Jun Yoshida, NEC Corporation; Taichiro Sano, NEC Corporation; Daiki Mori, NEC Corporation; Katsuaki Taya, NEC Corporation
https://doi.org/10.64861/FNPO3282
Keywords: Initial Orbit Determination (IOD), Angles-Only Observation, Geostationary Orbit (GEO), Space Domain Awareness (SDA), Hybrid Neural-Algebraic Approach, Algebraic Geometry, Homotopy Continuation Method, Deep Learning, Noise Robustness, Space Debris
Abstract:
Angles-only initial orbit determination (IOD), which relies solely on right ascension (RA) and declination (Dec) observations, is a core challenge in space domain awareness (SDA). Geostationary orbit (GEO) satellites, in particular, pose an acute need for high-accuracy orbit determination from angle-only measurements, as their orbital characteristics make range information extremely difficult to obtain. Recently, a groundbreaking purely geometric approach based on algebraic geometry and homotopy continuation methods was proposed, requiring neither observation timestamps nor prior initial-value estimates. This method elegantly formulates orbits as three-dimensional quadric surfaces and guarantees global convergence; however, it suffers from a critical vulnerability to real-world observation noise. In particular, singular observation geometries where the orbital plane and the line of sight are nearly coplanar, or extremely short observation intervals, cause even slight measurement errors in RA and Dec to severely degrade estimation accuracy. Although extending the problem to an overdetermined formulation (six or more observations) can mitigate noise effects, this causes an explosive increase in tracking paths within the homotopy continuation method — from 66 to over 1,000 — dramatically raising the computational cost and creating a practical dilemma. This study proposes a novel hybrid neural-algebraic approach that bridges the gap between “mathematical ideals” and “real-world noise” by fusing the representational power of deep learning with the rigor of algebraic geometry. The core of our framework lies in exploring an integrative mechanism that achieves system-level mutual complementation between the outstanding noise robustness of deep learning and the global, absolute orbital constraints provided by algebraic geometry. By designing a cooperative computational pipeline that maximizes the respective strengths of data-driven learning and rigorous mathematical structures, our approach aims to fundamentally circumvent the “explosive growth of computational paths associated with overdetermined problems” that conventional algebraic-geometric methods have required to maintain accuracy. Validation using real observational data (RA and Dec) of GEO satellites demonstrates that the proposed method achieves stable orbit estimation accuracy even under high-noise conditions where conventional algebraic-geometric methods suffer significant degradation, thereby confirming remarkable robustness against noise. By realizing improved accuracy under severe noise environments while minimizing computational overhead, this approach establishes a powerful foundation for next-generation autonomous and computationally efficient orbit determination systems for unknown celestial objects and the ever-growing population of space debris.
Date of Conference: September 15-18, 2026
Track: Astrodynamics