Document Type : Original Research Paper
Authors
1 Department of Satellite Engineering, School of Advanced Technologies, Iran University of Science & Technology, Tehran, Iran
2 Department of Satellite Engineering, School of Advanced Technologies, Iran University of Science & Technology, Tehran, Iran
Abstract
Background and Objectives: Optical navigation for spacecraft in low Earth orbit is increasingly valued as a primary or backup solution when radio-frequency positioning becomes unreliable due to interference, intermittent coverage, or mission constraints. This study addresses the need for a robust, low-overhead processing chain that can estimate both state and position using only onboard imaging sensors. The approach intentionally combines two complementary sources of information: a star sensor, which stabilizes attitude estimation and improves the linearization needed for filtering, and an Earth-horizon sensor, which imposes a strong geometric constraint along the radial direction of the orbit. The overarching objective is to design and validate a non-synchronous fusion architecture that produces accurate and temporally well-behaved estimates without relying on external radio navigation. Specifically, the study aims to: develop a geometry-aware weighting strategy aligned with the radial, along-track, and cross-track frame; enforce principled statistical گیتینگ (ناحیه بندی) to ensure measurement quality; and apply selective post-processing to reduce short-period fluctuations in the along-track and cross-track directions while preserving the radial constraint provided by the Earth-horizon sensor. The intended outcome is a practical chain suitable for small satellites and missions with limited computational resources, and for operational contexts that are sensitive to transient estimation oscillations.
Methods: The investigation is performed in a high-fidelity simulation of a representative low Earth orbit with truth data generated by an orbital propagator and environmental models suitable for that regime. Two complementary measurement models are employed. The star sensor provides direction vectors that primarily stabilize the attitude solution and the associated linearization of the dynamics. The Earth-horizon sensor provides limb observations that yield a strong constraint on radial position. Because the sensors operate at different update rates, fusion is event-driven: measurement updates are processed whenever new data arrive, while state predictions evolve continuously according to the orbital dynamics and disturbance models. Temporal alignment across the two streams is handled through state interpolation. Measurement quality is controlled by statistical گیتینگ (ناحیه بندی) based on the Mahalanobis distance to reject outliers without discarding informative data. To respect the physics of the orbit geometry, an elliptical weighting scheme is formulated in the radial, along-track, and cross-track frame so that information is emphasized where each sensor is most informative. After filtering, a Rauch–Tung–Striebel smoother is applied selectively to the along-track and cross-track components, leaving the radial estimate unchanged to avoid weakening the Earth-horizon constraint. Performance is evaluated across multiple noise regimes and viewing conditions. Error behavior is characterized using root-mean-square and mean-absolute measures, together with time-domain analyses of innovations, acceptance rates for measurement updates, and qualitative inspection of position-component traces in the orbital frame.
Findings: The non-synchronous fusion of star and Earth-horizon measurements yields a clear and consistent reduction in overall position error relative to a filter-only baseline. The radial component exhibits rapid convergence and remains tightly constrained throughout, reflecting the strong geometric information provided by the Earth-horizon sensor. The selective post-processing smooths the along-track and cross-track components, attenuating short-period oscillations without introducing noticeable bias or drift, and doing so while intentionally leaving the radial component unaffected. Analyses of the innovations and the evolution of their orientation confirm that temporal alignment is effective and that the geometry-aware weighting is well tuned. Acceptance rates for measurement updates remain steady across scenarios, indicating that statistical گیتینگ (ناحیه بندی) is neither overly permissive nor excessively conservative. Under more challenging noise conditions, the chain maintains stable behavior: convergence persists, error growth is bounded, and the largest variability continues to appear in the along-track and cross-track directions, where the smoother delivers the most visible benefit. Visual inspection of the component-wise time histories corroborates these conclusions, showing consistent damping of fluctuations in the orbital plane and a preserved, physically plausible trajectory along the radial direction. Computational demands remain modest, supporting deployment on resource-limited platforms.
Conclusion: The proposed fusion chain—built on complementary sensors, event-driven filtering, geometry-aware weighting, principled گیتینگ (ناحیه بندی), and selective post-processing—offers a practical and deployable framework for optical navigation in low Earth orbit. Beyond improving accuracy, the method delivers temporally orderly estimates that are well suited to threshold-based decision making in flight operations. The approach is especially relevant for small satellites and missions that must tolerate intermittent or degraded radio-frequency positioning. Nevertheless, several factors warrant further investigation before routine operational use. Because the present results are obtained in simulation, progression to ground and hardware-in-the-loop testing with real sensors is essential, together with careful calibration of installation matrices. Sensitivity to Earth-horizon sensor bias, scattered light, extended eclipse periods, and short maneuver segments should be quantified. From an estimation standpoint, exploring alternative variants of the Kalman filter family, stronger constraints on the radial channel during smoothing, higher-fidelity environmental and dynamical models, and more precise handling of non-synchronous timing may yield additional gains. Taken together, these directions chart a clear path toward an operational, image-only navigation capability that can function independently of external radio infrastructure while meeting the accuracy and stability expectations of contemporary space missions.
Keywords
Main Subjects
COPYRIGHTS
© 2026 The Author(s). This is an open-access article distributed under the terms and conditions of the Creative Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)
)