Print Recently, the research team from the National Time Service Center (NTSC), Chinese Academy of Sciences (CAS), studied the probability distribution and fitting accuracy of the ephemeris parameters of LEO satellites flying at different altitudes, revealing the key aspects that require attention in the generation of LEO navigation satellite ephemeris.
This study was published in the international journal GPS Solutions on February 10, 2026, entitled "Characteristics of probability distribution and fitting accuracy for LEO satellite ephemeris".
LEO satellites have demonstrated great potential to enhance the existing GNSSs for better Positioning, Navigation, and Timing (PNT) services. The availability of high-accuracy and reliable broadcast ephemeris for LEO satellites is a crucial prerequisite for such augmentation, as it determines whether accurate satellite orbital information can be effectively transmitted to ground users. Although extensive research on broadcast ephemeris modeling for GNSS satellites has been conducted since the last century, those established strategies cannot be directly applied to LEO navigation augmentation systems. LEO satellites orbit much closer to the Earth, resulting in significantly faster speeds and greater susceptibility to high-order gravity terms and atmospheric drag. For generating high-accuracy and reliable broadcast ephemeris for LEO satellites, proper ephemeris fitting is required. Meanwhile, the distribution of various ephemeris parameters is also of concern, as setting proper thresholds is important when designing the satellite navigation message, yet it is rarely studied.
According to Prof. Kan Wang, the team leader of the LEO-augmented PNT from the NTSC, the research helped to ensure sustained and reliable ephemeris design of LEO navigation satellite systems.
Twelve LEO satellites flying at different altitudes (300-1400 km) with different orbital characteristics are selected for 16-, 18-, 20-, and 22-parameter ephemeris fitting. Three critical factors: the orbital height, the ephemeris fitting interval, and the number of ephemeris parameters, are considered in the investigation of the probability distributions of various ephemeris parameters and the ephemeris fitting accuracy. The results revealed that increasing the orbital altitude (Fig. 1) and extending the fitting interval can both enhance concentration in the distributions of ephemeris parameters, whereas increasing the number of ephemeris parameters induces the opposite effect. Meanwhile, the distributions of several crucial ephemeris parameters exhibit certain correlations with the satellite orbital altitude and inclination, which requires special attention when designing LEO broadcast ephemeris. Regarding the ephemeris fitting accuracy, it was found that increasing the orbital altitude and the number of ephemeris parameters can both improve the fitting accuracy, whereas extending the fitting interval degrades the fitting accuracy. Furthermore, for LEO satellites operating at higher altitudes (e.g., above 1000 km), enhanced flexibility in fitting strategies is exhibited in producing high-accuracy ephemeris (Fig. 2).
Fig. 1 Probability density distribution of the orbital inclination rate using the 16-parameter model with a 10-min fitting interval for the 12 selected LEO satellites. The satellites are ranked from low to high altitudes in the legend (Image by Wei and Wang 2026)
Fig. 2 Available strategies for LEO satellite ephemeris fitting with a fitting accuracy below 1 cm (Image by Wei and Wang 2026)
The analysis in this research reveals an inherent trade-off in future architecture design of LEO satellite navigation messages: increasing the ephemeris fitting accuracy inevitably exacerbates the dispersion of the ephemeris parameters. This implies that blindly pursuing small fitting errors may lead to larger variations in the ephemeris parameters, which increases the required thresholds for healthy ephemeris parameters and, indirectly, influences the required resources for data transmission and the reliability of the message.