Analytical representations of precise orbit predictions for Earth orbiting space objects

• Published in: Advances in space research Vol. 59; no. 2; pp. 698 - 714
• Main Authors: Sang, Jizhang, Li, Bin, Chen, Junyu, Zhang, Pin, Ning, Jinsheng
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.01.2017
• Subjects: Accuracy; Catalogue management; Computational efficiency; Computing time; Earth orbits; Mathematical analysis; Mathematical models; Meters; Orbit representation; Precise orbit prediction; Space objects; State vectors; Orbit representation; Space objects; Precise orbit prediction; Catalogue management
• ISSN: 0273-1177; 1879-1948
• DOI: 10.1016/j.asr.2016.10.031

Accurate orbits of Earth orbiting space objects are usually generated from an orbit determination/prediction process using numerical integrators, and presented to users in a tabulated form or a state vector including force model parameters. When dealing with hundreds of thousands of space objects such as in the space conjunction assessment, the memory required for the tabulated orbits or the computing time for propagating orbits using the state vector are both confronting to users. This paper presents two methods of analytically representing numerical orbits considering the accuracy, computing efficiency and memory. The first one is a two-step TLE-based method in which the numerical orbits are first fitted into a TLE set and then correction functions are applied to improve the position accuracy. In the second method, the orbit states are represented in equinoctial elements first, and then again correction functions are applied to reduce the position errors. Experiments using six satellite laser ranging (SLR) satellites and 12 debris objects with accurate orbits show that both methods can represent the accurate orbits over 5days in an accuracy of a few dozens of meters for the circular orbits and several hundred meters for the eccentric orbits. The computing time is similar to that using the NORAD TLE/SGP4 algorithm, and storage for the orbit elements and function coefficients is about 3–5KB. These features could make the two methods beneficial for the maintenance of orbit catalog of large numbers of space objects.