Satellites that navigate by talking to each other slowly lose their sense of direction, because nothing in a purely Earth-orbiting network provides a fixed reference in space. A new study shows that adding four satellites in elliptical lunar frozen orbits (ELFO) to China's BeiDou-3 navigation constellation can eliminate this drift. Using real inter-satellite link (ISL) ranging data from BeiDou-3 Medium Earth Orbit (MEO) satellites together with simulated lunar link measurements, the researchers kept the constellation's orientation stable for 60 days and held the mean user range error (URE) at 0.35 m, while the lunar satellites themselves were located to within 2.3 m in three dimensions.
Autonomous orbit determination (AOD) lets navigation satellites calculate their own orbits using only inter-satellite ranging, removing dependence on ground stations that can fail or be disrupted. But because relative range measurements cannot sense the overall rotation of a constellation, the whole network gradually drifts in orientation. Predicted orbit forecasts can slow this drift but cannot stop it, and the error grows over time, especially during eclipse seasons. Because of these challenges, there is a need for an external, dynamics-based reference that can make the constellation's absolute orientation observable over long missions.
The study, led by Xia Lin and Baojun Lin of the Chinese Academy of Sciences, was published (DOI: 10.1186/s43020-026-00217-9) in Satellite Navigation on 17 September 2026. The team combined 24 BeiDou-3 Medium Earth Orbit (MEO) satellites with four elliptical lunar frozen orbits (ELFO) satellites in a centralized extended Kalman filter (EKF), processing 60 days of real onboard BeiDou-3 inter-satellite link (ISL) measurements alongside simulated Earth-moon links. Three cases were compared: no rotational correction, traditional prediction-based correction, and the joint Earth-moon solution.
The key insight is that lunar gravity dominates the motion of ELFO satellites, breaking the dynamical symmetry that makes a GNSS (Global Navigation Satellite System) constellation's rotation unobservable. The team's observability analysis showed that the condition number of the position information matrix fell from roughly 10¹⁵–10¹⁸ with MEO satellites alone — effectively a singular, rank-deficient case — to about 10² once four ELFO satellites were added. In the joint solution, three-axis rotational biases stayed within 13.59, 10.27, and 4.04 milliarcseconds (mas) over 60 days, compared with more than 300 mas without correction and about 18 mas with prediction-based correction. The BeiDou-3 user range error (URE) remained at 0.35 m, versus 7.85 m and 0.60 m in the other two cases. The ELFO satellites also achieved high accuracy, with maximum radial, along-track, and cross-track errors below 0.16 m, 1.7 m, and 1.8 m.
The authors said the work addresses a limitation that has persisted since the earliest autonomous navigation concepts. They said that because the moon's gravity acts so differently on lunar satellites than Earth's gravity acts on MEO satellites, the two constellations respond differently to the same rotation, making that rotation visible in the ranging data. They added that using real BeiDou-3 inter-satellite link measurements, rather than simulations alone, gives a more realistic picture of what today's operational system can achieve, and that the lunar satellites essentially act as an anchor for the entire network.
The approach could support future lunar navigation and communication constellations. The ELFO, our paper studied，offers favorable coverage of the polar regions while requiring low station-keeping budgets. Both ESA's Moonlight program(ESA, 2024) and NASA’s LunaNet initiative (NASA, 2021) have selected ELFO as the reference orbit for their planned lunar navigation and communication constellations to cover the lunar south pole. Beyond the moon, the method offers a path to long-duration autonomous navigation for Earth-orbiting constellations, reducing reliance on ground infrastructure and improving resilience. The authors note that future work will replace simulated lunar links with real onboard observations once lunar satellite missions are operational, and will develop link scheduling strategies that also provide continuous positioning, navigation, and timing (PNT) services to lunar users.
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References
DOI
Original Source URL
https://doi.org/10.1186/s43020-026-00217-9
Funding information
Supported by the Strategic Priority Research Program of the Chinese Academy of sciences (Grant No. XDA 0350405) and the National Natural Science Foundation of China (Grant No. 42374044).
About Satellite Navigation
Satellite Navigation (ISSN: 2662-1363; ISSN: 2662-9291) Satellite Navigation is the official journal of the Aerospace Information Research Institute . The journal aims to report innovative ideas, new results, and progress in the theories, techniques, and applications of satellite navigation. The journal welcomes original articles, reviews and commentaries.
Satellite Navigation
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Preliminary analysis for the joint autonomous orbit determination of the BDS-3 MEO satellites and lunar ELFO satellites based on inter-satellite links
17-Sep-2026
The authors declare that they have no competing interests.