Abstract
The real-time kinematic precise point positioning (PPP-RTK) technique enables integer ambiguity resolution by providing single-receiver users with information on the satellite phase biases next to the standard PPP corrections. Using undifferenced and uncombined observations, rank deficiencies existing in the design matrix need to be eliminated to form estimable parameters. In this contribution, the estimability of the parameters was studied in single-frequency ionosphere-weighted scenario, given a dynamic satellite-clock model in the network Kalman filter. In case of latency of the network corrections, the estimable satellite clocks, satellite phase biases, and ionospheric delays need to be predicted over short time spans. With and without satellite-clock models incorporated in the network Kalman filter, different approaches were used to predict the network corrections. This contribution shows how the predicted network corrections responded to the presence and absence of satellite-clock models. These differences in the predicted network corrections were also reflected in the user positioning results. Using three different 1-Hz global positioning system (GPS) single-frequency data sets, two user stations in one small-scale network were used to compute the positioning results, applying predicted network corrections. The latency of the network products ranges from 3 to 10 s. It was observed that applying strong satellite-clock constraints in the network Kalman filter (i.e., with the process noise of 1 or 0.5 mm per square root of second) reduced the root-mean squares (RMS) of the user positioning results to centimeters in the horizontal directions and decimeters in the vertical direction for latencies larger than 6 s, compared to the cases without a satellite-clock model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank the IGS, GA, and Vicmap Position—GPSnet (Victoria State Government) for providing the orbit and the clock products, the precise coordinates, and the observation data of the stations. The orbit and clock products were obtained through the online archives of the Crustal Dynamics Data Information System (CDDIS), NASA Goddard Space Flight Center, Greenbelt, MD (ftp://cddis.gsfc.nasa.gov/gnss/products/). The authors also thank their colleagues in the GNSS Research Centre, Curtin University, for their contributions on the development of the Curtin PPP-RTK Software. P. J. G. Teunissen is recipient of an Australian Research Council (ARC) Federation Fellowship (Project FF0883188).
References
Allan, D. W. (1987). “Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators.” IEEE T. Ultrason. Ferroelectr. Freq. Control, 34(6), 647–654.
Baarda, W. (1981). S-transformations and criterion matrices. Vol. 5(1) of Publications on Geodesy, 2nd Rev. Ed. Netherlands Geodetic Commission, Delft, Netherlands.
Banville, S., Collins, P., Zhang, W., and Langley, R. B. (2014). “Global and regional ionospheric corrections for faster PPP convergence.” Navigation, 61(2), 115–124.
Bevis, M., Businger, S., Herring, T., Rocken, C., Anthes, R., and Ware, R. (1992). “GPS meteorology: Sensing of atmospheric water vapor using the Global Positioning System.” J. Geophys. Res., 97(D14), 15787–15801.
Collins, P. (2008). “Isolating and estimating undifferenced GPS integer ambiguities.” Proc., 2008 National Technical Meeting of the Institute of Navigation, Institute of Navigation, Manassas, VA, 720–732.
Dach, R., Hugentobler, U., Fridez, P., and Meindl, M. (2007). Bernese GNSS software version 5.0. User manual, Astronomical Institute, Univ. of Bern, Bern, Switzerland.
Dow, J. M., Neilan, R. E., and Rizos, C. (2009). “The International GNSS service in a changing landscape of global navigation satellite systems.” J. Geod., 83(3–4), 191–198.
Eueler, H. J., and Goad, C. C. (1991). “On optimal filtering of GPS dual frequency observations without using orbit information.” Bull. Geod. 65(2), 130–143.
GA (Geoscience Australia). (2017). “Daily SINEX files”. ⟨ftp://ftp.ga.gov.au/geodesy-outgoing/gnss/solutions/final/⟩ (May 2017).
Ge, M., Gendt, G., Rothacher, M., Shi, C., and 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., Teferle, F. N., Meng, X., and Dodson, A. H. (2011). “Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning.” Adv. Space Res., 47(10), 1664–1673.
Google Earth. (2017). “Google earth imagery.” (October 18, 2017). Google earth 7.0.3.8542. Victoria, Australia. 37° 47′13.50′′S, 144° 58′57.07′′E, Eye alt 66.19 km. TerraMetrics 2017. DigitalGlobe 2017. ⟨https://www.google.com/earth/⟩ (December 2017).
Hauschild, A., and Montenbruck, O. (2009). “Kalman-filter-based GPS clock estimation for near real-time positioning.” GPS Solut., 13(3), 173–182.
Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2008). GNSS—Global navigation satellite systems: GPS, GLONASS, Galileo, and more, Springer-Verlag, Wien, Austria.
Huisman, L., Teunissen, P. J. G., and Hu, C. (2012). “GNSS precise point positioning in regional reference frames using real-time broadcast corrections.” J. Appl. Geod., 6(1), 15–23.
IGS (International GNSS Service) Clock. (2017). “International GNSS Service, GNSS final combined satellite and receiver clock solution (30 second) product.” NASA Crustal Dynamics Data Information System, Greenbelt, MD ⟨ftp://cddis.gsfc.nasa.gov/⟩ (June 2017).
Khodabandeh, A., and Teunissen, P. J. G. (2015). “An analytical study of PPP-RTK corrections: Precision, correlation and user-impact.” J. Geod., 89(11), 1109–1132.
Laurichesse, D., and Mercier, F. (2007). “Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP.” Proc., ION GNSS 2007, Institute of Navigation, Manassas, VA, 839–848.
Laurichesse, D., Mercier, F., and Berthias, J. P. (2010). “Real-time PPP with undifferenced integer ambiguity resolution, experimental results.” Proc., ION GNSS 2010, Institute of Navigation, Manassas, VA, 2534–2544.
Leandro, R., et al. (2011). “RTX positioning: The next generation of cm-accurate real-time GNSS positioning.” Proc., ION GNSS 2011, Institute of Navigation, Manassas, VA, 1460–1475.
Li, W., Nadarajah, N., Teunissen, P. J. G., Khodabandeh, A., and Chai, Y. (2017). “Array-aided single-frequency state-space RTK with combined GPS, Galileo, IRNSS, and QZSS L5/E5a observations.” J. Surv. Eng., 04017006.
Loyer, S., Perosanz, F., Mercier, F., Capdeville, H., and Marty, J. C. (2012). “Zero-difference GPS ambiguity resolution at CNES-CLS IGS analysis center.” J. Geod., 86(11), 991–1003.
Odijk, D. (2002). “Fast precise GPS positioning in the presence of ionospheric delays.” Ph.D. thesis, Delft Univ. of Technology ⟨https://repository.tudelft.nl/islandora/object/uuid:40d49779-2ef4-4641-9ae4-f591871063fa?collection=research⟩ (December 2017).
Odijk, D., et al. (2017). “PPP-RTK by means of S-system theory: Australian network and user demonstration.” J. Spat. Sci., 62(1), 3–27.
Odijk, D., Arora, B. S., and Teunissen, P. J. G. (2014a). “Predicting the success rate of long-baseline GPS+Galileo (partial) ambiguity resolution.” J. Navig., 67(3), 385–401.
Odijk, D., Teunissen, P. J. G., and Huisman, L. (2012a). “First results of mixed GPS-GIOVE single-frequency RTK in Australia.” J. Spat. Sci., 57(1), 3–18.
Odijk, D., Teunissen, P. J. G., and Khodabandeh, A. (2014b). “Single-frequency PPP-RTK: Theory and experimental results.” Earth on the edge: Science for a sustainable planet. IAG symposia, Vol. 139, C. Rizos and P. Willis, eds., Springer, Berlin, Heidelberg, 571–578.
Odijk, D., Teunissen, P. J. G., and Zhang, B. (2012b). “Single-frequency integer ambiguity resolution enabled GPS precise point positioning.” J. Surv. Eng., 193–202.
Odolinski, R., and Teunissen, P. J. G. (2017). “Low-cost, high-precision, single-frequency GPS-BDS RTK positioning.” GPS Solut., 21(3), 1315–1330.
Riley, W. J. (2008). Handbook of frequency stability analysis. NIST Special Publication 1065, U.S. Government Printing Office, Washington, DC.
Saastamoinen, J. (1972). “Contribution to the theory of atmospheric refraction.” Bull. Geod., 105(1), 279–298.
Senior, K. L., Ray, J. R., and Beard, R. L. (2008). “Characterization of periodic variations in the GPS satellite clocks.” GPS Solut., 12(3), 211–225.
Springer, T. A., and Hugentobler, U. (2001). “IGS ultra rapid products for (near-) real-time applications.” Phys. Chem. Earth, Part A., 26(6–8), 623–628.
Teunissen, P. J. G. (1985). “Zero order design: Generalized inverses, adjustment, the datum problem and S-transformations.” Optimization and design of geodetic networks, E. W. Grafarend and F. Sansò, eds., Springer, Berlin, Heidelberg, 11–55.
Teunissen, P. J. G., and Khodabandeh, A. (2015). “Review and principles of PPP-RTK methods.” J. Geod., 89(3), 217–240.
Teunissen, P. J. G., and Montenbruck, O. (2017). Springer handbook of global navigation satellite systems, Springer International Publishing, Cham, Switzerland.
Teunissen, P. J. G., Odijk, D., and Zhang, B. (2010). “PPP-RTK: Results of CORS network-based PPP with integer ambiguity resolution.” J. Aeronaut., Astronaut. Aviation, Ser. A, 42(4), 223–230.
van Bree, R. J. P., and Tiberius, C. C. J. M. (2012). “Real-time single-frequency precise point positioning: Accuracy assessment.” GPS Solut., 16(2), 259–266.
van Dierendonck, A. J., McGraw, J. B., and Brown, R. G. (1984). “Relationship between Allan variances and Kalman filter parameters.” Proc., PTTI 1984, NASA Goddard Space Flight Center, Greenbelt, MD, 273–293.
Wang, K., Khodabandeh, A., and Teunissen, P. J. G. (2017). “A study on predicting network corrections in PPP-RTK processing.” Adv. Space Res., 60(7), 1463–1477.
Wübbena, G., Schmitz, M., and Bagge, A. (2005). “PPP-RTK: Precise point positioning using state-space representation in RTK networks.” Proc., ION GNSS 2005, Institute of Navigation, Manassas, VA, 2584–2594.
Younes, S. A. M. (2016). “Modeling investigation of wet tropospheric delay error and precipitable water vapor content in Egypt.” Egypt. J. Remote Sens. Space Sci., 19(2), 333–342.
Yu, X., and Gao, J. (2017). “Kinematic precise point positioning using multi-constellation global navigation satellite system (GNSS) observations.” ISPRS Int. J. Geo-Inf., 6(1), 6.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 144 • Issue 2 • May 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Sep 1, 2017
Accepted: Dec 21, 2017
Published online: Mar 12, 2018
Published in print: May 1, 2018
Discussion open until: Aug 12, 2018
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.