Abstract
The Low Earth Orbit (LEO) enhanced Global Navigation Satellite System (LeGNSS) relies on LEO satellites to broadcast GNSS-like navigation signals, providing real-time satellite orbit and clock information to enhance GNSS service performance. To ensure real-time positioning service, a period of orbit prediction becomes necessary due to the limited signal bandwidth and computation time delay. In contrast to traditional dynamic model, on-board accelerometers offer more accurate non-gravitational acceleration for LEO satellites. In this study, we improve the accuracy of short-term (1 h) LEO satellite orbit prediction by utilizing predicted accelerometer data instead of the traditional dynamic model. We combine the Least Squares (LS) and Autoregressive (AR) methods to model and predict accelerometer data from the GRACE-A and GRACE-B (500 km) satellites. In the experiment, the 1-h prediction accuracy of the accelerometer data in the 3-Dimensional (3D) direction is 57.1 nm/s2 for the GRACE-A satellite and 56.5 nm/s2 for the GRACE-B satellite, respectively. When utilizing the predicted accelerometer data for 1-h orbit predictions, the predicted orbit precision in the 3D direction is 0.19 m for both GRACE-A and GRACE-B satellites. The orbit prediction accuracy shows an improvement of more than 65% compared to the traditional dynamic model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The GRACE satellites data in this experiment are public and can be downloaded at following address. GRACE-A/B: https://search.earthdata.nasa.gov/.
References
Adhya S, Ziebart M, Sibthorpe A, Arrowsmith P, Cross P (2005) Thermal force modeling for precise prediction and determination of spacecraft orbits. Navig 52(3):131–144. https://doi.org/10.1002/j.2161-4296.2005.tb01740.x
Avanzini G, de Angelis EL, Giulietti F, Serrano N (2019) Attitude control of low earth orbit satellites by reaction wheels and magnetic torquers. Acta Astronaut 160:625–634. https://doi.org/10.1016/j.actaastro.2019.03.013
Berger C, Biancale R, Barlier F (1998) Improvement of the empirical thermospheric model DTM: DTM94–a comparative review of various temporal variations and prospects in space geodesy applications. J Geod 72:161–178. https://doi.org/10.1007/s001900050158
Ge H, Li B, Ge M, Zang N, Nie L, Shen Y, Schuh H (2018) Initial assessment of precise point positioning with LEO enhanced global navigation satellite systems (LeGNSS). Remote Sens 10(7):984. https://doi.org/10.3390/rs10070984
Ge H, Li B, Ge M, Nie L, Schuh H (2020a) Improving low earth orbit (LEO) prediction with accelerometer data. Remote Sens 12(10):1599. https://doi.org/10.3390/rs12101599
Ge H, Li B, Nie L, Ge M, Schuh H (2020b) LEO constellation optimization for LEO enhanced global navigation satellite system (LeGNSS). Adv Space Res 66(3):520–532. https://doi.org/10.1016/j.asr.2020.04.031
Guo J, Qi L, Liu X, Chang X, Ji B, Zhang F (2023) High-order ionospheric delay correction of GNSS data for precise reduced-dynamic determination of LEO satellite orbits: cases of GOCE, GRACE, and SWARM. GPS Solut 27(1):13. https://doi.org/10.1007/s10291-022-01349-6
Huang H, Guo S, Liang W, Wang K, Zomaya AY (2019) Green data-collection from geo-distributed IoT networks through low-earth-orbit satellites. IEEE Trans Green Commun Netw 3(3):806–816. https://doi.org/10.1109/tgcn.2019.2909140
Li R, Lei J (2021) The determination of satellite orbital decay from POD data during geomagnetic storms. Sp Weather. https://doi.org/10.1029/2020SW002664
Li B, Ge H, Ge M, Nie L, Shen Y, Schuh H (2018) LEO enhanced global navigation satellite system (LeGNSS) for real-time precise positioning services. Adv Space Res 63(1):73–93. https://doi.org/10.1016/j.asr.2018.08.017
Li M, Lei Z, Li W, Jiang K, Wang Y, Zhao Q (2022) Calibration of GRACE on-board accelerometers for thermosphere density derivation. Geo Spat Inf Sci 25(1):74–87. https://doi.org/10.1080/10095020.2021.2010506
Liu J, Ge M (2003) PANDA software and its preliminary result of positioning and orbit determination. Wuhan Univ J Natl Sci 8(2):603–609. https://doi.org/10.1007/bf02899825
Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: modern insights from FES2004. Ocean Dyn 56:394–415. https://doi.org/10.1007/s10236-006-0086-x
Mao X, Visser PNAM, van Ijssel J (2017) Impact of GPS antenna phase center and code residual variation maps on orbit and baseline determination of GRACE. Adv Space Res 59(12):2987–3002. https://doi.org/10.1016/j.asr.2017.03.019
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res-Sol Earth. https://doi.org/10.1029/2011JB008916
Petit G, Luzum B (2010) IERS technical note No. 36, IERS conventions, international earth rotation and reference systems service. Frankfurt, Germany
Prol FS, Ferre RM, Saleem Z, Valisuo P, Pinell C, Lohan ES, Elsanhoury M, Elmusrati M, Islam S, Celikbilek K, Selvan K, Yliaho J, Rutledge K, Ojala A, Ferranti L, Praks J, Bhuiyan MZH, Kaasalainen S, Kuusniemi H (2022) Position, navigation, and timing (PNT) through low earth orbit (LEO) satellites: a survey on current status, challenges, and opportunities. IEEE Access 10:83971–84002. https://doi.org/10.1109/ACCESS.2022.3194050
Rebischung P, Griffiths J, Ray J, Schmid R, Collilieux X, Garayt B (2012) IGS08: the IGS realization of ITRF2008. GPS Solut 16:483–494. https://doi.org/10.1007/s10291-011-0248-2
Reid TG, Neish AM, Walter T, Enge PK (2018) Broadband LEO constellations for navigation. Navig J Inst Navig 65(2):205–220. https://doi.org/10.1002/navi.234
Shi C, Zhao Q, Li M, Tang W, Hu Z, Lou Y, Zhang H, Niu X, Liu J (2012) Precise orbit determination of beidou satellites with precise positioning. Sci China Earth Sci 55:1079–1086. https://doi.org/10.3390/s18010135
Van Helleputte T, Visser P (2008) GPS based orbit determination using accelerometer data. Aerosp Sci Technol 12(6):478–484. https://doi.org/10.1016/j.ast.2007.11.002
Wang K, El-Mowafy A (2020) Proposed orbital products for positioning using mega-constellation LEO satellites. Sensors 20(20):5806. https://doi.org/10.3390/s20205806
Wang YF, Zhong SM, Wang HT, Ou JK (2016) Precision analysis of LEO satellite orbit prediction. Acta Geod Et Cartogr Sin 45(9):1035
Wang K, Teunissen PJ, El-Mowafy A (2020b) The ADOP and PDOP: two complementary diagnostics for GNSS positioning. J Surv Eng 146(2):04020008. https://doi.org/10.1061/(asce)su.1943-5428.0000313
Wang K, Liu J, Su H, El-Mowafy A, Yang X (2022) Real-time LEO satellite orbits based on batch least-squares orbit determination with short-term orbit prediction. Remote Sens 15(1):133. https://doi.org/10.3390/rs15010133
Wei C, Shao K, Gu D, Zhang Z, Zhu J, An Z, Wang J (2023) Enhanced orbit and baseline determination for formation-flying LEO satellites with spaceborne accelerometer measurements. J Geod 97(7):64. https://doi.org/10.1007/s00190-023-01753-x
Wöske F, Kato T, Rievers B, List M (2019) GRACE accelerometer calibration by high precision non-gravitational force modeling. Adv Space Res 63(3):1318–1335. https://doi.org/10.1016/j.asr.2018.10.025
Bowman B (2002) True satellite ballistic coefficient determination for HASDM. In: AIAA/AAS Astrodynamics Specialist Conference. Monterey, CA, p. 4887
Cassel RS, Scherer DR, Wilburne DR, Hirschauer JE, Burke JH (2022) Impact of improved oscillator stability on LEO-based satellite navigation. In: Proceedings of the 2022 International technical meeting of the institute of navigation, pp 893–905. https://doi.org/10.33012/2022.18258
Hauschild A, Tegedor J, Montenbruck O, Visser H, Markgraf M (2016) Precise onboard orbit determination for LEO satellites with real-time orbit and clock corrections. In: Proceedings of ION GNSS+ 2016, Institute of Navigation, Portland, Oregon, USA, pp 3715–3723. https://doi.org/10.33012/2016.14717
Li X, Guo X, Zhu B, Geng S (2020) Performance analysis of a navigation system combining BeiDou with LEO communication constellation. In: China satellite navigation conference (CSNC) 2020 Proceedings: Volume II, Springer, Singapore, pp 643–650. https://doi.org/10.1007/978-981-15-3711-057
Liu X, Yuan B, Meng Z (2018) Microsatellite autonomous orbit propagation method based on SGP4 model and GPS data. In: Proceedings of 2018 IEEE CSAA Guidance, navigation and control conference, **amen, Fujian, China, pp 1–6. https://doi.org/10.1109/gncc42960.2018.9018639
Morales JJ, Khalife J, Cruz US, Kassas ZM (2019) Orbit modeling for simultaneous tracking and navigation using LEO satellite signals. In: Proceedings of ION GNSS+ 2019, Institute of Navigation, Missouri, Florida, USA, pp 2090–2099. https://doi.org/10.33012/2019.17029
Mortlock T, Kassas ZM (2021) Assessing machine learning for LEO satellite orbit determination in simultaneous tracking and navigation. In: Proceedings of the 2021 IEEE Aerospace Conference (50100), Big Sky, MT, USA, March, 6–13, pp 1–8. https://doi.org/10.1109/aero50100.2021.9438144
Reid TG, Neish AM, Walter TF, Enge PK (2016) Leveraging commercial broadband LEO constellations for navigating. In: Proceedings of the ION GNSS+ 2016, Institute of Navigation, Portland, OR, USA, pp 2300–2314. https://doi.org/10.33012/2016.14729
Rim HJ, Webb C, Yoon S, Schutz B (2006) Radiation pressure modeling for icesat precision orbit determination. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Tampa, Florida, pp. 6666. https://doi.org/10.2514/6.2006-6666
Standish E (1998) JPL planetary and lunar ephemerides DE405/LE405 interoffice memorandum IOM 312.F-98–048. Jet Propulsion Laboratory, Pasadena
Acknowledgements
Thanks to JPL for providing the raw observation data and post-processing precision orbits of the GRACE satellites, respectively. We are also grateful to the Supercomputing Center of Wuhan University for their support in providing numerical calculation services.
Funding
This study is supported by the Key Research and Development Program of Hubei Province (No. 2022BAA054) and the National Natural Science Foundation of China (42374033). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
Author information
Authors and Affiliations
Contributions
Junfeng Du: Methodology, Software, Writing-original draft. **aolei Dai: Conceptualization, Writing-review & editing. Yidong Lou: Supervision. Yun Qing: Software, External guidance. Yaquan Peng: Validation, Data curation. **ngang Li: Writing editing.
Corresponding author
Ethics declarations
Conflict of interest
All authors disclosed no relevant relationships.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Du, J., Dai, X., Lou, Y. et al. An improved method for LEO orbit prediction using predicted accelerometer data. GPS Solut 28, 132 (2024). https://doi.org/10.1007/s10291-024-01676-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-024-01676-w