Abstract
Improved broadcast ephemerides of BDS-3 and Galileo systems provide new opportunities for precise point positioning with broadcast ephemerides (BE-PPP) instead of using precise ephemeris products. We propose an approach of BDS-3 and GPS/Galileo integrated BE-PPP, emphasizing modeling and mitigating specific errors of broadcast ephemerides. First, the standard precise point positioning (PPP) model is extended by considering systematic rotation errors implied in BDS-3 broadcast orbits. For each station, a comprehensive bias is then considered to account for the known signal-in-space error (SISE) bias and the satellite/receiver hardware delay unavailable for some observations before the positioning. Besides, an explicit parameter is included in the PPP model to compensate for the remaining errors of SISE for each satellite. Considering that the SISE discontinuity of BDS-3 is larger than that of Galileo, the SISE parameters for BDS-3 satellites are reset in all the BE-PPP solutions except the BDS-3 only kinematic positioning when broadcast ephemerides are updated. Tests performed with 64 global stations demonstrate that the three-dimensional (3D) position errors of BDS-3/GPS/Galileo integrated PPP can be 8.6 cm in static mode and 23.4 cm in simulated kinematic mode. Although suffering from fewer BDS-3 observations tracked by ground stations, triple-constellation solutions with BDS-3 still offer a 9% performance improvement for static mode and 20% for simulated kinematic mode compared to GPS/Galileo solutions. On the other hand, the orientation errors in BDS-3 broadcast orbits have been successfully mitigated by explicit estimations of rotation parameters in the integrated BE-PPP. The averaged rotation estimates derived from BDS-3/Galileo solutions agree well with those from orbit comparisons, and correlations of 0.79, 0.88 and 0.94 are obtained for x-, y- and z-rotations, respectively. With considering orientation and translation errors of BDS-3 orbits in integrated solutions, improvements of 3D position accuracy up to 1.7 cm (static) and 0.9 cm (kinematic) can be achieved, where the horizontals offer the dominating improvements.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The merged MGEX ephemerides data, the multi-GNSS precise orbits, and observation of global stations are openly available by an anonymous user via ftp://igs.gnsswhu.cn.
References
Bahadur B, Nohutcu M (2018) PPPH: a MATLAB-based software for multi-GNSS precise point positioning analysis. GPS Solut. https://doi.org/10.1007/s10291-018-0777-z
Cai C, Gao Y (2013) Modelling and assessment of combined GPS/GLONASS precise point positioning. GPS Solut 17(2):223–236. https://doi.org/10.1007/s10291-012-0273-9
Carlin L, Hauschild A, Montenbruck O (2021) Precise point positioning with GPS and Galileo broadcast ephemerides. GPS Solut. https://doi.org/10.1007/s10291-021-01111-4
Chen G, Zhou R, Hu Z, Lv Y, Wei N, Zhao Q (2021) Statistical characterization of the signal-in-space errors of the BDS: a comparison between BDS-2 and BDS-3. GPS Solut. https://doi.org/10.1007/s10291-021-01150-x
Chen G, Wei N, Li M, Zhao Q, Niu Y, Cai H, Meng Y (2022) Assessment of BDS-3 terrestrial reference frame realized by broadcast ephemeris: comparison with GPS/Galileo. GPS Solut. https://doi.org/10.1007/s10291-021-01204-0
European GNSS Service Centre (2022) Galileo open service - quarterly performance report: https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo-OS-Quarterly-Performance_Report-Q3-2021.pdf
Enderle W (2018) Galileo terrestrial reference frame (GTRF)- status, fourteenth meeting of the international committee on GNSS, ICG-13, November 4–9, 2018, Xi’an, China, UNOOSA. https://www.unoosa.org/documents/pdf/icg/2018/icg13/wgd/wgd_06.pdf
Gong X, Sang J, Wang F, Li X (2020) LEO onboard real time orbit determination using GPS/BDS data with an optimal stochastic model. Remote Sens 12(20):3458. https://doi.org/10.3390/rs12203458
Kouba J, Héroux P (2001) GPS precise point positioning using IGS orbit products. GPS Solut 5(2):12–28. https://doi.org/10.1007/PL00012883
Liu L, Xu J, Zhou S, Wu F (2019) Update on the BeiDou coordinate system (BDCS). In: Fourteenth meeting of the international committee on GNSS, ICG-14, December 8–13, 2019, Bangalore, India, UNOOSA. https://www.unoosa.org/documents/pdf/icg/2019/icg14/WGD/icg14_wgd_01.pdf.
Malys S, Jensen PA (1990) Geodetic point positioning with GPS carrier beat phase data from the CASA UNO experiment. Geophys Res Lett 17(5):651–654
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 67:834–844
Montenbruck O, Ramos-Bosch P (2008) Precision real-time navigation of LEO satellites using global positioning system measurements. GPS Solut 12(3):187–198. https://doi.org/10.1007/s10291-007-0080-x
Montenbruck O et al (2017) The Multi-GNSS experiment (MGEX) of the international GNSS service (IGS) – achievements, prospects and challenges. Adv Space Res 59:1671–1697
Montenbruck O, Steigenberger P, Hauschild A (2018) Multi-GNSS signal-in-space range error assessment – methodology and results. Adv Space Res-Ser 61(12):3020–3038. https://doi.org/10.1016/j.asr.2018.03.041
Montenbruck O, Steigenberger P, Hauschild A (2020) Comparing the ‘Big 4’ – a user’s view on GNSS performance. In: 2020 IEEE/ION position, location and navigation symposium (PLANS), April 20–23, 2020, Portland, OR
Montenbruck O, Kunzi F, Hauschild A (2022) Performance assessment of GNSS-based real-time navigation for the Sentinel-6 spacecraft. GPS Solut. https://doi.org/10.1007/s10291-021-01198-9
NGA (2021) Recent update to WGS 84 reference frame and NGA transition to IGS ANTEX. Effective date Jan 3, 2021. National Geospatial-Intelligence Agency. https://earth-info.nga.mil/php/download.php?file=(U)WGS%2084(G2139).pdf
Steigenberger P, Montenbruck O, Bradke M, Ramatschi M, Hessels U (2022) Evaluation of earth rotation parameters from modernized GNSS navigation messages. GPS Solut. https://doi.org/10.1007/s10291-022-01232-4
Togedor J, Østedal O, Vigen E (2014) Precise orbit determination and point positioning using GPS, GLONASS, Galileo, and BeiDou. J Geodetic Sci 4(1):65–73. https://doi.org/10.2478/jogs-2014-0008
Wang F, Ling S, Gong X, Guo L (2020) Decimeter-level orbit determination for FY3C satellite based on space-borne GPS/BDS measurements. Geomat Inf Sci Wuhan Univ 45(1):810–821. https://doi.org/10.13203/j.whugis20180385
Wang N, Yuan Y, Li Z, Montenbruck O, Tan B (2016) Determination of differential code biases with multi-GNSS observations. J Geod 90:209–228. https://doi.org/10.1007/s00190-15-0867-4
Wu W, Guo F, Zheng J (2020) Analysis of Galileo signal-in-space range error and positioning performance during 2015–2018. Satell Navig 1(1):6. https://doi.org/10.1186/s43020-019-0005-1
Zhang Y, Chen J, Gong X, Chen Q (2020a) The update of BDS-2 TGD and its impacts on positioning. Adv Space Res 65:2645–2661
Zhang Y, Kubo N, Chen J, Chu F, Wang A, Wang J (2020b) Apparent clock and TGD biases between BDS-2 and BDS-3. GPS Solut. https://doi.org/10.1007/s10291-019-0933-0
Zhao Q, Guo J, Liu S, Tao J, Hu Z, Chen G (2021) A variant of raw observation approach for BDS/GNSS precise point positioning with fast integer ambiguity resolution. Satell Navig. https://doi.org/10.1186/s43020-021-00059-7
Zheng F, Gong X, Lou Y, Gu S, Jing G, Shi C (2019) Calibration of BeiDou triple-frequency receiver-related pseudorange biases and their application in BDS precise positioning and ambiguity resolution. Sensors 19(16):3500
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017. https://doi.org/10.1029/96JB03860
Acknowledgements
This study is sponsored by the National Natural Science Foundation of China (42174028, 42030109), Fundamental Research Funds for the Central Universities (2042021kf0064), and the Foundation supported by Wuhan Science and Technology Bureau (2020010601012186). We would like to express thanks to IGS for providing multi-GNSS observations and broadcast and precise products. We would like to thank three anonymous reviewers and the Editor-in-Chief Alfred Leick for their valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
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 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
Chen, G., Wei, N., Li, M. et al. BDS-3 and GPS/Galileo integrated PPP using broadcast ephemerides. GPS Solut 26, 129 (2022). https://doi.org/10.1007/s10291-022-01311-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-022-01311-6