Abstract
Due to errors of earth rotation parameters (ERPs) adopted when generating the broadcast ephemeris, GNSS broadcast ephemeris suffers orientation deficiencies called constellation rotation errors. Moreover, significant rotation inconsistencies are indicated among different GNSS ephemerides as they utilize different sets of ERPs. Based on the ERP datasets from broadcast navigation messages, we investigate the correlation between broadcast ERPs and ephemeris rotation errors for GPS and BDS-3, and then explore orbital rotation correction using broadcast ERPs. Evaluation of the broadcast ERPs indicates the average root mean square errors (RMSEs) of GPS xp, yp, and UT1-UTC are 1.00, 0.67 mas, and 0.17 ms, respectively, while those of BDS-3 are 2.52, 1.51 mas, and 0.44 ms. BDS-3 performs about 2–3 times worse due to its longer update latency. Comparing to the rotation parameters derived from Helmert transformation between broadcast and precise ephemerides, we demonstrate that the GPS and BDS-3 broadcast ERPs exhibit a prominent correlation with orbital orientation. The correlation coefficients between polar motion errors and X/Y-axis rotation parameters exceed 0.88 for GPS and 0.77 for BDS, whereas no significant correlation is found between the UT1-UTC error and the Z-axis rotation. We propose to correct the orbital orientation inconsistencies between BDS-3 and GPS by aligning their broadcast ERPs, explicitly the polar motion. The GPS ERPs are utilized as a reference due to higher precision and real-time availability. The BDS-3 broadcast orbit after correction reveals precision improvement of approximately 3.0 and 1.0 cm in the along-track and cross-track components, respectively. Static precise point positioning test with GPS and BDS-3 ephemerides also indicates a remarkable positioning improvement in north direction of 21.9% when BDS-3 ephemeris is corrected by the ERP alignment approach.
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Data availability
The RINEX 4.00 version broadcast navigation message files during 2020–2021 can be requested from Dr. Peter Steigenberger and those after 01-01-2022 can be publicly accessed from IGS data center. The precise C04 EOP product is available at IERS data center. The GFZ precise orbit product is available from ftp://ftp.gfz-potsdam.de. The MGEX observation is available from ftp://igs.gnsswhu.cn.
References
Bizouard C, Lambert S, Gattano C, Becker O, Richard J-Y (2019) The IERS EOP 14C04 solution for Earth orientation parameters consistent with ITRF 2014. J Geod 93(5):621–633. https://doi.org/10.1007/s00190-018-1186-3
Capitaine N (1986) The earth rotation parameters-conceptual and conventional definitions. Astron Astrophys 162:323–329
Carlin L, Hauschild A, Montenbruck O (2021) Precise point positioning with GPS and Galileo broadcast ephemerides. GPS Solut 25(2):77. https://doi.org/10.1007/s10291-021-01111-4
Chen G, Wei N, Li M, Zhao Q, Niu Y, Cai H, Meng Y (2021a) Assessment of BDS-3 terrestrial reference frame realized by broadcast ephemeris: comparison with GPS/Galileo. GPS Solut 26(1):18. https://doi.org/10.1007/s10291-021-01204-0
Chen G, Zhou R, Hu Z, Lv Y, Wei N, Zhao Q (2021b) Statistical characterization of the signal-in-space errors of the BDS: a comparison between BDS-2 and BDS-3. GPS Solut 25(3):1–15. https://doi.org/10.1007/s10291-021-01150-x
Chen G, Wei N, Li M, Zhao Q, Zhang J (2022) BDS-3 and GPS/Galileo integrated PPP using broadcast ephemerides. GPS Solut 26(4):1–16. https://doi.org/10.1007/s10291-022-01311-6
CSNO (2020) BeiDou navigation satellite system signal in space interface control document: open service signal B2b (Version 1.0). URL http://www.beidou.gov.cn/xt/gfxz/202008/P020200803362059116442.pdf
Dach R (2023) Dependency of satellite geodesy on UT1-UTC from VLBI. In: International VLBI Service for Geodesy and Astrometry 2022 General Meeting Proceedings, Finnish, March 28-April 1 in 2022, pp 3–9
Dehant V, Mathews PM. 3.10 - Earth Rotation Variations. In: Schubert G, editor. Treatise on Geophysics (Second Edition). Oxford: Elsevier; 2015. pp 263–305
Deng Z, Wang J, Ge M (2022) The GBM rapid product and the improvement from undifferenced ambiguity resolution. Acta Geod Cartogr Sin 51(4):544
Enderle W (2018) Galileo terrestrial reference frame (GTRF)-status. In: fourteenth meeting of the international committee on GNSS, ICG-13, Xi’an, China. pp 04–9. https://www.unoosa.org/documents/pdf/icg/2018/icg13/wgd/wgd_06.pdf
Griffiths J, Ray J (2013) Sub-daily alias and draconitic errors in the IGS orbits. GPS Solut 17(3):413–422. https://doi.org/10.1007/s10291-012-0289-1
Han C, Liu L, Cai Z, Lin Y (2021) The space–time references of BeiDou navigation satellite system. Satell Navig 2(1):1–10. https://doi.org/10.1186/s43020-021-00044-0
IS-GPS-800H (2021) Navstar GPS space segment/user segment L1C interfaces. Tech. rep., Global Positioning System Directorate Systems Engineering and Integration. http://www.gps.gov/technical/icwg/IS-GPS-800H.pdf
IS-QZSS-PNT-004 (2021) Quasi-zenith satellite system interface specification satellite positioning, navigation and timing service. Tech. rep., Cabinet Office, http://qzss.go.jp/en/technical/download/pdf/ps-is-qzss/is-qzss-pnt-004.pdf
ISRO (2017) Indian regional navigation satellite system signal in space ICD for standard positioning service, Version 1.1. Tech. Rep. Bangalore: ISRO Satellite Centre, Indian Space Research Organization.
Kalarus M, Schuh H, Kosek W, Akyilmaz O, Bizouard C, Gambis D, Gross R, Jovanović B, Kumakshev S, Kutterer H (2010) Achievements of the Earth orientation parameters prediction comparison campaign. J Geod 84(10):587–596. https://doi.org/10.1007/s00190-010-0387-1
Kouba J, Héroux P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5(2):12–28. https://doi.org/10.1007/pl00012883
Malys S, Solomon R, Drotar J, Kawakami T, Johnson T (2021) Compatibility of terrestrial reference frames used in GNSS broadcast messages during an 8 week period of 2019. Adv Space Res 67(2):834–844. https://doi.org/10.1016/j.asr.2020.11.029
McCarthy D, Petit G (2004) IERS conventions (2003). Germany: International Earth Rotation and Reference Systems Service (IERS)
Montenbruck O, Kunzi F, Hauschild A (2022) Performance assessment of GNSS-based real-time navigation for the Sentinel-6 spacecraft. GPS Solut 26(1):1–11. https://doi.org/10.1007/s10291-021-01198-9
Montenbruck O, Gill E (2000) Satellite orbits: models, methods, and applications. Berlin, Heidelberg: Springer Science and Business Media
NGA (2020) NGA GNSS division earth orientation. Tech. rep., URL ftp://ftp.nga.mil/pub2/gandg/website/gnss/data/prod_docs/NGAGNSSEOPPParameters.pdf
Petit G, Luzum B, Al E (2010) IERS conventions (2010) IERS technical note. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main
Romero I (2021) The receiver independent exchange format version 4.00.
Rothacher M, Beutler G, Herring TA, Weber R (1999) Estimation of nutation using the global positioning system. J Geophys Res-Solid Earth 104(B3):4835–4859. https://doi.org/10.1029/1998JB900078
Steigenberger P, Montenbruck O, Bradke M, Ramatschi M, Hessels U (2022) Evaluation of earth rotation parameters from modernized GNSS navigation messages. GPS Solut 26(2):1–12. https://doi.org/10.1007/s10291-022-01232-4
Xu X, Zhou Y (2015) EOP prediction using least square fitting and autoregressive filter over optimized data intervals. Adv Space Res 56(10):2248–2253. https://doi.org/10.1016/j.asr.2015.08.007
Xu X, Zhou Y, Liao X (2012) Short-term earth orientation parameters predictions by combination of the least-squares, AR model and Kalman filter. J Geodynamics 62:83–86. https://doi.org/10.1016/j.jog.2011.12.001
Acknowledgements
We are grateful to Dr. Peter Steigenberger for providing the RINEX 4.00 broadcast navigation message files and thank IGS, IERS and GFZ for providing multi-GNSS observations, EOP and precise orbits, respectively. This study is sponsored by the National Natural Science Foundation of China (42004020, 42204019, 42030109), Fundamental Research Funds for the Central Universities (2042021kf0064, 2042021kf0060), China Postdoctoral Science Foundation (2021M692460) and the Key Research and Development Plan Project of Hubei Province (2020BIB006).
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All the authors contributed to the design of this study. WWL, ML and QLZ came up with the idea. WWL and GC processed the evaluation of broadcast ERP, generated the results and wrote the draft. NW, WWL, GC and ML revised the manuscript, YBW participated in collection of broadcast ERP and C04 products, and carried out the data edit. All authors read and approved the final manuscript.
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Li, W., Chen, G., Li, M. et al. Evaluation of GPS and BDS-3 broadcast earth rotation parameters: a contribution to the ephemeris rotation error. GPS Solut 27, 115 (2023). https://doi.org/10.1007/s10291-023-01458-w
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DOI: https://doi.org/10.1007/s10291-023-01458-w