A Satellite Ephemeris Correction Calculating Algorithm Based on the Hill Differential Equation

Abstract:

The Hill differential equation is used to describe the change characteristic of the ephemeris prediction error in order to calculate the satellite broadcast ephemeris error and the error change rate. After the ECEF coordinate system converses the satellite inertial coordinate system, both the satellite ephemeris correction and the correction accuracy can be calculated by the Kalman filter. When the GEO, IGSO and MEO satellites move over the China, the calculation algorithms based on the weighted least square, the velocity model of the Kalman filter and the Hill differential equation are compared in the computing performance of the ephemeris corrections by using the reference date of IGS website. The simulation results show that: the ephemeris correction solver value based on the Hill differential equation can accurately reflect the ephemeris error characteristics at the current time. And it is able to correctly reflect the perturbation impact for the satellite ephemeris error. The Hill differential equation method is more suitable at the master station for engineering application about the MEO, IGSO and GEO satellites.

• Periodical: Applied Mechanics and Materials (Volumes 336-338)
• Pages: 1682-1687
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.336-338.1682
• Online since: July 2013
• Authors: Rui Bin Zhao, Bo Shao, Rui Li, Zhi Gang Huang
• Keywords: Calculating Algorithm, Hill Differential Equation, Kalman Filter (KF), Satellite Ephemeris Correction, Satellite Navigation

References

[1] T. M. Corrigan, J. F. Hartranft, et al. GPS Risk Assessment Study Final Report. VS-99-007, (1999).

[2] Todd Walter, Per Enge. Modernizing WAAS. ION GNSS 17th International Technical Meeting of the Satellite Division. 2004; 1683-1690.

[3] Xue Rui, Zhang Jun, Zhu Yanbo. Cascade dual frequency smoothing for local area augmentation system. Chinese Journal of Aeronautics 2008; Vol. 22: 49-55.

DOI: 10.1016/s1000-9361(08)60068-0

[4] Hans Habereder, Timothy Schempp, Michael Bailey. Performance enhancements for the next phase of WAAS. ION GNSS 17th International Technical Meeting of the Satellite Division, 2004; 1350-1358.

[5] WAAS PS2008. Global positioning system wide area augmentation system (WAAS) performance standard. 1st ed. Washington D.C.: FAA, (2008).

[6] ICD-GPS-200C．The Interface Control Document of the Global Positioning System [S]．USA：ARINC Research Corporation，2000：23-67.

[7] Lu Boying, Chen Zongji. Linear Estimation and Stochastic Control[M]. Beijing: National Defense Industry Press, 1990：120-145.

[8] Colombo O. L, The Dynamics of Global Positioning System Orbits and the Determination of Precise Ephemeredes [J]. Journal of Geophysics Research, 1989, 94(B7): 9169-9182.

[9] Remondi B W．NGS second generation ASCII and orbit formats and associated interpolation studies [J]．Proceedings of the Twentieth General Assembly, Intermational Union of Geodesy andGeophysics，1991，1(1)：12-20.

[10] J. Kouba and P. Heroux, Precise Point Positioning Using IGS Orbit and Clock Products[J]. GPS Solutions. 2001, 5(2): 12-28.

DOI: 10.1007/pl00012883

[11] Cai Chenglin, Li Xiaohui, Wu Haitao. Anaysis of the DOP and Positioning Performance of Composite Satellite Constellation[J]. Science of Surveying and Mapping, 2009, 34(3): 67-69.

[12] Cai Chengling, Li Xiaohui, Wu Haitao. An Analysis of the Wide Area Differential Method of Geostationary Orbit Satelites[J]. Science in China Series: Physics Mechanics & Astronomy, 2009, 52(2): 310-314.

DOI: 10.1007/s11433-009-0036-y

[13] Oscar L. Colombo．Real-Time, Wide-Area, Precise Kinematic Positioning Using Data from Internet NTRIP Streams [A]．Proceedings of The 21th International Technical Metting of the Satellite Division of The Institute of Navigation [C]．Savannah：Institute of Navigation，2008：327-337.

[14] Crowell D, Clemens GM, Celestial Mechanics Methods [M]. Beijing Science Press. 1986: 388-440.