Abstract
In recent years, numerous low earth orbit (LEO) satellites have been launched for different scientific tasks such as the Earth’s magnetic field, gravity recovering and ocean altimetry. The LEO satellites can cover the ocean area and are less affected by atmospheric delays and multipath errors, which provides new opportunities for calibrating the phase biases of the Global Navigation Satellite System (GNSS). In this contribution, we propose an alternative approach for uncalibrated phase delay (UPD) estimation by making full use of onboard observations of LEO satellites. Stable wide-lane (WL) and narrow-lane (NL) UPDs can be obtained from spaceborne GNSS observations and agree well with the UPD products derived from 106 IGS stations. To further verify the feasibility of the proposed method for UPD estimation, zero-difference (ZD) ambiguity resolution (AR) for precise point positioning (PPP) and LEO precise orbit determination (POD) are implemented. After applying the LEO-based UPDs, the averaged convergence time for PPP AR can be reduced to 15.2 min, with an improvement of 24% compared to float solutions. As for LEO AR, the fixing rates of WL and NL ambiguities exceed 98 and 92%, respectively. The accuracies of ambiguity-fixed orbits are validated by comparing with external satellite laser ranging (SLR) and K-band ranging (KBR) observations. Compared to float solutions, the standard deviations (STDs) of SLR residuals can be reduced by 8 ~ 43%, and the KBR residuals of 3.75 mm can be achieved for fixed solutions using LEO-based UPDs, with an improvement of 60%. Although the current UPD results derived from LEO satellites are slightly worse than those of ground-based UPD, it is anticipated that the performance of LEO-based UPD can be further improved in the near future with the rapidly increasing number of LEO satellites and the continuous refinements of the POD method.
Similar content being viewed by others
Data availability
The onboard GNSS observations of LEO satellites are available from: ftp://swarm-diss.eo.esa.int; ftp://isdcftp.gfz-potsdam.de; ftp://ftp-access.aviso.altimetry.fr; https://scihub.copernicus.eu/gnss; ftp://cdaac-www.cosmic.ucar.edu. The GNSS raw observations of IGS stations and broadcast ephemeris are from: ftp://igs.gnsswhu.cn/pub/gps/data/daily. The precise orbit and clock products are from: ftp://igs.gnsswhu.cn/pub/gps/products/mgex.
References
Aschbacher J, Milagro-Pérez MP (2012) The European Earth monitoring (GMES) programme: status and perspectives. Remote Sens Environ 120:3–8
Banville S, Geng J, Loyer S, Schaer S, Springer T, Strasser S (2020) On the interoperability of IGS products for precise point positioning with ambiguity resolution. J Geod 94(1):10
Blewitt G (1989) Carrier phase ambiguity resolution for the Global Positioning System applied to geodetic baselines up to 2000 km. J Geophys Res 94(B8):10187–10203. https://doi.org/10.1029/JB094iB08p10187
Bock H, Jäggi A, Meyer U, Visser P, van den Ijssel J, van Helleputte T, Heinze M, Hugentobler U (2011) GPS-derived orbits for the GOCE satellite. J Geod 85(11):807–818
Collins P, Lahaye F, Herous P, Bisnath S (2008) Precise point positioning with AR using the decoupled clock model. In: Proceedings of the ION GNSS 2008, Savannah, GA, USA, pp 1315–1322, 16–19 Sept
Dach R, Schaer S, Arnold D, Prange L, Sidorov D, Susnik A, Villiger A, Jaeggi A (2017) CODE final product series for the IGS. Astronomical Institute, University of Bern, Bern. http://www.aiub.unibe.ch/download/CODE. https://doi.org/10.7892/boris.75876.2
Dong D, Bock Y (1989) Global positioning system network analysis with phase ambiguity resolution applied to crustal deformation studies in California. J Geophys Res 94(B4):3949–3966
Feng Y, Wang J (2008) GPS RTK performance characteristics and analysis. J Glob Pos Syst 7(1):1–8
Friis-Christensen E, Lühr H, Knudsen D, Haagmans R (2008) Swarm-an Earth observation mission investigating geospace. Adv Space Res 41(1):210–216
Gabor MJ, Nerem RS (1999) GPS carrier phase AR using satellite-satellite single difference. In: Proceedings of ION GPS 1999. Institute of Navigation, Nashville, pp 1569–1578, 14–17 Sept
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, Meng X, Dodson AH, Teferle FN (2010) Integer ambiguity resolution in precise point positioning: method comparison. J Geod 84(9):569–581
Geng J, Shi C, Ge M, Dodson AH, Lou Y, Zhao Q, Liu J (2012) Improving the estimation of fractional-cycle biases for ambiguity resolution in precise point positioning. J Geod 86(8):579–589
Han S (1997) Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning. J Geod 71(6):351–361
Hatch R (1982) The synergism of GPS code and carrier measurements. In: Proceedings of the third international symposium on satellite Doppler positioning at physical sciences laboratory of New Mexico State University, vol 2, pp 1213–1231, 8–12 Feb
Hu J, Zhang X, Li P, Ma F, Pan L (2020) Multi-GNSS fractional cycle bias products generation for GNSS ambiguity-fixed PPP at Wuhan University. GPS Solut 24(1):15
Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beutler G (2009) Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J Geod 83:1145. https://doi.org/10.1007/s00190-009-0333-2
Kang Z, Tapley B, Bettadpur S, Ries J, Nagel P, Pastor R (2006) Precise orbit determination for the GRACE mission using only GPS data. J Geod 80(6):322–331
Katsigianni G, Loyer S, Perosanz F, Mercier F, Zajdel R, Sośnica K (2019) Improving Galileo orbit determination using zero-difference ambiguity fixing in a Multi-GNSS processing. Adv Space Res 63:2952–2963
Lambin J, Morrow R, Fu L-L, Willis J, Bonekamp H, Lillibridge J, Perbos J, Zaouche G, Vaze P, Bannoura W, Parisot F, Thouvenot E, Coutin-Faye S, Lindstrom E, Mignogno M (2010) The OSTM/Jason-2 mission. Mar Geod 33(S1):4–25
Laurichesse D, Mercier F, Berthias JP, Broca P, Cerri L (2009) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navigation 56(2):135–149
Li X, Zhang X (2012) Improving the estimation of uncalibrated fractional phase offsets for PPP ambiguity resolution. Navigation 65(3):513–529
Li X, Li X, Yuan Y, Zhang K, Zhang X, Wickert J (2018) Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geod 92:579–608
Li X, Li X, Liu G, Feng G, Yuan Y, Zhang K, Ren X (2019a) Triple-frequency PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo. J Geod. https://doi.org/10.1007/s00190-019-01229-x
Li X, Ma F, Li X, Lv H, Bian L, Jiang Z, Zhang X (2019b) LEO constellation-augmented multi-GNSS for rapid PPP convergence. J Geod 93(5):749–764
Li X, Wu J, Zhang K, Li X, Xiong Y, Zhang Q (2019c) Real-time kinematic precise orbit determination for LEO satellites using zero-differenced ambiguity resolution. Remote Sens 11(23):2815
Li X, Zhang K, Meng X, Zhang Q, Zhang W, Li X, Yuan Y (2020) LEO-BDS-GPS integrated precise orbit modeling using FengYun-3D, FengYun-3C onboard and ground observations. GPS Solut 24(2):48
Li X, Han X, Li X, Liu G, Feng G, Wang B, Zheng H (2021) GREAT-UPD: an open-source software for uncalibrated phase delay estimation based on multi-GNSS and multi-frequency observations. GPS Solut 25(2):1–9
Loyer S, Perosanz F, Mercier F, Capdeville H, Marty J (2012) Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center. J Geod 86(11):991–1003
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
Melbourne WG (1985) The case for ranging in GPS-based geodetic systems. In: Proceedings of the first international symposium on precise positioning with the global positioning system, Rockville, MD, USA, 5–19 April
Ménard Y, Fu L-L, Escudier P, Parisot F, Perbos J, Vincent P, Desai S, Haines B, Kunstmann G (2003) The Jason-1 mission special issue: Jason-1 calibration/validation. Mar Geod 26(3–4):147–157
Montenbruck O, Hackel S, Jäggi A (2017) Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations. J Geod. https://doi.org/10.1007/s00190-017-1090-2
Petit G, Luzum B (2010) IERS conventions 2010. No.36 in IERS Technical Note, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main, Germany
Picone JM, Hedin AE, Drob DP, Aikin AC (2002) NRLMSISE-00 empirical model of the atmosphere: statistical comparisons and scientific issues. J Geophys Res. https://doi.org/10.1029/2002JA009430
Priestley KJ, Smith GL, Thomas S, Cooper D, Lee RB, Walikainen D, Hess P, Szewczyk ZP, Wilson R (2011) Radiometric performance of the CERES earth radiation budget climate record sensors on the eos aqua and terra spacecraft through April 2007. J Atmos Ocean Technol 28(1):3–21
Shako R, Förste C, Abrikosov O, Bruinsma S, Marty J-C, Lemoine JM, Dahle C (2013) EIGEN-6C: a high-resolution global gravity combination model including GOCE data. Observation of the system earth from space-CHAMP, GRACE, GOCE and future missions, pp 155–161
Standish EM (1998) JPL planetary and lunar ephemerides, DE405/LE405. NASA Jet Propulsion Laboratory, Pasadena, IOM 312.F-98-048
Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(9):L09607
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1):65–82
van den Ijssel J, Forte B, Montenbruck O (2016) Impact of Swarm GPS receiver updates on POD performance. Earth Planets Space 68(1):1–7
Wautelet G, Loyer S, Mercier F, Perosanz F (2017) Computation of GPS P1–P2 differential code biases with Jason-2. GPS Solut 21(4):1619–1631
Wübbena G (1985) Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements. In: Proceedings of the first international symposium on precise positioning with the global positioning system, Rockville, MD, 5–19 April
Zhang K, Li X, Wu J, Yuan Y, Li X, Zhang X, Zhang W (2021) Precise orbit determination for LEO satellites with ambiguity resolution: improvement and comparison. J Geophys Res. https://doi.org/10.1029/2021JB022491
Acknowledgements
This study is financially supported by the National Natural Science Foundation of China (No. 41974027), the National Key Research and Development Program of China (2021YFB2501100) and the Sino-German mobility programme (Grant No. M-0054). 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
XXL and JQW provided the initial idea and wrote the manuscript; XL and GGL helped with paper writing and data analysis; QZ, KKZ and WZ contributed to LEO data processing. All authors reviewed the manuscript.
Corresponding author
Rights and permissions
About this article
Cite this article
Li, X., Wu, J., Li, X. et al. Calibrating GNSS phase biases with onboard observations of low earth orbit satellites. J Geod 96, 8 (2022). https://doi.org/10.1007/s00190-022-01600-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00190-022-01600-5