Abstract
The dearth of frequency-specific satellite antenna phase centers (APCs), such as GPS Block IIF L5 phase center offsets (PCOs) and BeiDou System (BDS) phase variations (PVs), inconveniences multi-frequency precise point positioning (PPP). We find that the GNSS observation biases caused by incorrect frequency-specific APCs are both spatially incoherent and time variable. This spatiotemporal incoherency will be magnified by over a hundred times in the case of multi-frequency PPP wide-lane ambiguity resolution (PPP-WAR) and is likely to defer PPP convergences. We hence first impose deliberate errors on the Galileo frequency-specific APCs to mimic the common faulty operations of equating the GPS L5 with the L1/L2 ionosphere-free PCOs and ignoring the BDS PVs in typical high-precision GNSS. We then investigate how such APC errors can harm multi-frequency PPP using one month of E1/E5a/E5b data from 43 globally distributed stations. Although the APC errors tested in this study have minimal impact on dual-frequency PPP, a 5-mm horizontal PCO error does prolong multi-frequency PPP convergences by 15%; a 200-mm vertical PCO error or a PV error of up to 10 mm can even grow the convergence times by 60%. The vertical positioning precision of single-epoch PPP-WAR is deteriorated on average by 15 cm under a 200-mm vertical PCO error. Therefore, accurate frequency-specific GPS/BDS satellite APCs should be determined for multi-frequency PPP to maximize its convergence advantages over dual-frequency PPP.
Similar content being viewed by others
Data availability
All raw data in this article are publicly accessible. The Galileo data and products can be obtained at https://cddis.nasa.gov/archive/ and ftp://ftp.ga.gov.au.
References
Bertiger W, Sibthorpe A, Heflin MB, Hemberger D, Moore AW, David MW, Ries PA, Sibois AE, Watson R (2020) Multi-GNSS reference frame consistency as realized through PPP. In: AGU fall meeting, online everywhere, 1–17 Dec
Boehm J, Niell AE, Tregoning P, Schuh H (2006) The global mapping function (GMF): a new empirical mapping function based on data from numerical weather model data. Geophys Res Lett 33:L07304. https://doi.org/10.1029/2005GL025546
Boehm J, Heinkelmann R, Schuh H (2007) Short note: a global model of pressure and temperature for geodetic applications. J Geod 81(10):679–683
China Satellite Navigation Office (2019) Release of the BDS-2/3 satellite related parameters. http://en.BDS.gov.cn/SYSTEMS/Officialdocument/201912/P020200323536112807882.atx. Accessed 6 Jun 2020
Dilssner F (2010) GPS IIF-1 satellite antenna phase center and attitude modeling. Inside GNSS 2010(9–10):59–64
Dilssner F, Springer T, Schönemann E, Enderle W (2016) Evaluating the pre-flight GPS Block IIR/IIR-M antenna phase pattern measurements. IGS workshop 2016, Sydney, Australia, 8–12 Feb
Euler HJ, Schaffrin B (1990) On a measure of the discernibility between different ambiguity solutions in the static-kinematic GPS mode. In: Schwarz KP, Lachapelle G (eds) Kinematic systems in geodesy, surveying and remote sensing. Springer, New York, pp 285–295
European GNSS Service Centre (2017) Galileo satellite metadata. https://www.gsc-europa.eu/support-to-developers/galileo-satellite-metadata. Accessed 6 June 2020
Fan L, Shi C, Li M, Wang C, Zheng F, Jing G, Zhang J (2019) GPS satellite inter-frequency clock bias estimation using triple-frequency raw observations. J Geod 93(12):2465–2479
Ge M, Gendt G, Dick G, Zhang FP, Reigber C (2005) Impact of GPS satellite antenna offsets on scale changes in global network solutions. Geophys Res Lett 32(6):L06310. https://doi.org/10.1029/2004GL022224
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
Geng J, Bock Y (2013) Triple-frequency GPS precise point positioning with rapid ambiguity resolution. J Geod 87(5):449–460
Geng J, Teferle FN, Meng X, Dodson AH (2011) Towards PPP-RTK: ambiguity resolution in real-time precise point positioning. Adv Space Res 47(10):1664–1673
Geng J, Chen X, Pan Y, Zhao Q (2019a) A modified phase clock/bias model to improve PPP ambiguity resolution at Wuhan University. J Geod 93(10):2053–2067
Geng J, Guo J, Chang H, Li X (2019b) Towards global instantaneous decimeter-level positioning using tightly-coupled multi-constellation and multi-frequency GNSS. J Geod 93(7):977–991. https://doi.org/10.1007/s00190-018-1219-y
Geng J, Guo J, Meng X, Gao K (2020) Speeding up PPP ambiguity resolution using triple-frequency GPS/BDS/Galileo/QZSS data. J Geod 94:6. https://doi.org/10.1007/s00190-019-01330-1
Gong X, Gu S, Lou Y, Zheng F, Yang X, Wang Z, Liu J (2020) Research on empirical correction models of GPS Block IIF and BDS satellite inter-frequency clock bias. J Geod 94:36. https://doi.org/10.1007/s00190-020-01365-9
Guo J, Geng J (2018) GPS satellite clock determination in case of inter-frequency clock biases for triple-frequency precise point positioning. J Geod 92(10):1133–1142
Guo F, Zhang X, Wang J, Ren X (2016) Modeling and assessment of triple-frequency BDS precise point positioning. J Geod 90(11):1223–1235
Huang G, Yan X, Zhang Q, Liu C, Wang L, Qin Z (2018) Estimation of antenna phase center offset for BDS IGSO and MEO satellites. GPS Solut 22:49. https://doi.org/10.1007/s10291-018-0716-z
IGS AC Coordinator (2019) Conventions and modeling for Repro3. http://acc.igs.org/repro3/repro3.html. Accessed 6 June 2020
Mader GL, Czopek F (2001) Calibrating the L1 and L2 phase centers of a block IIA antenna. In: Proceedings of ION GPS 14th international technical meeting of the satellite division, Salt Lake City, UT, 11–14 Sep, pp 1979–1984
Marquis WA, Reigh DL (2015) The GPS Block IIR and IIR-M broadcast L-band antenna panel: its pattern and performance. Navigation 62(4):329–347
Montenbruck O, Hugentobler U, Dach R, Steigenberger P, Hauschild A (2011) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solut 16(3):303–313
Montenbruck O, Steigenberger P, Hugentobler U (2015) Enhanced solar radiation pressure modeling for Galileo satellites. J Geod 89(3):283–297
Petit G, Luzum B (eds) (2010) IERS Conventions (2010). Verlag des Bundes für Kartographie und Geodäsie, Frankfurt a. M., Germany, p 179
Rebischung P, Villiger A, Herring T, Moore M (2019) Preparations for the 3rd IGS reprocessing campaign. In: AGU fall meeting, San Francisco, CA, USA, 9–13 Dec
Saastamoinen J (1973) Contribution to the theory of atmospheric refraction: refraction corrections in satellite geodesy. Bull Geod 107(1):13–34
Schmid R, Rothacher M (2003) Estimation of elevation-dependent satellite antenna phase center variations of GPS satellites. J Geod 77(10):440–446
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
Schmid R, Dach R, Collilieux X, Jäggi A, Schmitz M, Dilssner F (2016) Absolute IGS antenna phase center model igs08.atx: status and potential improvements. J Geod 90(4):343–364
Schmitz M, Wübbena G, Propp M (2008) Absolute robot-based GNSS antenna calibration: features and findings. In: International symposium on GNSS, space-based and ground-based augmentation systems and applications, Berlin, Germany, 11–14 Nov
Steigenberger P, Fritsche M, Dach R, Schmid R, Montenbruck O, Uhlemann M, Prange L (2016) Estimation of satellite antenna phase center offsets for Galileo. J Geod 90(8):773–785
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82
The Cabinet Office, Government of Japan (2017) QZSS satellite information. https://qzss.go.jp/en/technical/qzssinfo/index.html. Accessed 6 June 2020
Villiger A, Dach R, Schaer S, Prange L, Zimmermann F, Kuhlmann H, Wübbena G, Schmitz M, Beutler G, Jäggi A (2020) GNSS scale determination using calibrated receiver and Galileo satellite antenna patterns. J Geod 94:93
Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geod 18(2):91–98
Xiao G, Li P, Gao Y, Heck B (2019) A unified model for multi-frequency PPP ambiguity resolution and test results with Galileo and BDS triple-frequency observations. Remote Sens 11(2):116. https://doi.org/10.3390/rs11020116
Xin S, Geng J, Guo J, Meng X (2020) On the choice of the third-frequency Galileo signals in accelerating PPP ambiguity resolution in case of receiver antenna phase center errors. Remote Sens 12(8):1315. https://doi.org/10.3390/rs12081315
Yan X, Huang G, Zhang Q, Wang L, Qin Z, Xie S (2019) Estimation of the antenna phase center correction model for the BDS-3 MEO satellites. Remote Sens 11(23):2850. https://doi.org/10.3390/rs11232850
Zhang B, Teunissen PJG, Odijk D, Ou J, Jiang Z (2012) Rapid integer ambiguity-fixing in precise point positioning. Chin J Geophys 55(7):2203–2211 ((in Chinese))
Zhao Q, Wang C, Guo J, Wang B, Liu J (2017) Precise orbit and clock determination for BDS-3 experimental satellites with yaw attitude analysis. GPS Solut 22:4. https://doi.org/10.1007/s10291-017-0673-y
Zhu SY, Massmann FH, Yu Y, Reigber C (2003) Satellite antenna phase center offsets and scale errors in GPS solutions. J Geod 76(11–12):668–672
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017
Acknowledgements
This work is funded by National Science Foundation of China (42025401). We thank IGS and ARGN for the Galileo data and the high-quality satellite products. We are grateful to Paul Rebischung and Florian Dilssner for the discussion on this study. All computations were carried out on the high-performance computing facility of Wuhan University.
Author information
Authors and Affiliations
Contributions
JHG devised the project and the main conceptual ideas. JHG and JG worked out all technical details. JG, CW and QZ performed the computation tasks. JHG wrote the paper. All authors approved of the manuscript.
Corresponding author
Rights and permissions
About this article
Cite this article
Geng, J., Guo, J., Wang, C. et al. Satellite antenna phase center errors: magnified threat to multi-frequency PPP ambiguity resolution. J Geod 95, 72 (2021). https://doi.org/10.1007/s00190-021-01526-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00190-021-01526-4