LEO Augmentation in Large-Scale Ionosphere-Float PPP-RTK Positioning
Publication: Journal of Surveying Engineering
Volume 150, Issue 2
Abstract
Precise point positioning-real-time kinematic (PPP-RTK) positioning combines the advantages of PPP and RTK, which enables the integer ambiguity resolution (IAR) without requiring a reference station nearby. The ionospheric corrections are delivered to users to enable fast IAR. For large-scale networks, precise interpolation of ionospheric delays is challenging. The ionospheric delays are often independently estimated by the user, in the so-called ionosphere-float mode. The augmentation of low Earth orbit (LEO) satellites can bridge this shortcoming thanks to their fast speeds and the resulting rapid geometry change. Using 30-s real dual-frequency Global Positioning System (GPS) and Beidou Navigation Satellite System (BDS) observations within a large-scale network of thousands of kilometers, this contribution tests the effects of LEO augmentation using simulated dual-frequency LEO signals from the navigation-oriented LEO constellation, CentiSpace. Results showed that the LEO augmentation makes the solution convergence less sensitive to the original Global Navigation Satellite System (GNSS)-based model strength. The improvements in the convergence times are significant. For example, in the kinematic mode, the convergence time of the 90% lines of the GPS/BDS-combined ambiguity-float horizontal solutions to 0.05 m is shortened from more than 60 to 3.5 min, and that of the GPS-only partial ambiguity resolution (PAR)-enabled horizontal solutions is shortened from more than 20 to 4.5 min. In both the ambiguity-float and PAR-enabled cases, the 68.27% () lines of both the kinematic and static horizontal and height errors can converge to 0.05 m within 4 min, and for the 90% lines, within 6.5 min in all cases. The 90% line of the GPS/BDS/LEO combined PAR-enabled solutions can converge to 0.05 m within 2.5 and 3 min in the horizontal and up direction, respectively. Results also showed that enlarged projection of the mismodeled biases on the user coordinates were observed in the LEO-augmented scenario after convergence or ambiguity resolution. This is mainly due to the lower orbital height and low elevation angles of the LEO satellites, which requires further research when real LEO navigation signals are available.
Formats available
You can view the full content in the following formats:
Data Availability Statement
Some data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies. This includes the CNES real-time GNSS products available at http://www.ppp-wizard.net/products/REAL_TIME/. Some data, models, or code generated or used during the study are available from the corresponding author by reasonable request. This includes the station observation data, which can be made available upon reasonable request and with the permission of the BDS High-precision Spatiotemporal Service Characteristic Science Database.
Acknowledgments
This research is funded by the National Time Service Center, Chinese Academy of Sciences (CAS) (No. E167SC14), the National Natural Science Foundation of China (No. 12073034), the CAS “Light of West China” Program (XAB2021YN25), Shaanxi Province Key R&D Program Project (2022KW-29), and the Australian Research Council—discovery project (No. DP 190102444). We acknowledge the support of the BDS High-Precision Spatiotemporal Service Characteristic Science Database, the international GNSS monitoring and assessment system (iGMAS) at the National Time Service Center, and the National Space Science Data Center, National Science & Technology Infrastructure of China (http://www.nssdc.ac.cn).
References
Baarda, W. 1981. “S-transformations and criterion matrices.” In Publications on geodesy. 2nd ed. Delft, Netherlands: Netherlands Geodetic Commission.
Cakaj, S., B. Kamo, A. Lala, and A. Rakipi. 2014. “The coverage analysis for low earth orbiting satellites at low elevation.” Int. J. Adv. Comput. Sci. Appl. 5 (Jun): 6. https://doi.org/10.14569/IJACSA.2014.050602.
Collins, P. 2008. “Isolating and estimating undifferenced GPS integer ambiguities.” In Proc., 2008 National Technical Meeting of the Institute of navigation, 720–732. Manassas, VA: Institute of Navigation.
Ge, H., B. Li, M. Ge, N. Zang, L. Nie, Y. Shen, and H. Schuh. 2018. “Initial assessment of precise point positioning with LEO enhanced global navigation satellite systems (LeGNSS).” Remote Sens. 10 (7): 984. https://doi.org/10.3390/rs10070984.
Ge, M., G. Gendt, M. Rothacher, C. Shi, and J. Liu. 2008. “Resolution of GPS carrier phase ambiguities in precise point positioning (PPP) with daily observations.” J. Geod. 82 (7): 389–399. https://doi.org/10.1007/s00190-007-0187-4.
Geng, J., X. Meng, A. H. Dodson, M. Ge, and F. N. Teferle. 2010. “Rapid re-convergences to ambiguity-fixed solutions in precise point positioning.” J. Geod. 84 (12): 705–714. https://doi.org/10.1007/s00190-010-0404-4.
Hassan, T., A. El-Mowafy, and K. Wang. 2020. “A review of system integration and current integrity monitoring methods for positioning in intelligent transport systems.” IET Intel. Transport Syst. 15 (1): 43–60. https://doi.org/10.1049/itr2.12003.
Hauschild, A., J. Tegedor, O. Montenbruck, H. Visser, and M. Markgraf. 2016. “Precise onboard orbit determination for LEO satellites with real-time orbit and clock corrections.” In Proc., 29th Int. Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2016), 3715–3723. Portland, OR: Institute of Navigation.
Hong, J., R. Tu, P. Zhang, J. Han, L. Fan, S. Wang, and X. Lu. 2023. “GNSS rapid precise point positioning enhanced by low Earth orbit satellites.” Satell. Navig. 4 (1): 11. https://doi.org/10.1186/s43020-023-00100-x.
Ifadis, I. 1986. The atmospheric delay of radio waves: Modeling the elevation dependence on a global scale. Göteborg, Sweden: Chalmers Univ. of Technology.
Kazmierski, K., K. Sosnica, and T. Hadas. 2018. “Quality assessment of multi-GNSS orbits and clocks for real-time precise point positioning.” GPS Solutions 22 (Jan): 11. https://doi.org/10.1007/s10291-017-0678-6.
Li, Q., W. Yao, R. Tu, Y. Du, and M. Liu. 2023. “Performance assessment of multi-GNSS PPP ambiguity resolution with LEO-augmentation.” Remote Sens. 15 (12): 2958. https://doi.org/10.3390/rs15122958.
Li, X., X. Li, F. Ma, Y. Yuan, K. Zhang, F. Zhou, and X. Zhang. 2019. “Improved PPP ambiguity resolution with the assistance of multiple LEO constellations and signals.” Remote Sens. 11 (4): 408. https://doi.org/10.3390/rs11040408.
Li, X., F. Ma, X. Li, H. Lv, L. Bian, Z. Jiang, and X. Zhang. 2018. “LEO constellation-augmented multi-GNSS for rapid PPP convergence.” J. Geod. 93 (Aug): 749–764. https://doi.org/10.1007/s00190-018-1195-2.
Lv, Y., T. Geng, Q. Zhao, X. Xie, F. Zhang, and X. Wang. 2020. “Evaluation of BDS-3 orbit determination strategies using ground-tracking and inter-satellite link observation.” Remote Sens. 12 (16): 2647. https://doi.org/10.3390/rs12162647.
Montenbruck, O., and E. Gill. 2000. “Around the world in a hundred minutes.” In Satellite orbits. 1st ed., 1–13. Berlin: Springer.
Montenbruck, O., F. Kunzi, and A. Hauschild. 2021. “Performance assessment of GNSS–based real–time navigation for the Sentinel–6 spacecraft.” GPS Solutions 26 (Jun): 12. https://doi.org/10.1007/s10291-021-01198-9.
Nadarajah, N., A. Khodabandeh, K. Wang, M. Choudhury, and P. J. G. Teunissen. 2018. “Multi-GNSS PPP-RTK: From large- to small-scale networks.” Sensors 18 (4): 1078. https://doi.org/10.3390/s18041078.
Nardo, A., B. Li, and P. J. G. Teunissen. 2016. “Partial ambiguity resolution for ground and space-based applications in a GPS + Galileo scenario: A simulation study.” Adv. Space Res. 57 (1): 30–45. https://doi.org/10.1016/j.asr.2015.09.002.
Odijk, D., A. Khodabandeh, N. Nadarajah, M. Choudhury, B. Zhang, W. Li, and P. J. G. Teunissen. 2016. “PPP-RTK by means of S-system theory: Australian network and user demonstration.” J. Spatial Sci. 62 (1): 3–27. https://doi.org/10.1080/14498596.2016.1261373.
Odijk, D., P. Teunissen, and B. Zhang. 2012. “Single-frequency integer ambiguity resolution enabled GPS precise point positioning.” J. Surv. Eng. 138 (4): 193–202. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000085.
Odijk, D., B. Zhang, A. Khodabandeh, R. Odolinski, and P. J. G. Teunissen. 2015. “On the estimability of parameters in undifferenced, uncombined GNSS network and PPPRTK user models by means of S-system theory.” J. Geod. 90 (1): 15–44. https://doi.org/10.1007/s00190-015-0854-9.
Perez, R. 1998. “Introduction to satellite systems and personal wireless communications.” In Wireless communications design handbook, 1–30. London: Academic Press. https://doi.org/10.1016/S1874-6101(99)80014-3.
Psychas, D., and S. Verhagen. 2020. “Real-time PPP-RTK performance analysis using ionospheric corrections from multi-scale network configurations.” Sensors 20 (11): 3012. https://doi.org/10.3390/s20113012.
Pullen, S., Y. S. Park, and P. Enge. 2009. “Impact and mitigation of ionospheric anomalies on ground-based augmentation of GNSS.” Radio Sci. 44 (1): RS0A21. https://doi.org/10.1029/2008RS004084.
Rebischung, P., and R. Schmid. 2016. “IGS14/igs14.atx: A new framework for the IGS products.” In Proc., Fall Meeting 2016. San Francisco: American Geophysical Union.
Teunissen, P. J. G. 1985. “Zero order design: Generalized inverses, adjustment, the datum problem and S-transformations.” In Optimization and design of geodetic networks, 11–55. Berlin: Springer. https://doi.org/10.1007/978-3-642-70659-2_3.
Teunissen, P. J. G. 1993. “Least-squares estimation of the integer GPS ambiguities. Invited lecture, Section IV theory and methodology.” In Proc., IAG General Meeting, Beijing, China. Masala, Finland: International Association of Geodesy.
Teunissen, P. J. G. 1995. “The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation.” J. Geod. 70 (1–2): 65–82. https://doi.org/10.1007/BF00863419.
Teunissen, P. J. G., and A. Khodabandeh. 2015. “Review and principles of PPP-RTK methods.” J. Geod. 89 (3): 217–240. https://doi.org/10.1007/s00190-014-0771-3.
Teunissen, P. J. G., D. Odijk, and B. Zhang. 2010. “PPP-RTK: Results of CORS network-based PPP with integer ambiguity resolution.” J. Aeronaut. Astronaut. Aviat. 42 (4): 223–230.
Walker, J. G. 1984. “Satellite constellations.” J. Br. Interplanet. Soc. 37 (Dec): 559–571.
Wang, K., A. El-Mowafy, W. Wang, L. Yang, and X. Yang. 2022a. “Integrity monitoring of PPP-RTK positioning; Part II: LEO augmentation.” Remote Sens. 14 (7): 1599. https://doi.org/10.3390/rs14071599.
Wang, K., B. Sun, W. Qin, X. Mi, A. El-Mowafy, and X. Yang. 2022b. “A method of real-time long-baseline time transfer based on the PPP-RTK.” Adv. Space Res. 71 (3): 1363–1376. https://doi.org/10.1016/j.asr.2022.10.062.
Wu, J., S. Wu, G. Hajj, W. Bertiguer, and S. Lichten. 1993. “Effects of antenna orientation on GPS carrier phase measurements.” Manuscr. Geod. 18 (Jun): 91–98.
Wübbena, G., M. Schmitz, and A. Bagge. 2005. “PPP-RTK: Precise point positioning using state-space representation in RTK networks.” In Proc., 18th Int. Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2005), 2584–2594. Manassas, VA: Institute of Navigation.
Yang, L. 2019. “The CentiSpace-1: A LEO satellite-based augmentation system.” In Proc., 14th Meeting of the Int. Committee on Global Navigation Satellite Systems, Bengaluru, India. Vienna, Austria: United Nations Office for Outer Space Affairs.
Zhang, B., P. Hou, and R. Odolinski. 2022. “PPP-RTK: From common-view to all-in-view GNSS networks.” J. Geod. 96 (Jun): 102. https://doi.org/10.1007/s00190-022-01693-y.
Zhao, Q., S. Pan, C. Gao, W. Gao, and Y. Xia. 2020. “BDS/GPS/LEO triple-frequency uncombined precise point positioning and its performance in harsh environments.” Measurement 151 (Jun): 107216. https://doi.org/10.1016/j.measurement.2019.107216.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 150 • Issue 2 • May 2024
Copyright
This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Oct 11, 2022
Accepted: Oct 11, 2023
Published online: Jan 4, 2024
Published in print: May 1, 2024
Discussion open until: Jun 4, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.