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Velocity-coupled Representation Refinement for Satellite Orbit Prediction

Yue Yang, Zhiqiang Wu, Saiyu Qi, Fan Ma

arXiv:2608.23728v1cs.CV

TL;DR

Existing satellite orbit predictors often focus on position sequences while insufficiently exploiting position–velocity coupling. OrbitNet refines positional representations with velocity-aware interactions and models orbital segments, achieving the best in-domain performance and zero-shot MAE across six unseen constellations.

  • Problem

    Existing learning-based approaches insufficiently exploit the intrinsic relationship between position and velocity in satellite orbit prediction.

  • Method

    OrbitNet integrates velocity-coupled refinement with orbital segment modeling to learn position–velocity interactions and temporal orbital patterns.

  • Results

    OrbitNet achieves the best in-domain performance and the best zero-shot MAE across six unseen satellite constellations, while maintaining competitive RMSE on most zero-shot datasets.

  • Takeaways & Limitations

    The results suggest that explicitly exploiting structured relationships among position, velocity, and temporal orbital segments is critical for accurate orbit prediction.

  • Takeaways & Limitations

    The framework is mainly data-driven and does not explicitly incorporate richer orbital-mechanics priors, environmental perturbations, or control-related factors.

Abstract

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Satellite orbit prediction, which aims to forecast future orbital trajectories from historical observations, is important for collision warning and safe space operations. With advances in time-series forecasting, learning-based methods have emerged as a promising solution for satellite prediction. In orbital dynamics, a satellite state is typically described by position and velocity, where position characterizes trajectory geometry and velocity reflects its instantaneous direction and rate of change. However, most existing methods mainly focus on temporal dependencies within position sequences while rarely exploiting the intrinsic coupling between position and velocity, which is essential for modeling satellite motion. To this end, we propose OrbitNet, a velocity-aware representation learning method for accurate satellite orbit prediction. It lifts conventional position-sequence forecasting to a position-velocity coupled representation learning paradigm by exploiting relationships among satellite state variables. Specifically, we develop a velocity-coupled representation refinement strategy to enhance positional representations through cross-variable interactions between position and velocity. We further introduce orbital segment modeling, which partitions historical trajectories into temporal segments and performs segment-level temporal learning to capture local motion variations and long-range evolution patterns. Extensive experiments show that OrbitNet outperforms large time-series foundation models and representative general forecasting methods under both in-domain evaluation on Starlink and zero-shot evaluation across six unseen satellite constellations. We expect this work to encourage further exploration of satellite-aware representation learning for trajectory time-series forecasting.

1 Introduction

Satellite orbit prediction supports satellite monitoring and space situational awareness, but existing approaches often underuse the coupled position–velocity structure of orbital states. OrbitNet addresses this gap by refining positional representations with velocity-aware interactions and modeling trajectories in temporal segments.

  • Satellite orbit prediction forecasts future orbital trajectories from historical observations for satellite monitoring and space situational awareness.
  • Physics-based methods are interpretable but can be constrained by handcrafted dynamical assumptions and unmodeled perturbations.
  • Most existing learning-based approaches rely on position-only inputs, which may limit characterization of orbital evolution and predictive performance.
  • Position and velocity jointly determine orbital evolution, so effective representations should preserve historical positional information while encoding velocity-aware motion cues.
  • OrbitNet explicitly injects velocity-aware cues into positional representations through cross-variable refinement rather than merely appending velocity channels.
  • Orbital segment modeling partitions trajectories into temporal segments, capturing local motion variations while preserving long-range dependencies.
  • OrbitNet outperforms large time-series foundation models and general forecasting methods in in-domain forecasting and zero-shot evaluation across six unseen constellations.

2 Related Work

Prior orbit-prediction methods use physics-based, hybrid, TLE-oriented, or neural forecasting approaches, but often underexplore the intrinsic coupling between position and velocity. OrbitNet addresses this gap through velocity-aware positional representation refinement and segment-level temporal modeling.

  • Satellite Orbit Prediction: Physics-based propagators are efficient and interpretable, but uncertain initial conditions and unmodeled perturbations can degrade prediction accuracy.Examples of perturbations include atmospheric drag and solar radiation pressure.
  • Satellite Orbit Prediction: Learning-based orbit prediction methods have explored propagation-error correction, direct orbital-evolution learning, recurrent architectures, attention, decomposed temporal modules, and TLE-oriented prediction.These approaches differ in whether they correct physical propagation, directly model orbital evolution, or predict TLE-related quantities.
  • Deep Learning for Time-series Forecasting: OrbitNet refines positional representations with velocity-aware motion cues and studies satellite prediction from a representation-learning perspective.Its overview combines velocity-coupled refinement with orbital segment modeling for patch-wise temporal learning.
  • Deep Learning for Time-series Forecasting: Time-series foundation models broaden forecasting through general-purpose temporal representations learned from large-scale corpora and transfer across diverse scenarios.Representative models include TTM, TimesFM, MOIRAI, and Times-MoE.
  • Deep Learning for Time-series Forecasting: Generic forecasting models capture temporal dependencies but usually treat variables as ordinary channels rather than explicitly encoding position-velocity coupling.This limitation motivates a domain-aware representation-learning perspective for satellite orbit prediction.

3 Methodology

OrbitNet forecasts future positions from historical position and velocity sequences by refining positional representations with velocity-aware interactions, then modeling orbital evolution in temporal segments.

  • Problem Setup: The problem is formulated as forecasting future positions conditioned on historical position and velocity sequences.The predictor maps historical inputs to a future position sequence, with learnable parameters.
  • Velocity-coupled Refinement: Velocity-coupled refinement injects cross-variable velocity correlations into the positional representation space instead of merely concatenating velocity channels.Position remains the primary prediction-relevant signal while velocity supplies motion cues.
  • Velocity-coupled Refinement: The refinement module concatenates position and velocity representations and applies a temporal convolution that captures correlations across their channels.The resulting representation remains aligned with the positional representation space.
  • Orbital Segment Modeling: Orbital segment modeling partitions the refined sequence into non-overlapping temporal patches and performs patch-wise temporal learning.This design captures local orbital variations within segments while retaining a global view of the historical trajectory.
  • Orbital Segment Modeling: Each segment is projected into a latent representation and combined with learnable segment positional embeddings to preserve temporal order.The integrated representation captures intra-segment motion trends and inter-segment temporal dependencies before prediction.
  • Network Architecture: Normalization operates on each input sequence before representation learning, and denormalization restores predicted positions to the original physical scale.The scheme uses sample-specific temporal means and standard deviations.

4 Experiments

The experiments evaluate OrbitNet on curated orbital state sequences, using Starlink for source-domain training and testing and six unseen constellations for zero-shot testing.

  • Experimental Design: The evaluation includes in-domain Starlink forecasting, zero-shot testing across six unseen constellations, qualitative visualization, ablations, long-term forecasting, and variable-correlation analysis.The unseen constellations are ASTROCAST, CAPELLA, ICEYE, KINEIS, LEMUR, and SKYSAT.
  • Dataset Construction: The datasets originate from publicly accessible two-line element records collected from the Space-Track platform.These records provide orbital-element information for subsequent state-sequence generation.
  • Dataset Construction: Orekit converts sparse, irregular TLE updates into uniformly sampled orbital state sequences at a 1-minute interval.Each state contains three position and three velocity variables.
  • Dataset Split: The six zero-shot datasets are used only for testing and cover the period from 2025-02-26 to 2026-03-13.This setup evaluates cross-constellation generalization without source-domain training on those constellations.

4.2 Experimental Setup

The experimental setup uses uniformly sampled six-dimensional orbital histories to predict future three-dimensional positions, evaluating accuracy in both Starlink and zero-shot cross-constellation settings.

  • Forecasting Protocol: The historical look-back window is T=512 time steps and the prediction horizon is S=90 future steps.The sliding stride is fixed to T+S.
  • Testing: OrbitNet is evaluated in-domain on Starlink using a satellite-level 8:2 split and zero-shot on six unseen constellations without fine-tuning.The two settings assess source-constellation accuracy and cross-constellation generalization.
  • Baselines: The comparison includes Transformer, linear, MLP, CNN, time-series foundation, and orbit-specific learning baselines under the same forecasting protocol.The baselines include AutoFormer, FEDformer, iTransformer, DLinear, TimeXer, DropPatch, WPMixer, TimesNet, TTM, TimesFM, MOIRAI, Times-MoE, KiGRU, and DASR.
  • Forecasting Protocol: Each sample uses the same six-dimensional historical state sequence as input and predicts a future three-dimensional position sequence.The state variables are (x,y,z,v_x,v_y,v_z), while the target is (x,y,z).
  • Evaluation Metrics: Forecasting accuracy is measured with RMSE and MAE after denormalization, with errors reported in meters and averaged over three spatial coordinates.These metrics evaluate physical-scale prediction accuracy.

4.3 Main Results

OrbitNet achieves the best in-domain Starlink results among the compared methods and remains effective in zero-shot transfer across six unseen constellations. It also uses substantially fewer parameters than competing models.

  • OrbitNet achieves the best Starlink performance among foundation models, Transformer-based baselines, and domain-specific orbit prediction methods.
  • 48.6% lower MAE than the second-best DropPatch baseline, reducing prediction error from 6.50 m to nearly half.
  • OrbitNet achieves 3.34 m MAE and 22.80 m RMSE on Starlink, compared with 22.92 m RMSE for TimesNet.
  • 78,432 parameters make OrbitNet approximately 5.4× smaller than DropPatch and 7.0× smaller than DLinear.
  • OrbitNet achieves the best MAE on all six zero-shot datasets and reduces average MAE to 14.07 m, versus 45.47 m for DASR and 193.20 m for KiGRU.
  • OrbitNet shows more stable MAE across diverse constellations, while several generic and domain-specific baselines degrade sharply on particular datasets.

4.5 Qualitative Results

Qualitative comparisons on Starlink show that OrbitNet follows ground-truth trajectories more closely than TimesNet, iTransformer, and DLinear. It captures both global trends and local orbital variations.

  • The figure compares TimesNet, iTransformer, DLinear, and OrbitNet with ground-truth trajectories along all three spatial coordinates.
  • OrbitNet more closely aligns with the ground-truth trajectories than the competing methods.
  • TimesNet and iTransformer capture the global trend but exhibit substantial offsets, especially around trajectory peaks and valleys.
  • DLinear preserves the overall periodic pattern more stably than Transformer-based baselines, but clear discrepancies remain.
  • OrbitNet predictions almost overlap with the ground truth across the three spatial coordinates.

4.6 Ablation Study

Ablations show that velocity-coupled refinement and orbital segment modeling are complementary, while adaptive fusion and positional embeddings further improve OrbitNet. Hyperparameter analysis selects moderate patch length and hidden dimension.

  • Core components: Adding orbital segment modeling decreases MAE from 14.48 m to 4.27 m relative to the position-only baseline.
  • Core components: The full OrbitNet achieves 3.34 m MAE and 22.80 m RMSE, outperforming variants using either core component alone.
  • Fusion strategies: Using only the correlation-aware representation worsens MAE/RMSE from 14.48/31.94 m to 91.56/136.93 m.
  • Fusion strategies: The proposed coupling strategy outperforms concatenation and summation, for which summation achieves 8.73 m MAE and 34.06 m RMSE.
  • Fusion coefficient: Learnable fusion achieves 3.34 m MAE and 22.80 m RMSE, outperforming fixed coefficients by adaptively balancing positional and velocity-coupled representations.
  • Positional embedding: Positional embeddings improve segment modeling; sinusoidal embeddings reduce MAE from 6.95 m to 5.29 m, while learnable embeddings perform better.
  • Hyperparameter analysis: MAE is best at patch length L_p=16 and hidden dimension d=512, degrading when either setting is enlarged further.

4.7 Application to Long-term Orbit Prediction

OrbitNet maintains the best performance among selected baselines across forecasting horizons of 180, 360, and 720 steps. Longer horizons generally increase errors because of error accumulation.

  • Long-term orbit prediction is evaluated for downstream applications including collision avoidance and space traffic management.
  • OrbitNet achieves the best performance across all three long-term forecasting settings among the selected baselines.
  • Longer forecasting horizons generally produce larger prediction errors, attributed to error accumulation over extended future steps.
  • OrbitNet preserves relatively stable prediction quality under longer forecasting horizons.

4.8 Variable Correlation Analysis

OrbitNet's refinement module learns cross-variable interactions rather than processing orbital variables independently, with notable position–velocity dependencies that support positional representation refinement.

  • Variable Correlation Analysis: The convolution operator analyzes dependencies among the six concatenated orbital-state variables to produce a variate-wise dependency matrix.The inputs are (x,y,z,v_x,v_y,v_z), and absolute convolution weights are aggregated along the kernel dimension.
  • Variable Correlation Analysis: The learned dependency matrix has clear non-diagonal responses, indicating cross-variable interactions in the refinement module.This contrasts with independently processing orbital variables.
  • Variable Correlation Analysis: Position–velocity dependencies include x←v_x (0.187), z←v_x (0.186), and x←v_y (0.152), showing velocity cues for refining positional representations.The matrix also reveals dependencies within position variables and within velocity variables.
  • Variable Correlation Analysis: The observed dependencies provide interpretability support for velocity-coupled representation refinement and meaningful dependencies across orbital variables.These findings support informative representation learning from orbital-state interactions.

5 Conclusion and Discussion

The paper presents OrbitNet as a forecasting framework that combines velocity-coupled refinement with orbital segment modeling for satellite orbit prediction. It reports strong in-domain and zero-shot performance, while noting limited integration of explicit physical mechanisms and proposing broader orbital foundation models as future work.

  • Conclusion: OrbitNet addresses insufficient exploitation of the intrinsic relationship between position and velocity in learning-based orbit prediction.The framework is designed for accurate satellite orbit prediction.
  • Conclusion: Velocity-coupled refinement injects velocity-aware motion cues into positional representations, while segment modeling learns orbital evolution patterns at the segment level.Together, these components integrate state-variable interactions with temporal representation learning.
  • Conclusion: OrbitNet achieves the best in-domain performance and the best zero-shot MAE across six unseen satellite constellations.It maintains competitive RMSE on most zero-shot datasets.
  • Conclusion: The results suggest that explicitly exploiting position, velocity, and temporal orbital segments is critical for the reported orbit-prediction performance.The conclusion links these structured elements to the model's results.
  • Discussion: The current framework uses data-driven sequence learning without richer orbital mechanics priors, environmental perturbations, or maneuver information.The paper states that tighter integration with orbital dynamics may improve physical consistency and long-horizon stability.
  • Discussion: The work suggests developing orbital time-series foundation models beyond trajectory prediction for tasks including uncertainty estimation and anomaly detection.The paper also mentions conjunction risk assessment and space traffic management as potential downstream tasks.
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