Improving Stochastic Model of GNSS Precise Point Positioning with Triple-Frequency Geometry-Free Combination
Publication: Journal of Surveying Engineering
Volume 150, Issue 2
Abstract
The triple-frequency global positioning system (GPS), BeiDou navigation satellite system-3 (BDS-3), and Galileo can form the geometry-free and ionosphere-free (GFIF) carrier phase and pseudorange combinations, respectively. These combinations provide a precondition for which the accuracies of the carrier phase and pseudorange observations can be evaluated, respectively. The stochastic model of precise point positioning (PPP) processing is constructed using the evaluated results. The 176 International GNSS Service (IGS) stations are used to validate the presented method. The evaluated results show that accuracies of the GPS, BDS-3, and Galileo carrier phase observations are at the millimeter level, while those of pseudorange observations reach the decimeter level. In addition, BDS-3, GPS, and Galileo have different precisions. The stochastic model, which is reestablished from the evaluated accuracies, is tested using single Global Navigation Satellite System (GNSS) and multiGNSS PPP performances. The single-GNSS PPP shows that its convergence time has a mean improvement of 24%, and its 1- and 2-h mean three dimensions (3D) positioning accuracies are improved by about 17.7% and 4.5%, respectively, compared with those of empirical accuracies-based stochastic models. It also has the best performance in the multiGNSS PPP. Its mean convergence time of GPS+Galileo for 3 days is shorter than 35 min, while that of GPS+BDS-3 is less than 30 min. The mean improvements for the convergence time and 1- and 2-h 3D positioning reach 28%, 9.4%, and 2.8%, respectively, when the GPS+Galileo and GPS+BDS-3 PPP use the reestablished stochastic model instead of the empirical methods.
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Data Availability Statement
Some data, models, or code used during the study were provided by a third party (GNSS observation data, satellite orbit, and clock products are available). Direct requests for these materials may be made to the provider as indicated in the Acknowledgments.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (NSFC) (Nos. 41974025 and 42174019) and the Fundamental Research Funds for the Central Universities. IGS is acknowledged for providing GNSS data and products.
References
Brunner, F., H. Hartinger, and L. Troyer. 1999. “GPS signal diffraction modelling: The stochastic SIGMA−δ model.” J. Geod. 73 (Jun): 259–267. https://doi.org/10.1007/s001900050242.
Cai, C., and Y. Gao. 2013. “Modeling and assessment of combined GPS/GLONASS precise point positioning.” GPS Solutions 17 (Mar): 223–236. https://doi.org/10.1007/s10291-012-0273-9.
Chang, G. 2015. “On least-squares solution to 3D similarity transformation problem under Gauss-Helmert model.” J. Geod. 89 (6): 573–576. https://doi.org/10.1007/s00190-015-0799-z.
Chen, J., Y. Zhang, J. Wang, S. Yang, D. Dong, J. Wang, W. Qu, and B. Wu. 2015. “A simplified and unified model of multi-GNSS precise point positioning.” Adv. Space Res. 55 (1): 125–134. https://doi.org/10.1016/j.asr.2014.10.002.
Dow, J., R. Neilan, and C. Rizos. 2009. “The international GNSS Service in a changing landscape of global navigation satellite systems.” J. Geod. 83 (Mar): 191–198. https://doi.org/10.1007/s00190-008-0300-3.
Gu, S., Y. Lou, C. Shi, and J. Liu. 2015. “BeiDou phase bias estimation and its application in precise point positioning with triple-frequency observable.” J. Geod. 89 (10): 979–992. https://doi.org/10.1007/s00190-015-0827-z.
Guo, J., X. Li, Z. Li, L. Hu, G. Yang, C. Zhao, D. Fairbairn, D. Watson, and M. Ge. 2018. “Multi-GNSS precise point positioning for precision agriculture.” Precis. Agric. 19 (5): 895–911. https://doi.org/10.1007/s11119-018-9563-8.
Hadas, T., and J. Bosy. 2015. “IGS RTS precise orbits and clocks verification and quality degradation over time.” GPS Solutions 19 (Feb): 93–105. https://doi.org/10.1007/s10291-014-0369-5.
Hartinger, H., and F. K. Brunner. 1999. “Variances of GPS phase observations: The SIGMA- model.” GPS Solutions 2 (4): 35–43. https://doi.org/10.1007/PL00012765.
Hatch, R. 1982. “The synergism of GPS code and carrier measurements.” In Vol. 2 of Proc., 3rd Int. Geodetic Symposium on Satellite Doppler Positioning, 1213–1231. Las Cruces, NM: New Mexico State Univ.
Hauschild, A., and O. Montenbruck. 2009. “Kalman-filter-based GPS clock estimation for near real-time positioning.” GPS Solutions 13 (3): 173–182. https://doi.org/10.1007/s10291-008-0110-3.
Héroux, P., Y. Gao, J. Kouba, F. Lahaye, Y. Mireault, P. Collins, K. Macleod, P. Tetreault, and K. Chen. 2004. “Products and applications for precise point positioning-moving towards real-time.” In Proc., 17th Int. Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004), 1832–1843. Long Beach, CA: Institute of Navigation.
Howind, J., H. Kutterer, and B. Heck. 1999. “Impact of temporal correlations on GPS-derived relative point positions.” J. Geod. 73 (5): 246–258. https://doi.org/10.1007/s001900050241.
Hu, H., F. Zhou, and S. Jin. 2021. “Improved stochastic modeling of multi-GNSS single point positioning with additional BDS-3 observations.” Meas. Sci. Technol. 32 (4): 045105. https://doi.org/10.1088/1361-6501/abd1fd.
Jin, S., J. Wang, and P. Park. 2005. “An improvement of GPS height estimations: Stochastic modeling.” Earth Planets Space 57 (4): 253–259. https://doi.org/10.1186/BF03352561.
Kazmierski, K., T. Hadas, and K. Sośnica. 2018. “Weighting of Multi-GNSS observations in real-time precise point positioning.” Remote Sens. 10 (Mar): 84. https://doi.org/10.3390/rs10010084.
Kouba, J., and P. Héroux. 2001. “Precise point positioning using IGS Orbit and Clock products.” GPS Solution 5 (2): 12–28. https://doi.org/10.1007/PL00012883.
Leick, A., L. Rapoport, and D. Tatarnikov. 2015. GPS satellite surveying. 4th ed. New York: Wiley.
Li, B. 2016. “Stochastic modeling of triple-frequency BeiDou signals: Estimation, assessment and impact analysis.” J. Geod. 90 (7): 593–610. https://doi.org/10.1007/s00190-016-0896-7.
Li, B., Y. Shen, and P. Xu. 2008. “Assessment of stochastic models for GPS measurements with different types of receivers.” Chin. Sci. Bull. 53 (20): 3219–3225. https://doi.org/10.1007/s11434-008-0293-6.
Li, H., H. Ding, B. Feng, and Q. Kang. 2022a. “Improved method for BDS-3 satellite clock parameterization in the broadcast ephemeris, real-time service (RTS) and IGS final products.” Measurement 204 (Nov): 112059. https://doi.org/10.1016/j.measurement.2022.112059.
Li, H., B. Li, G. Xiao, J. Wang, and T. Xu. 2016a. “Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS.” GPS Solutions 20 (4): 751–760. https://doi.org/10.1007/s10291-015-0486-9.
Li, H., J. Xiao, and B. Li. 2019a. “Evaluation and application of the GPS code observable in precise point positioning.” J. Navig. 72 (6): 1633–1648. https://doi.org/10.1017/S0373463319000274.
Li, H., J. Xiao, and W. Zhu. 2019b. “Investigation and validation of the time-varying characteristic for the GPS differential code bias.” Remote Sens. 11 (4): 428. https://doi.org/10.3390/rs11040428.
Li, H., T. Xu, B. Li, S. Huang, and J. Wang. 2016b. “A new differential code bias (C1–P1) estimation method and its performance evaluation.” GPS Solutions 20 (3): 321–329. https://doi.org/10.1007/s10291-015-0438-4.
Li, H., X. Zhou, and B. Wu. 2013. “Fast estimation and analysis of the inter-frequency clock bias for Block IIF satellites.” GPS Solutions 17 (Jul): 347–355. https://doi.org/10.1007/s10291-012-0283-7.
Li, P., and X. Zhang. 2014. “Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning.” GPS Solutions 18 (3): 461–471. https://doi.org/10.1007/s10291-013-0345-5.
Li, X., M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh. 2015. “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo.” J. Geod. 89 (6): 607–635. https://doi.org/10.1007/s00190-015-0802-8.
Li, X., Q. Wang, J. Wu, Y. Yuan, Y. Xiong, X. Gong, and Z. Wu. 2022b. “Multi-GNSS products and services at iGMAS Wuhan Innovation Application Center: Strategy and evaluation.” Satell. Navig. 3 (Mar): 20. https://doi.org/10.1186/s43020-022-00081-3.
Liu, J., and M. Ge. 2003. “PANDA software and its preliminary result of positioning and orbit determination.” Wuhan Univ. J. Nat. Sci. 8 (2): 603–609. https://doi.org/10.1007/BF02899825.
Lou, Y., F. Zheng, S. Gu, C. Wang, H. Guo, and Y. Feng. 2016. “Multi-GNSS precise point positioning with raw single-frequency and dualfrequency measurement models.” GPS Solutions 20 (4): 849–862. https://doi.org/10.1007/s10291-015-0495-8.
Malys, S., and P. Jensen. 1990. “Geodetic point positioning with GPS carrier beat phase data from the CASA UNO experiment.” Geophys. Res. Lett. 17 (5): 651–654. https://doi.org/10.1029/GL017i005p00651.
Moulborne, W. G. 1985. “The case for ranging in GPS-based geodetic systems.” In Proc., 1st Int. Symp. on Precise Positioning with the Global Positioning System, 373–386. Washington, DC: US Dept. of Commerce.
Seepersad, G., and S. Bisnath. 2015. “Reduction of PPP convergence period through pseudorange multipath and noise mitigation.” GPS Solutions 19 (3): 369–379. https://doi.org/10.1007/s10291-014-0395-3.
Wang, J., M. Stewart, and M. Sakiri. 1998. “Stochastic modeling for static GPS baseline data processing.” J. Surv. Eng. 124 (4): 171–181. https://doi.org/10.1061/(ASCE)0733-9453(1998)124:4(171).
Wessel, P., J. F. Luis, L. Uieda, R. Scharroo, F. Wobbe, W. H. F. Smith, and D. Tian. 2019. “The generic mapping tools version 6.” Geochem. Geophys. Geosyst. 20 (11): 5556–5564. https://doi.org/10.1029/2019GC008515.
Wübbena, G. 1985. “Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements.” In Proc., 1st Int. Symp. on Precise Positioning with the Global Positioning System, 403–412. Washington, DC: US Dept. of Commerce.
Yang, L., B. Li, H. Li, C. Rizos, and Y. Shen. 2017. “The influence of improper stochastic modeling of Beidou pseudoranges on system reliability.” Adv. Space Res. 60 (12): 2680–2690. https://doi.org/10.1016/j.asr.2017.05.035.
Yang, Y., Q. Ding, W. Gao, J. Li, Y. Xu, and B. Sun. 2022. “Principle and performance of BDSBAS and PPP-B2b of BDS-3.” Satell. Navig. 3 (1): 5. https://doi.org/10.1186/s43020-022-00066-2.
Yang, Y., Y. Mao, and B. Sun. 2020. “Basic performance and future developments of BeiDou global navigation satellite system.” Satell. Navig. 1 (1): 1–8. https://doi.org/10.1186/s43020-019-0006-0.
Zhang, B., P. Hou, T. Liu, and Y. Yuan. 2020. “A single-receiver geometry-free approach to stochastic modeling of multi-frequency GNSS observables.” J. Geod. 94 (Mar): 37. https://doi.org/10.1007/s00190-020-01366-8.
Zhang, X., X. Li, and F. Guo. 2011. “Satellite clock estimation at 1 Hz for real time kinematic PPP applications.” GPS Solutions 15 (4): 315–324. https://doi.org/10.1007/s10291-010-0191-7.
Zhou, F., D. Dong, P. Li, X. Li, and H. Schuh. 2019. “Influence of stochastic modeling for inter-system biases on multi-GNSS undifferenced and uncombined precise point positioning.” GPS Solutions 23 (Jul): 59. https://doi.org/10.1007/s10291-019-0852-0.
Zumberge, J. F., M. B. Heflin, D. C. Jefferson, M. M. Watkins, and F. H. Webb. 1997. “Precise point positioning for the efficient and robust analysis of GPS data from large networks.” J. Geophys. Res. 102 (B3): 5005–5017. https://doi.org/10.1029/96JB03860.
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Published In
Journal of Surveying Engineering
Volume 150 • Issue 2 • May 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 3, 2022
Accepted: Oct 19, 2023
Published online: Jan 8, 2024
Published in print: May 1, 2024
Discussion open until: Jun 8, 2024
ASCE Technical Topics:
- Convergence (mathematics)
- Design (by type)
- Engineering fundamentals
- Geomatics
- Geometrics
- Global navigation satellite systems
- Global positioning systems
- Highway and road design
- Mathematics
- Model accuracy
- Models (by type)
- Navigation (geomatic)
- Probability
- Stochastic processes
- Surveying methods
- Three-dimensional models
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