Abstract
Precise knowledge of the antenna phase center variations (PCVs) of global navigation satellite system (GNSS) is indispensable for GNSS high-precision applications. Currently, the PCV models of most GNSS satellites are exclusively estimated from ground observations, which reveals some drawbacks such as limited nadir coverage (usually < 14°) and high correlation with tropospheric parameters. Onboard observations from plenty of low Earth orbit (LEO) satellites launched in recent years offer us a great chance to investigate the LEO-based GNSS PCV calibration. We estimate GPS PCV model using ambiguity-fixed carrier phase observations from multiple LEO satellites to obtain more reliable GPS PCVs. Onboard data of eight LEO satellites from day of year (DOY) 122, 2019 to DOY 180, 2019 are processed. We first evaluate the contribution of integer ambiguity resolution (IAR) to the LEO PCV calibration. Compared with the traditional ambiguity-float PCVs, the ambiguity-fixed PCVs can contribute to the maximum reduction of 6.2% in carrier phase residuals and 8.0% in satellite laser ranging (SLR) residuals. After that the LEO-based GPS PCV calibration using different LEO satellites is performed and the impact of different estimation strategies and datum definitions is assessed in detail. The results show that the IAR can contribute to the stability improvement in GPS PCVs by (24.5%, 41.5%, 42.4%, and 45.2%) for four BLOCKs. As the number of LEO satellites increases, GPS PCVs gain an evident stability improvement. With the inclusion of eight LEO satellites, the PCV stability is mainly within 0.3 mm with the maximum improvement of 63.8% and the PCV difference w.r.t igs14.atx is less than 1 mm. Meanwhile, we also find that the LEO-based GPS PCV calibration is hardly influenced by the datum definition which is applied to decouple GPS PCVs and LEO PCVs. Validation results indicate that our GPS PCV estimates slightly outperform PCV model from igs14.atx with the LEO kinematic orbit accuracy improvement of 5.1% and the precise point positioning (PPP) error reduction of 1.1%. The reference frame scale of our GPS PCV estimates is also consistent with that from igs14.atx.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10291-023-01485-7/MediaObjects/10291_2023_1485_Fig13_HTML.png)
Similar content being viewed by others
Data availability
The LEO satellite onboard GNSS observation data are available publicly from GFZ (ftp://swarm-diss.eo.esa.int/Level1b/Latest_baselines/GPSx_RO), CNES (ftp://ftp-access.aviso.altimetry.fr/geophysical-data-record/doris/jason-3/), and ESA (https://scihub.copernicus.eu/dhus/#/home). All datasets which support the results mentioned above can be obtained from the corresponding author.
References
Bock H, Jäggi A, Meyer U, Dach R, Beutler G (2011) Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite. Adv Space Res 47(11):1885–1893. https://doi.org/10.1016/j.asr.2011.01.017
Dilssner F, Otten M, Springer T, Flohrer C, Svehla D, Zandbergen R (2011) GPS satellite antenna parameters from combined ground-based and space-borne data processing. EGU2011–12263, European Geosciences Union General Assembly 2011, Vienna
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:L06310. https://doi.org/10.1029/2004GL022224
Gu D, Lai Y, Liu J, Ju B, Tu J (2016) Spaceborne GPS receiver antenna phase center offset and variation estimation for the Shiyan 3 satellite. Chin J Aeronaut 29(5):1335–1344. https://doi.org/10.1016/j.cja.2016.08.016
Guo J (2014) The impacts of attitude, solar radiation and function model on precise orbit determination for GNSS satellites. Dissertation, Wuhan University
Haines B, Bar-Sever Y, Bertiger W, Desai S, Harvey N, Sibois A, Weiss J (2015) Realizing a terrestrial reference frame using the global positioning system. J Geophys Res Solid Earth 120:5911–5939. https://doi.org/10.1002/2015JB012225
Jäggi A, Dach R, Montenbruck O (2009) Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J Geod 83(12):1145–1162. https://doi.org/10.1007/s00190-009-0333-2
Jäggi A, Dilssner F, Schmid R, Dach R, Springer T, Peter H, Steigenberger P, Andres Y, Enderle W (2012) Extension of the GPS satellite antenna patterns to nadir angles beyond 14°. In: European Geosciences Union General Assembly 2012, Vienna, Austria
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
Li X, Zhang K, Zhang Q, Zhang W, Yuan Y, Li X (2018) Integrated orbit determination of FengYun-3C, BDS, and GPS satellites. J Geophys Res Solid Earth 123:8143–8160. https://doi.org/10.1029/2018JB015481
Li X, Zhang W, Zhang K, Zhang Q, Li X, Jiang Z, Ren X, Yuan Y (2021) GPS satellite differential code bias estimation with current eleven low earth orbit satellites. J Geod 95:76. https://doi.org/10.1007/s00190-021-01536-2
Männel B (2016) Co-location of Geodetic Observation Techniques in Space. Dissertation, ETH Zurich. https://doi.org/10.3929/ethz-a-010811791
Montenbruck O, Hackel S, Jaggi A (2018a) Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations. J Geod 92(7):711–726. https://doi.org/10.1007/s00190-017-1090-2
Montenbruck O, Hackel S, van den Ijssel J, Arnold D (2018b) Reduced dynamic and kinematic precise orbit determination for the Swarm mission from 4 years of GPS tracking. GPS Solut 22:79. https://doi.org/10.1007/s10291-018-0746-6
Rebischung P, Altamimi Z, Ray J, Garayt B (2016) The IGS contribution to ITRF2014. J Geod 90:611–630. https://doi.org/10.1007/s00190-016-0897-6
Schaer S, Villiger A, Arnold D, Dach R, Prange L, Jäggi A (2021) The CODE ambiguity-fixed clock and phase bias analysis products: generation, properties, and performance. J Geod 95:81. https://doi.org/10.1007/s00190-021-01521-9
Schmid R (2014) IGS Antenna Working Group. In: Dach R, Jean Y (eds) IGS Technical Report 2013. IGS Central Bureau, Pasadena, pp 133–136
Schmid R, Rothacher M (2003) Estimation of elevation-dependent satellite antenna phase center variations of GPS satellites. J Geod 77:440–446. https://doi.org/10.1007/s00190-003-0339-0
Schmid R, Rothacher M, Thaller D, Steigenberger P (2005) Absolute phase center corrections of satellite and receiver antennas. GPS Solut 9(4):283–293. https://doi.org/10.1007/s10291-005-0134-x
Schmid R, Dach R, Collilieux X, Jäggi A, Schmitz M, Dilssner F (2016) Absolute IGS antenna phase center model igs08atx: status and potential improvements. J Geod 90(4):343–364. https://doi.org/10.1007/s00190-015-0876-3
Wu S, Yunck T, Thornton C (1991) Reduced-dynamic technique for precise orbit determination of low Earth satellites. J Guid Control Dyn 14(1):24–30
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 Solid Earth 126:9. https://doi.org/10.1029/2021JB022491
Acknowledgements
This study is financially supported by the National Natural Science Foundation of China (Grant No. 41974027), the Hubei Province Natural Science Foundation (Grant No. 2020CFA002), and the Sino-German mobility programme (Grant No. M-0054). The numerical calculations have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
Author information
Authors and Affiliations
Contributions
WZ, KZ, and XL proposed the general idea of this manuscript, analyzed the data, and wrote the paper. BY, SH, YY, JW, and HZ contributed to the paper writing and the data analyzes.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
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 (e.g. a society or other partner) 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
Zhang, W., Zhang, K., Li, X. et al. GPS phase center variation modeling using ambiguity-fixed carrier phase observations from low Earth orbit satellites. GPS Solut 27, 146 (2023). https://doi.org/10.1007/s10291-023-01485-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-023-01485-7