Abstract
A key limitation in the precise orbit determination (POD) of BeiDou geostationary Earth orbit (GEO) satellites is the relatively static observation geometry, which results in strong correlations between orbital elements, solar radiation pressure (SRP) parameters, and ambiguities. Satellite laser ranging (SLR) residuals of BeiDou G01 satellite orbits display a clear dependence on the Sun elongation angle ε, as well as a bias of approximately − 40 cm. These indicate the low performance of BeiDou GEO orbits. In this study, we confirmed that the perturbation caused by the communication antenna generates the ε-angle-dependent variation and the bias of approximately − 14.9 cm in BeiDou G01 SLR residuals. Besides, the orbit-normal (ON) attitude mode used by BeiDou GEO satellites as well as an orbital inclination of nearly 0° results in strong linear correlations between the POD estimated parameters, i.e., satellite’s initial position on the Z-axis and the constant Y-bias along the cross-track direction. Hence, the solar pressure models, such as Extended CODE Orbit Model (ECOM) in ON mode, with the Y-axis along the cross-track direction are deficient for SRP estimation of BeiDou GEO satellites. In this study, an empirical a priori SRP model was established for BeiDou GEO satellites to enhance the ECOM using an empirical fitting approach. This proposed model is expressed in DYB frame using eight parameters. With this model, precise BeiDou GEO orbits in 2016 were determined. SLR validation indicated that the systematic ε-angle-dependent error was reduced and the large negative bias almost vanished. In general, better than 10-cm root-mean-square of SLR validation was achieved, and also an improvement of 4–5 times over the five-parameter ECOM model was obtained.
Similar content being viewed by others
Abbreviations
- ABW:
-
Adjustable box-wing
- BETN:
-
BeiDou Experimental Tracking Network
- CA:
-
Communication antenna
- CODE:
-
Center for Orbit Determination in Europe
- ECOM:
-
Extended CODE Orbit Model
- ECOM-ON:
-
ECOM for orbit-normal mode
- ECOM-YS:
-
ECOM for yaw-steering mode
- GEO:
-
Geostationary Earth orbit
- GNSS:
-
Global Navigation Satellite System
- IGSO:
-
Inclined geosynchronous orbit
- LRA:
-
Laser retroreflector array
- MEO:
-
Medium Earth orbit
- MGEX:
-
Multi-GNSS Experiment
- OBD:
-
Orbit boundary discontinuity
- ON:
-
Orbit-normal mode
- POD:
-
Precise orbit determination
- RDSS:
-
Radio determination satellite service
- RNSS:
-
Radio navigation satellite service
- SLR:
-
Satellite Laser Ranging
- SRP:
-
Solar radiation pressure
- SP:
-
Solar panel
- YS:
-
Yaw steering mode
References
Arnold D, Meindl M, Beutler G, Dach R, Schaer S, Lutz S, Prange L, Sośnica K, Mervart L, Jäggi A (2015) CODE’s new solar radiation pressure model for GNSS orbit determination. J Geod 89(8):775–791. https://doi.org/10.1007/s00190-015-0814-4
Bar-Sever YE (1996) A new model for GPS yaw attitude. J Geod 70(11):714–723. https://doi.org/10.1007/BF00867149
Bar-Sever Y, Kuang D (2004) New empirically derived solar radiation pressure model for Global Positioning System satellites. Jet Propulsion Laboratory, Pasadena, CA, USA, pp 1–11. https://ipnpr.jpl.nasa.gov/progress_report/42-159/159I.pdf. Accessed 10 June 2018
Bar-Sever Y, Kuang D (2005) New empirically derived solar radiation pressure model for Global Positioning System satellites during eclipse seasons. Interplanetary Network Progress Report 42-160, Jet Propulsion Laboratory, Pasadena, CA, USA, pp 1–4. https://ipnpr.jpl.nasa.gov/progress_report/42-160/160I.pdf. Accessed 10 June 2018
Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M, Verdun A (1994) Extended orbit modeling techniques at the CODE processing center of the International GPS Service for Geodynamics (IGS): theory and initial results. Manuscr Geod 19(6):367–386
Dilssner F (2010) GPS IIF-1 satellite antenna phase center and attitude modelling. Inside GNSS. September, 2010, pp 59–64
Dilssner F, Springer T, Gienger G, Dow J (2011) The GLONASS-M satellite yaw-attitude model. Adv Space Res 47(1):160–171. https://doi.org/10.1016/j.asr.2010.09.007
Dow JM, Neilan RE, Rizos C (2009) The International GNSS Service in a changing landscape of global navigation satellite systems. J Geod 83(3–4):191–198. https://doi.org/10.1007/s00190-008-0300-3
Dudok de Wit T, Kopp G, Fröhlich C, Schöll M (2017) Methodology to create a new total solar irradiance record: making a composite out of multiple data records. Geophys Res Lett 44:1196–1203. https://doi.org/10.1002/2016GL071866
Eastes RW, McClintock WE, Burns AG, Anderson DN, Andersson L, Codrescu M, Correira JT, Daniell RE, England SL, Evans JS, Harvey J, Krywonos A, Lumpe JD, Richmond AD, Rusch DW, Siegmund O, Solomon SC, Strickland DJ, Woods TN, Aksnes A, Budzien SA, Dymond KF, Eparvier FG, Martinis CR, Oberheide J (2017) The Global-Scale Observations of the Limb and Disk (GOLD) mission. Space Sci Rev 212:383–408. https://doi.org/10.1007/s11214-017-0392-2
Fliegel HF, Gallini TE (1996) Solar force modeling of block IIR Global Positioning System satellites. J Spacecraft Rockets 33(6):863–866. https://doi.org/10.2514/3.26851
Fliegel HF, Gallini TE, Swift ER (1992) Global Positioning System radiation force model for geodetic applications. J Geophys Res 97(B1):559–568. https://doi.org/10.1029/91JB02564
Früh C, Jah MK (2014) Coupled orbit-attitude motion of high area-to-mass ratio (HAMR) objects including efficient self-shadowing. Acta Astronaut 95:227–241. https://doi.org/10.1016/j.actaastro.2013.11.017
Ge H, Li B, Ge M, Shen Y, Schuh H (2017) Improving BeiDou precise orbit determination using observations of onboard MEO satellite receivers. J Geod 91(12):1447–1460. https://doi.org/10.1007/s00190-017-1035-9
Griffiths J, Ray JM (2009) On the precision and accuracy of IGS orbits. J Geod 83(3–4):277–287. https://doi.org/10.1007/s00190-008-0237-6
Guo J, Xu X, Zhao Q, Liu J (2016) Precise orbit determination for quad-constellation satellites at Wuhan University: strategy, result validation, and comparison. J Geod 90(2):143–159. https://doi.org/10.1007/s00190-015-0862-9
Guo F, Li X, Zhang X, Wang J (2017a) Assessment of precise orbit and clock products for Galileo, BeiDou, and QZSS from IGS Multi-GNSS Experiment (MGEX). GPS Solut 21(1):279–290. https://doi.org/10.1007/s10291-016-0523-3
Guo J, Chen G, Zhao Q, Liu J, Liu X (2017b) Comparison of solar radiation pressure models for BDS IGSO and MEO satellites with emphasis on improving orbit quality. GPS Solut 21(2):511–522. https://doi.org/10.1007/s10291-016-0540-2
Guo J, Wang C, Zhao Q, Li Z, Liu J (2017c) Solar radiation pressure model for BeiDou GEO satellites. In: IGS workshop, 3–7 July 2017, Paris, France
Kouba J (2009) A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solut 13(1):1–12. https://doi.org/10.1007/s10291-008-0092-1
Liu J, Gu D, Ju B, Shen Z, Lai Y, Yi D (2016) A new empirical solar radiation pressure model for BeiDou GEO satellites. Adv Space Res 57(1):234–244. https://doi.org/10.1016/j.asr.2015.10.043
Luthcke SB, Marshall JA, Rowton SC et al (1997) Enhanced radiative force modeling of the tracking and data relay satellites. J Astronaut Sci 45(3):349–370
Marshall JA, Luthcke SB (1994) Modeling radiation forces acting on TOPEX/Poseidon for precision orbit determination. J Spacecr Rockets 31(1):99–105. https://doi.org/10.2514/3.26408
Mazarico E, Zuber MT, Lemoine FG, Smith DE (2009) Effects of self-shadowing on nonconservative force modeling for mars-orbiting spacecraft. J Spacecr Rockets 46(3):662–669. https://doi.org/10.2514/1.41679
Milani A, Nobili AM, Farinella P (1987) Non-gravitational perturbations and satellite geodesy. Adam Hilger, Bristol
Montenbruck O, Schmid R, Mercier F, Steigenberger P, Noll C, Fatkulin R, Kogure S, Ganeshan AS (2015a) GNSS satellite geometry and attitude models. Adv Space Res 56(6):1015–1029. https://doi.org/10.1016/j.asr.2015.06.019
Montenbruck O, Steigenberger P, Hugentobler U (2015b) Enhanced solar radiation pressure modeling for Galileo satellites. J Geod 89(3):283–297. https://doi.org/10.1007/s00190-014-0774-0
Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Romero I, Noll C, Stürze A, Weber G, Schmid R, MacLeod K, Schaer S (2017a) The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)—achievements, prospects and challenges. Adv Space Res 59(7):1671–1697. https://doi.org/10.1016/j.asr.2017.01.011
Montenbruck O, Steigenberger P, Darugna F (2017b) Semi-analytical solar radiation pressure modeling for QZS-1 orbit-normal and yaw-steering attitude. Adv Space Res 59(8):2088–2100. https://doi.org/10.1016/j.asr.2017.01.036
Pearlman MR, Degnan JJ, Bosworth JM (2002) The International Laser Ranging Service. Adv Space Res 30(2):135–143. https://doi.org/10.1016/S0273-1177(02)00277-6
Petit G, Luzum B (2010) IERS conventions 2010, technical report. IERS Convention Center
Rodriguez-Solano CJ, Hugentobler U, Steigenberger P (2012) Adjustable box-wing model for solar radiation pressure impacting GPS satellites. Adv Space Res 49(7):1113–1128. https://doi.org/10.1016/j.asr.2012.01.016
Rodriguez-Solano CJ, Hugentobler U, Steigenberger P, Allende-Alba G (2013) Improving the orbits of GPS block IIA satellites during eclipse seasons. Adv Space Res 52(8):1511–1529. https://doi.org/10.1016/j.asr.2013.07.013
Springer TA, Beutler G, Rothacher M (1999) A new solar radiation pressure model for GPS satellites. GPS Solut 2(3):50–62. https://doi.org/10.1007/PL00012757
Steigenberger P, Hugentobler U, Hauschild A, Montenbruck O (2013) Orbit and clock analysis of Compass GEO and IGSO satellites. J Geod 87(6):515–525. https://doi.org/10.1007/s00190-013-0625-4
Steigenberger P, Montenbruck O, Hugentobler U (2015) GIOVE-B solar radiation pressure modeling for precise orbit determination. Adv Space Res 55(5):1422–1431. https://doi.org/10.1016/j.asr.2014.12.009
Steigenberger P, Thoelert S, Montenbruck O (2018) GNSS satellite transmit power and its impact on orbit determination. J Geod 92(6):1–16. https://doi.org/10.1007/s00190-017-1082-2
Sun B, Su H, Zhang Z, Kong Y, Yang X (2016) GNSS GEO satellites precise orbit determination based on carrier phase and SLR observations. In: IGS workshop 2016, 8–12 Feb 2016, Sydney, Australia
Tan B, Yuan Y, Zhang B, Hsu H, Ou J (2016) A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM. Sci Rep 6:32967. https://doi.org/10.1038/srep32967
Zhao Q, Guo J, Li M, Qu L, Hu Z, Shi C, Liu J (2013) Initial results of precise orbit and clock determination for COMPASS navigation satellite system. J Geod 87(5):475–486. https://doi.org/10.1007/s00190-013-0622-7
Zhao Q, Chen G, Guo J, Liu J, Liu X (2017a) An a priori solar radiation pressure model for the QZSS Michibiki satellite. J Geod. https://doi.org/10.1007/s00190-017-1048-4
Zhao Q, Wang C, Guo J, Yang G, Liao M, Ma H, Liu J (2017b) Enhanced orbit determination for BeiDou satellites with FengYun-3C onboard GNSS data. GPS Solut 21(3):1179–1190. https://doi.org/10.1007/s10291-017-0604-y
Zhao Q, Wang C, Guo J, Wang B, Liu J (2018) Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis. GPS Solut 22:4. https://doi.org/10.1007/s10291-017-0673-y
Ziebart M (2004) Generalized analytical solar radiation pressure modeling algorithm for spacecraft of complex shape. J Spacecr Rockets 41(5):840–848. https://doi.org/10.2514/1.13097
Acknowledgements
The IGS MGEX, iGMAS, and ILRS are greatly acknowledged for providing the Multi-GNSS and SLR tracking data. The research is partially supported by the National Natural Science Foundation of China (Grant No. 41504009, 41574030). Finally, the authors are also grateful for the comments and remarks of three reviewers and editor, which helped to significantly improve the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, C., Guo, J., Zhao, Q. et al. Empirically derived model of solar radiation pressure for BeiDou GEO satellites. J Geod 93, 791–807 (2019). https://doi.org/10.1007/s00190-018-1199-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-018-1199-y