a broad view of model behavior across the satellite constellation. As shown in Figure 5, we evaluated the prediction accuracy at each location by computing the MAE. The x-axis indicates the selected test location $L_n$, while the y-axis reflects the corresponding prediction error, representing model performance under varying orbital conditions.

The results demonstrate a consistent advantage of the clustered models over the global model. Taking the VN8 dataset as an example, compared to Cluster_1 (no clustering), the MAE values for $L_1$ through $L_6$ in Cluster_6 decreased by 8.2%, 17.0%, 10.9%, 16.6%, 26.5%, and 16.7%, respectively. Similar patterns were observed in the other datasets.

These findings confirm that clustering based on satellite location and energy behavior significantly enhances model accuracy. A suitable cluster number can group similar behavior patterns effectively, enabling the model to better capture context-specific dynamics without sacrificing generalization.

6.4. Energy Efficiency Evaluation

To assess the impact of dynamic training control on energy usage, we conducted a series of experiments designed to evaluate how Dueling DQN adjustment of local training rounds influences both model convergence and energy consumption. Two experimental groups were considered:

• Group Static: Satellites are divided into six clusters, and each satellite performs a fixed number of local training rounds.
• Group DQN: Satellites are also divided into six clusters, but the number of training rounds for each satellite is dynamically adjusted by the Dueling DQN agent, within a bounded range of 3 to 15.

The upper and lower bounds on training rounds were determined empirically. Fewer than 3 rounds often led to underfitting, while more than 15 rounds incurred high energy costs without significant accuracy gains. We evaluated both convergence dynamics and model performance on the VN5 and IN11 datasets:

• Convergence Behavior: As shown in Figure 6a and Figure 7a, Group DQN exhibits a smoother and more consistent decrease in training loss, indicating effective convergence. This demonstrates that dynamic adjustment does not hinder training stability and can lead to faster convergence.
• Performance Comparison: Figure 6b and Figure 7b compare the model MAE between the two groups. In early training rounds, Group DQN achieves significantly lower MAE. For example, within the first 10 communication rounds on VN5, MAE is reduced by 11.2.

We further analyzed the energy efficiency by measuring the energy consumption ratio across methods with different cluster counts. As shown in Figure 8, the energy consumption ratio improves as the number of clusters increases. Compared to the Cluster_1 baseline without dynamic adjustment, the energy consumption ratios for Cluster_3, Cluster_6, Cluster_9, and Cluster_12 decreased by 2.1%, 4.8%, 8.3%, and 9.9%, respectively.

These results validate our hypothesis: by enabling finer-grained control over local update schedules based on clustered energy profiles, Dueling DQN-based adjustment significantly enhances training efficiency without compromising accuracy.

6.5. Comprehensive Performance Evaluation

In this experiment, we designed a comprehensive evaluation involving seven FL schemes to assess their performance in terms of model accuracy, energy consumption, and overall training efficiency. In addition to the proposed ObsBattery framework, we incorporated two widely recognized FL baselines—FedProx and EAFL—to facilitate a broader comparison. The experimental group settings are as follows:

• Standard Group: A conventional FL method resembling FedAvg, where satellites share a single global model without clustering or adaptive training round control.
• FedProx: An FL algorithm that extends FedAvg by introducing a proximal term in the local objective to address heterogeneity in data and computation capabilities [29].
• EAFL: An energy-aware FL strategy that selectively involves satellites with sufficient battery levels, aiming to optimize time-to-accuracy while minimizing energy depletion [17].
• Clustering Only (6): An enhanced FL method that partitions satellites into six clusters to train localized models, but does not apply dynamic adjustment of training epochs.
• ObsBattery (6): The proposed method with six clusters and Dueling DQN-based adaptive training round control to optimize both performance and energy efficiency.
• ObsBattery (9): A variant of ObsBattery using nine clusters, found to achieve the best overall balance between accuracy and energy consumption.
• ObsBattery (12): A variant using twelve clusters, which further improves energy allocation granularity but may reduce accuracy due to over-segmentation of data.

To provide a comprehensive comparison across different FL algorithms, we calculate three performance metrics for each method: prediction accuracy, energy consumption efficiency, and an aggregated comprehensive score. These metrics are derived from Equation (13), with weighting coefficients ${\lambda }_1=0.6$ and ${\lambda }_2=0.4$ to emphasize prediction accuracy. Since both accuracy error and energy consumption are cost-type indicators, we apply negative exponential normalization to convert them into utility-type scores, such that higher values correspond to better performance.

Table 2. Comparison of comprehensive performance of different algorithms.

Algorithm	Accuracy	Energy	Comprehensive
Standard Group	0.759	0.779	0.767
FedProx	0.811	0.785	0.801
EAFL	0.840	0.815	0.830
Clustering only (6)	0.832	0.789	0.815
ObsBattery (6)	0.836	0.803	0.823
ObsBattery (9)	0.861	0.822	0.845
ObsBattery (12)	0.837	0.830	0.834

summarizes the performance scores of all compared algorithms. The proposed ObsBattery (9) achieves the best overall balance, with a comprehensive score of 0.845, outperforming the Standard Group by 10.2%, FedProx by 8.3%, and EAFL by 6.1%. These results demonstrate the benefit of jointly incorporating spatial clustering and dynamic training control for satellite-based FL tasks.

Figure 9 visualizes the performance profiles of each algorithm using a radar chart with normalized scores. The triangle formed by each method’s three normalized scores represents its relative performance footprint. For further quantification, we compute the area of each triangle to capture the overall effectiveness across all dimensions. The ObsBattery (9) configuration exhibits the largest coverage area (0.858), reinforcing its superior balance of accuracy and energy efficiency. Conversely, the Standard Group yields the smallest area (0.007), reflecting consistently lower scores across all metrics.

Interestingly, although ObsBattery (12) achieves the best energy score (0.830), its accuracy performance is slightly reduced compared to ObsBattery (9), likely due to over-segmentation which introduces distributional fragmentation and impairs model generalization within each cluster.

Meanwhile, existing methods such as FedProx and EAFL offer moderate improvements over the baseline, particularly in energy efficiency, but fall short in overall adaptability. These methods do not incorporate dynamic feedback from system state or satellite-specific constraints, limiting their responsiveness in the fast-changing environment.

In summary, the radar chart and area-based analysis together confirm that ObsBattery (9) provides the most favorable trade-off among all tested algorithms. Its design—combining spatial grouping with reinforcement-based training control—offers a practical and scalable solution for energy-constrained satellite FL scenarios.

7. Conclusions

This paper proposes ObsBattery, an energy-aware federated learning framework for satellite battery parameter prediction that jointly optimizes clustering and training effort through a Dueling DQN-based decision process. By adapting to real-time orbital and energy conditions, ObsBattery balances model accuracy and energy efficiency.

Experiments on real-world LEO satellite telemetry data show that ObsBattery outperforms methods such as FedProx and EAFL, as well as static clustering strategies. The results confirm its effectiveness in delivering accurate and energy-efficient learning across dynamic satellite environments. Specifically, ObsBattery (9) achieves a 10.2% improvement in comprehensive performance over standard FL approaches, with up to 23.5% reduction in prediction error through orbital-aware clustering and 9.9% energy consumption savings via dynamic training round adjustment. Our main contributions to the literature include the following: (1) the first integration of orbital motion and eclipse/shadow effects into FL scheduling for satellites, (2) a novel dual-objective optimization framework that explicitly balances accuracy and energy efficiency through Dueling DQN, and (3) empirical validation showing that moderate clustering granularity (9 clusters) provides optimal performance while avoiding over-segmentation issues.