Accuracy Loss in LEO Satellite Orbits and Clocks Using Different Interpolation Methods and Sampling Rates

Beixi Chen, Jinqian Wang, Kan Wang, Meifang Wu, Ahmed El-Mowafy, Xuhai Yang

Peer Reviewed

Abstract:	High-accuracy and real-time Low Earth Orbit (LEO) satellite orbits and clocks are needed when adding LEO observations to Global Navigation Satellite Systems (GNSS) observations to improve Positioning, Navigation, and Timing (PNT) services. LEO satellite orbital and clock products can be generated with different sampling intervals based on various user requirements. Unlike GNSS satellites, LEO satellites operate at much lower altitudes and fly with higher velocities, placing them in a highly dynamic environment with typically non-perfect temperature control. In such conditions, low-sampling-rate products could fail to accurately characterize satellite orbits and clocks. High-sampling-rate products, e.g., the kinematic orbits and clocks, could require higher-sampled observations that require higher capacity for data downlinking and longer computation times. The post-processed orbital and clock products may need to be converted between different time systems, e.g., the GPS Time (GPST) and the Beidou Navigation Satellite System Time (BDT), which are 14 s shifted from each other. This all presents the needs for convenient and mathematical interpolations based on LEO satellite orbital and clock products that were already determined. In this contribution, real GNSS observation data collected onboard LEO satellites, along with post-processed GNSS orbit and clock products, are utilized to generate LEO satellite orbits and clocks employing both the reduced-dynamic and kinematic Precise Orbit Determination (POD) methods. Various mathematical interpolation methods, such as the Lagrange interpolation, the linear/quadratic interpolation, the cubic spline interpolation and the Chebyshev interpolation, are then applied to interpolate the orbits and clocks at different sampling intervals (from 10 s to 400 s) to 5 s products, and their results are compared. In addition, this approach allows us to investigate the accuracy degradation of LEO satellite orbits and clocks according to the selected sampling interval, and these results are compared with those of the GNSS satellites. The experimental results demonstrate that the accuracy loss of the RD and the kinematic (KN) orbits in the radial, along-track, and cross-track directions, as well as the mean RMS of the Orbital User Range Errors (OURE), exhibits an exponential growth trend when extending the sampling interval from the original one of the determined LEO satellite orbits. The RD OURE accuracy loss reaches 1 cm at an interpolation sampling interval of approximately 190 s, while KN OURE reaches the same threshold at around 170 s. At a 300 s sampling interval, the RD accuracy loss remains at the centimeter level, whereas the KN results using the same data set degrade to the decimeter level. For LEO satellite clock interpolation, Lagrange and cubic spline methods achieve the highest precision, with values better than 0.06 ns for 600 (sample interval)-to-5 s (interpolation) and approximately 0.033 ns for 300-to-5 s interpolation. In comparison, GNSS satellite orbit interpolation accuracy loss remains within 1 mm even for 900- to-5 s interpolation, while GNSS clock interpolation accuracy loss remains below 0.02 ns for 600-to-5 s interpolation. The LEO satellites generally face a sharper rise in the interpolation accuracy loss than the GNSS satellites when extending the sampling intervals of the original clock and orbital products.
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	2456 - 2469
Cite this article:	Chen, Beixi, Wang, Jinqian, Wang, Kan, Wu, Meifang, El-Mowafy, Ahmed, Yang, Xuhai, "Accuracy Loss in LEO Satellite Orbits and Clocks Using Different Interpolation Methods and Sampling Rates," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 2456-2469. https://doi.org/10.33012/2025.20333
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