Skip to main content
SpringerLink
Log in

Joint estimation of GPS/BDS real-time clocks and initial results

  • Original Article
  • Published:
GPS Solutions Aims and scope Submit manuscript

Abstract

We present the joint estimation model for Global Positioning System/BeiDou Navigation Satellite System (GPS/BDS) real-time clocks and present the initial satellite clock solutions determined from 106 stations of the international GNSS service multi-GNSS experiment and the BeiDou experimental tracking stations networks for 1 month in December, 2012. The model is shown to be efficient enough to have no practical computational limit for producing 1-Hz clock updates for real-time applications. The estimated clocks were assessed through the comparison with final clock products and the analysis of post-fit residuals. Using the estimated clocks and corresponding orbit products (GPS ultra-rapid-predicted and BDS final orbits), the root-mean-square (RMS) values of coordinate differences from ground truth values are around 1 and 2–3 cm for GPS-only and BDS-only daily mean static precise point positioning (PPP) solutions, respectively. Accuracy of GPS/BDS combined static PPP solutions falls in between that of GPS-only and BDS-only PPP results, with RMS values approximately 1–2 cm in all three components. For static sites, processed in the kinematic PPP mode, the daily RMS values are normally within 4 and 6 cm after convergence for GPS-only and BDS-only results, respectively. In contrast, the combined GPS/BDS kinematic PPP solutions show higher accuracy and shorter convergence time. Additionally, the BDS-only kinematic PPP solutions using clock products derived from the proposed joint estimation model were superior compared to those computed using the single-system estimation model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Bar-Sever Y, Muellerschoen R, Reachert A, Vozoff M, Young L (2001) NASA’s internet-based global differential GPS system. In: Proceedings of NaviTech ESA/ESTEC, Noordwijk, Netherlands, pp 65–72

  • Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33:L07304

    Article  Google Scholar 

  • Coco DS, Coker C, Dahlke SR, Clynch JR (1991) Variability of GPS satellite differential group delay biases. IEEE Trans Aerosp Electron Syst 27(6):931–938

    Article  Google Scholar 

  • Collins P (2008) Isolating and estimating undifferenced GPS integer ambiguities. In: Proceedings of ION-NTM-2008, Institute of Navigation, San Diego, CA, pp 720–732

  • Colombo OL (2008) Real-time, wide-area, precise kinematic positioning using data from internet NTRIP streams. In: Proceedings of ION-GNSS-2008, Institute of Navigation, Savannah, Georgia, pp 327–337

  • 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

    Article  Google Scholar 

  • Ge M, Gendt G, Rothacher M, Shi C, Liu J (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geod 82(7):389–399

    Article  Google Scholar 

  • Ge M, Chen JP, Dousa J, Gendt G, Wickert JA (2012a) Computationally efficient approach for estimating high-rate satellite clock corrections in realtime. GPS Solut 16(1):9–17

    Article  Google Scholar 

  • Ge M, Zhang HP, Jia XL, Song SL, Wickert J (2012b) What is achievable with the current compass constellation? In: Proceedings of ION-GNSS-2012, Institute of Navigation, Nashville, Tennessee

  • Gendt G, Dick G, Reigber CH, Tomassini M, Liu Y, Ramatschi M (2003) Demonstration of NRT GPS water vapor monitoring for numerical weather prediction in Germany. J Meteorol Soc Jpn 82(1B):360–370

    Google Scholar 

  • Gong H, Yang W, Wang Y, Zhu X, Wang F (2012) Comparison of short-term stability estimation methods of GNSS on-board clock. In: Sun J, Liu J, Yang Y, Fan S (eds) China satellite navigation conference (CSNC) 2012 proceedings. Lecture notes in electrical engineering, vol 160. Springer, pp 503–513. doi:10.1007/978-3-642-29175-3_46

  • Han C, Yang Y, Cai Z (2011) BeiDou navigation satellite system and its time scales. Metrologia 48(4):S213–S218. doi:10.1088/0026-1394/48/4/S13

    Article  Google Scholar 

  • Hauschild A, Montenbruck O (2009) Kalman-filter-based GPS clock estimation for near realtime positioning. GPS Solut 13(3):173–182. doi:10.1007/s10291-008-0110-3

    Article  Google Scholar 

  • Kouba J (2009) A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solut 13(1):1–12. doi:10.1007/s10291-008-0092-1

    Article  Google Scholar 

  • Li Z, Yuan Y, Li H, Ou J, Huo X (2012) Two-step method for the determination of the differential code biases of COMPASS satellites. J Geod 86(11):1059–1076

    Article  Google Scholar 

  • Lou Y, Liu Y, Shi C, Yao X, Zheng F (2014a) Precise orbit determination of BeiDou constellation based on BETS and MGEX network. Sci Rep 4:4692. doi:10.1038/srep04692

    Google Scholar 

  • Lou Y, Zhang W, Wang C, Yao X, Shi C, Liu J (2014b) The impact of orbital errors on the estimation of satellite clock errors and PPP. Adv Space Res 54(8):1571–1580

    Article  Google Scholar 

  • McCarthy DD, Petit G (2004) IERS 2003 conventions. Verlag des Bundes fur Kartographie und Geodasie, Frankfurt am Main, p 127

    Google Scholar 

  • Montenbruck O, Hauschild A, Steigenberger P, Hugentobler U, Teunissen P, Nakamura S (2013) Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system. GPS Solut 17(2):211–222. doi:10.1007/s10291-012-0272-x

    Article  Google Scholar 

  • Montenbruck O, Hauschild A, Steigenberger P (2014a) Differential code bias estimation using multi-GNSS observations and global ionosphere map. In: Proceedings of ION-ITM-2014, Institute of Navigation, San Diego, CA, pp 26–28

  • Montenbruck O, Steigenberger P, Khachikyan R, Weber G, Langley RB, Mervart L, Hugentobler U (2014b) IGS-MGEX: preparing the ground for multi-constellation GNSS science. Inside GNSS 9(1):42–49

    Google Scholar 

  • Schaer S, Steigenberger S (2006) Determination and use of GPS differential code bias values. IGS Workshop 2006, May 8–11, Darmstadt, Germany

  • Schmid R, Steigenberger P, Gendt G, Ge M, Rothacher M (2007) Generation of a consistent absolute phase-center correction model for GPS receiver and satellite antennas. J Geod 81(12):781–798

    Article  Google Scholar 

  • Schönemann E, Becker M, Springer T (2011) A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. J Geod Sci 1(3):201–214

    Google Scholar 

  • Shi C, Zhao Q, Geng J, Lou Y, Ge M, Liu J (2008) Recent development of PANDA software in GNSS data processing. In: In: Proceedings of SPIE, international conference on earth observation data processing and analysis (ICEODPA), p 72851S. doi:10.1117/12.816261

  • 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(7):1079–1086

    Article  Google Scholar 

  • Shi C, Zhao Q, Hu Z, Liu J (2013) Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites. GPS Solut 17(1):103–119. doi:10.1007/s10291-012-0264-x

    Article  Google Scholar 

  • 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. doi:10.1007/s00190-013-0625-4

    Article  Google Scholar 

  • Weber G, Mervart L, Lukes Z, Rocken C, Dousa J (2007) Real-time clock and orbit corrections for improved point positioning via NTRIP. In: Proceedings of ION-GNSS-2007, Fort Worth, TX, 1992–1998

  • Wu J, Wu S, Hajj G, Bertiger W, Lichten S (1993) Effect of antenna orientation on GPS carrier phase. Manuscr Geod 18:91–98

    Google Scholar 

  • 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. doi:10.1007/s00190-013-0622-7

    Article  Google Scholar 

  • Zumberge J, Heflin M, Jefferson D, Watkins M, Webb F (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Nature Science Foundation of China (No.: 41374034), the National “863 Program” of China (Grant No. 2012AA12A202), the Fundamental Research Fund for the Central Universities (2042014kf0081) and the China Scholarship Council (No.: 201406270066). We would like to thank two anonymous reviewers and Jeffrey Sussman from UC San Diego for their valuable suggestions and comments. The MGEX data were provided by the IGS.

Author information

Authors and Affiliations

  1. School of Geodesy and Geomatics, Wuhan University, Wuhan, 430079, Hubei, China

    Weixing Zhang & Jingnan Liu

  2. GNSS Research Center, Wuhan University, Wuhan, 430079, Hubei, China

    Weixing Zhang, Yidong Lou, Shengfeng Gu, Chuang Shi & Jingnan Liu

  3. Scripps Institution of Oceanography, University of California, San Diego, CA, 92093, USA

    Weixing Zhang & Jennifer S. Haase

Authors
  1. Weixing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yidong Lou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shengfeng Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chuang Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jennifer S. Haase
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jingnan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yidong Lou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, W., Lou, Y., Gu, S. et al. Joint estimation of GPS/BDS real-time clocks and initial results. GPS Solut 20, 665–676 (2016). https://doi.org/10.1007/s10291-015-0476-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10291-015-0476-y

Keywords

Search

Navigation