Page 160 - 卫星导航2021年第1-2合期

Wang et al. Satell Navig (2021) 2:9 Page 10 of 11

improve 3D RMS by only 13.1% not as prominent as the more frequency observables. Hence, the multi-frequency
static solutions. FCB products will be generated in future work.

Conclusions Acknowledgements
Thanks to the iGMAS/MGEX for providing the data.
To achieve the fast and precise single station position-
ing service, the PPP AR technique is the key to speed up Authors’ contributions
the positioning bias convergence and improve the accu- QZ, JW and GH conceived and designed the experiments. JW and GH evalu-
ated the accuracy of products and wrote the paper. All authors read and
racy. Terefore, the FCB product is as essential as satellite approved the fnal manuscript.
orbit and clock products for PPP processing.
We frst introduced the FCB estimation method with Funding
The National Key Research and Development Program of China
the uncombined PPP model and the PPP AR strategy. Te (2018YFC1505102), the Programs of the National Natural Science Foundation
precision of the FCBs products and the PPP AR solutions of China (41774025, 41731066), the Special Fund for Technological Innovation
with GPS/BDS-2/Galileo are evaluated. Te uncom- Guidance of Shaanxi Province (2018XNCGG05), the Special Fund for Basic Sci-
entifc Research of Central Colleges (CHD300102269305, CHD300102268305),
bined PPP method is used to estimate the raw ambigui- the Grand Projects of the BDS-2 System (GFZX0301040308) supported this
ties on each frequency which are for the FCBs estimation. study.
Although we do not have to sequentially estimate the Availability of data and materials
WL, NL FCBs as in the IF PPP model, the integer coef- The data used in this study is obtained from iGMAS (http://www.igmas .org)
cients are used to reduce the correlation between the frst and MGEX (ftp://ftp.cddis .eosdi s.nasa.gov/pub/gnss/data/). The satellite pre-
two raw ambiguities in the uncombined PPP model. Te cise orbit and clock products are issued by Chang’an Universtiy (http://gnssc
enter .chd.edu.cn).
more stable FCBs on the new WL and NL combinations
which are formulated with integer vectors, (1, − 1) and Competing interests
(4, − 3), are used in the FCBs estimator. Te raw FCBs The authors declare no conficts of interest.
on each frequency recovered from the new WL and NL Received: 24 August 2020 Accepted: 2 February 2021
combinations are provided to users to fexibly achieve the
ambiguity-fxed solutions with a specifc PPP model.
With the proposed method, we estimated the precise
FCB products based on iGMAS satellite products. For References
the posterior residuals of the FCB estimation, the RMS Bisnath, S., & Gao, Y. (2008). Current state of precise point positioning and
future prospects and limitations. In M. G. Sideris (Ed.), Observing our
of the WL combination is signifcantly smaller than the changing Earth (pp. 615–623). Berlin, Heidelberg: Springer.
NL combination. Te longer wavelength of the WL com- Chen, J. P., Zhang, Y. Z., Wang, J. G., Yang, S. N., Dong, D. N., Wang, J. X., et al.
bination is helpful to resist errors and keep a high con- (2015). A simplifed and unifed model of multi-GNSS precise point
positioning. Advances in Space Research, 55(1), 125–134. https ://doi.
sistency among the FCB measurements. Te accuracy of org/10.1016/j.asr.2014.10.002.
BDS FCBs is degraded by the lower accuracy of satellite Collins, P., Lahaye, F., Héroux, P., & Bisnath, S. (2008). Precise point positioning
precise products. Tis will be improved in the BeiDou-3 with ambiguity resolution using the decoupled clock model. In Proceed-
ings of the 21st international technical meeting of the satellite division of the
Navigation Satellite System (BDS-3). Institute of Navigation (pp. 1315–1322). Savannah, GA, USA: ION.
After estimating the FCB products, the PPP AR with Gabor, M.J., & Nerem, R.S. (1999). GPS carrier phase ambiguity resolution using
GPS, BDS-2, and Galileo raw observations are processed satellite-satellite single diferences. In Proceedings of the 12th international
technical meeting of the satellite division of the Institute of Navigation (pp.
in static and kinematic modes. In daily static position- 1569–1578). Nashville, TN, USA: ION.
ing, the ambiguity-fxed solutions have not signifcant Ge, M., Gendt, G., Rothacher, M., Shi, C., & Liu, J. (2008). Resolution of GPS
improvements compared with the ambiguity-foat solu- carrier-phase ambiguities in Precise Point Positioning (PPP) with daily
observations. Journal of Geodesy, 82(7), 389–399. https ://doi.org/10.1007/
tions, while the stability and reliability of position- s0019 0-007-0187-4.
ing are enhanced with the PPP AR which is also found Geng, J. H., Chen, X. Y., Pan, Y. X., Mao, S. Y., Li, C. H., Zhou, J. N., & Zhang, K. L.
in kinematic mode. With hourly static solutions, 42.6% (2019a). PRIDE PPP-AR: An open-source software for GPS PPP ambigu-
ity resolution. GPS Solutions, 23(4), 91. https ://doi.org/10.1007/s1029
improvement and 97.7% ambiguity success fxing rate 1-019-0888-1.
are achieved for the ambiguity-fxed solutions compared Geng, J. H., Chen, X. Y., Pan, Y. X., & Zhao, Q. L. (2019b). A modifed phase clock/
with the foat solutions. Te signifcant improvement bias model to improve PPP ambiguity resolution at Wuhan University.
Journal of Geodesy, 93(10), 2053–2067. https ://doi.org/10.1007/s0019
of faster convergence time of positioning is also found. 0-019-01301 -6.
Finally, the 3D RMS for the ambiguity-fxed solutions is Geng, J. H., Shi, C., Ge, M. R., Dodson, A. H., Lou, Y. D., Zhao, Q. L., & Liu, J. N.
2.10 cm. (2012). Improving the estimation of fractional-cycle biases for ambiguity
resolution in precise point positioning. Journal of Geodesy, 86(8), 579–589.
Currently, only the BDS-2 data is adopted in our esti- https ://doi.org/10.1007/s0019 0-011-0537-0.
mation which will be improved with the available BDS-3 Gu, S. F., Lou, Y. D., Shi, C., & Liu, J. N. (2015b). BeiDou phase bias estimation and
satellites in the next work. Te uncombined PPP model its application in precise point positioning with triple-frequency observ-
able. Journal of Geodesy, 89(10), 979–992. https ://doi.org/10.1007/s0019
is fexible to process the triple-, quadruple-frequency or 0-015-0827-z.