Supervised Classification of LEO Debris Families Using Multi-Set Proper Elements

TL;DR

The paper tackles reconnecting unknown-origin debris objects to their parent fragments in low Earth orbit by leveraging multi-set proper elements and supervised learning. It extends prior MEE-based approaches by incorporating Poincaré and quaternion element sets, and introduces QTN$_p$ to preserve the semi-latus rectum and orbital scale, which significantly boosts classification performance. A modular synthetic pipeline simulates explosive breakups, propagates fragments with high-fidelity dynamics, extracts multiple proper-element representations, and trains neural networks on pairwise fragment data; the triple-set MEE + PNC + QTN model achieves ROC-AUC ≈ 0.858 and accuracy ≈ 0.75, outperforming single-set baselines. The findings demonstrate that combining complementary dynamical fingerprints improves debris-family discrimination in crowded LEO, with QTN$_p$ proving critical for quaternion-based features, and highlight considerations for domain shift, threshold tuning, and generalizability to real tracking data.

Abstract

Machine learning techniques using proper elements to reconnect families of satellite fragmentation debris have recently advanced, becoming key to space sustainability and domain awareness. However, an evolving circumterrestrial environment may limit their applicability, particularly when models are trained on outdated debris representations. In this work, we devise a computational pipeline using synthetic fragmentation data from explosive breakup events, generated via a Standard Breakup Model and propagated under a high-fidelity dynamical model. Proper elements are extracted using adapted algorithms for modified equinoctial (MEE), Poincar'e (PNC), and quaternion (QTN) sets. Extending beyond previous approaches limited to MEE space, we include PNC and QTN sets to broaden the dynamical fingerprints available to the classifier. Neural networks trained on various element combinations are used to determine if fragment pairs share a parent. Crucially, we identify a fundamental limitation when applying standard quaternion sets to neural networks: the loss of orbital size information during feature normalization. We introduce an augmented representation (QTN$_p$) that explicitly restores the semi-latus rectum, improving accuracy from 0.31 to 0.60 compared to the standard set. In synthetic Starlink-like LEO experiments, expanding proper-element sets generally improves discrimination. The best model, using a joint feature set (MEE + PNC + QTN), achieves an ROC-AUC of 0.858 compared to 0.789 for the MEE-only baseline, alongside higher accuracy and F1 scores.

Figures (10)

• Figure 1: Compute pipeline.
• Figure 2: Starlink element histograms for semi-major axis, eccentricity, and inclinations.
• Figure 3: The granularity of fragmentation is shown by varying the $k$ parameter. For explosions, Johnson suggests $k=1.6$evolve.
• Figure 4: Scatter plot of a sample of propagated fragments, distinguished by re-entry status. Thresholds were empirically derived for the satellite mass and velocity.
• Figure 5: Diagrams for the contiguous and spaced window inner loop algorithms.