Summary
When trying to predict how groups of satellites will behave, it’s important to have a wide range of accurate examples of their orbits. The authors found that when only a small number of reference orbits are available, traditional methods either fail to provide enough variety or generate unrealistic examples. They tested a new approach using constrained diffusion models that generate physically plausible new orbits similar to the original data but found that these models can only augment existing data locally and cannot fully replace the detailed physics needed for accurate satellite analysis. This means that while constrained diffusion models help increase orbital data diversity, they do not eliminate the need for physics-based methods.
What this means in practice
- •For satellite mission planners: Generate augmented orbital datasets to support limited-trajectory scenario analysis with improved physical realism.
- •For defense aerospace analysts: Use constrained diffusion to locally extend known satellite orbits for better simulations of space situational awareness campaigns.
Tested on simulated data.
Authors
Omar Ramadan, Sam Siavoshian, Amir Kashif Saeed, Benjamin A. Johnson, Amin M. E. -A. Diab, Benjamin M. Rodriguez
Abstract
Constellation Monte Carlo results depend on the orbital population used to evaluate a tasking policy. With scarce reference trajectories, replay limits geometric diversity, while independent orbital-element jitter can violate physical constraints. We study constrained diffusion for orbital-population augmentation. A force-conditioned diffusion model learns a 13-dimensional orbital prior, recovering semimajor axis from perigee altitude and eccentricity; Basilisk propagates each sample under one of five force-model tiers. Using 800 reference trajectories, we compare diffusion with jittered bootstrap, per-tier Gaussian mixtures, and a conditional variational autoencoder, and evaluate distributional fidelity, support shift, classical astrodynamics diagnostics, and 4,000 paired GoDSAT-compatible campaigns. The largest diffusion model achieves held-out trajectory MMD of 0.0171 +/- 0.0239, similar to bootstrap (0.0170) and the mixture (0.0198), but samples farther from training priors (median nearest-training distance 2.7 versus 0.10 standardized units). All generators fail to match the shifted-blind population (classifier AUC 0.991-0.998). Endpoint-conditioned samples satisfy Lambert boundaries but have greater interior error than the matched Lambert reference (29.2 versus 5.7 km mean RMSE). Residual diffusion improves selected sparse forecasts and catalog-mode recall but does not outperform classical estimators on custody ranking. In a fixed 16-satellite configuration, diffusion yields similar mean custody to replay and bootstrap, while the force-tier mixture shifts custody by about 5.5 percentage points. Constrained diffusion supports local, in-support augmentation but cannot replace orbital dynamics or serve as an operational posterior. Orbital-population construction is a consequential source of uncertainty in constellation analysis.