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PPP-RTK with augmentation from a single reference station

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Abstract

Precise point positioning (PPP) with augmentation by a network of continuously operating reference stations (CORS), known as PPP-RTK, enables fast ambiguity resolution with PPP. However, it suffers from the dependency of a CORS network for augmentation corrections generation. This paper proposes a new real-time PPP-RTK method that generates the augmentation corrections using undifferenced and uncombined PPP at a single reference station. This method enables high accuracy and fast convergence real-time PPP-RTK for both multi-frequency and single-frequency receivers without the need of PPP estimate convergence at the reference station. It provides potential flexibility to include any number of more local reference stations for augmentation correction generation. The method can be regarded as a state-space-representation based RTK approach that offers equivalent performance but can overcome the limitations associated with the observation-space-representation based positioning techniques, such as the high transmission rate and rigorous baseline length requirements. It can also be considered as a special case of the network-based PPP-RTK but it offers increased flexibility in system implementation and opens doors to develop new correction services for PPP-RTK applications. Field tests results validate the positioning performance of the proposed method. The static positioning test indicates that the method could instantly output cm-level positioning solutions even before the corrections estimate convergence at the reference station. And the kinematic vehicle-based test reveals that, the method can provide the rover station receiver cm-level positioning solutions with instant initialization and ambiguity resolution either using a dual-frequency Global Navigation Satellite System (GNSS) receiver or a low-cost single-frequency GNSS receiver with 100% ambiguity fix rate. Also, the test results with different baseline lengths prove that the proposed method will be gradually degraded into standard AR-enabled PPP when the baseline length grows longer, and the ambiguity can be effectively fixed even at the 1258 km baseline length.

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Data availability

Partial data and products used in this work are available for download from the Center for Orbit Determination in Europe (CODE), the rest data are available from the corresponding author on reasonable request.

References

  • Bock H, Jäggi A, Dach R, Schaer S, Beutler G (2009) GPS single-frequency orbit determination for low Earth orbiting satellites. Adv Space Res 43(5):783–791. https://doi.org/10.1016/j.asr.2008.12.003

    Article  Google Scholar 

  • Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett. https://doi.org/10.1029/2005GL025546

    Article  Google Scholar 

  • Boehm J, Heinkelmann R, Schuh H (2007) Short note: a global model of pressure and temperature for geodetic applications. J Geod 81(10):679–683. https://doi.org/10.1007/s00190-007-0135-3

    Article  Google Scholar 

  • Chen K, Gao Y (2005) Real-time precise point positioning using single frequency data, pp 1514–1523

  • Collins P (2008) Isolating and estimating undifferenced GPS integer ambiguities, pp 720–732

  • Collins P, Langley R, LaMance J (1996) Limiting factors in tropospheric propagation delay error modelling for GPS airborne navigation, p 10

  • Feng Y, Gu S, Shi C, Rizos C (2013) A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services. J Geod 87(10):945–960. https://doi.org/10.1007/s00190-013-0659-7

    Article  Google Scholar 

  • Gao Y, Li Z, McLellan JF (1997) Carrier phase based regional area differential GPS for decimeter-level positioning and navigation, pp 1305–1313

  • Gao Y, Zhang Y, Chen K (2006) Development of a real-time single-frequency precise point positioning system and road test results, pp 2297–2303

  • Ge M, Gendt G, Rothacher M, Shi C, Liu J (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

    Article  Google Scholar 

  • Geng J, Bock Y (2013) Triple-frequency GPS precise point positioning with rapid ambiguity resolution. J Geod 87(5):449–460. https://doi.org/10.1007/s00190-013-0619-2

    Article  Google Scholar 

  • Geng J, Bock Y (2016) GLONASS fractional-cycle bias estimation across inhomogeneous receivers for PPP ambiguity resolution. J Geod 90(4):379–396. https://doi.org/10.1007/s00190-015-0879-0

    Article  Google Scholar 

  • HAN S (1997) Carrier phase-based long-range GPS kinematic positioning. Ph.D. Thesis, p 185

  • Hatch R (1982) The synergism of GPS code and carrier measurements. In: Proceedings of the third international symposium on satellite doppler positioning at physical sciences laboratory of New Mexico State University. Las Cruces, NM, pp 1213–1231

  • Héroux P, Kouba J (1995) GPS precise point positioning with a difference. Natural Resources Canada, Geomatics Canada, Geodetic Survey Division

  • Jonge P, Tiberius CCJM (1996) The LAMBDA method for integer ambiguity estimation: implementation aspects. Delft Geodetic Computing Centre LGR Series 12

  • Khodabandeh A (2021) Single-station PPP-RTK: correction latency and ambiguity resolution performance. J Geod 95(4):42. https://doi.org/10.1007/s00190-021-01490-z

    Article  Google Scholar 

  • Khodabandeh A, Teunissen PJG (2015) An analytical study of PPP-RTK corrections: precision, correlation and user-impact. J Geod 89(11):1109–1132. https://doi.org/10.1007/s00190-015-0838-9

    Article  Google Scholar 

  • Klobuchar JA (1987) Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Trans Aerosp Electron Syst AES 23(3):325–331. https://doi.org/10.1109/TAES.1987.310829

    Article  Google Scholar 

  • Laurichesse D, Blot A (2015) New CNES real time products including Beidou. IGS Mail No 7183

  • Laurichesse D, Mercier F (2007) Integer ambiguity resolution on undifferenced gps phase measurements and its application to PPP, pp 839–848

  • Li X, Zhang X, Ge M (2011) Regional reference network augmented precise point positioning for instantaneous ambiguity resolution. J Geod 85(3):151–158. https://doi.org/10.1007/s00190-010-0424-0

    Article  Google Scholar 

  • Li Z, Yuan Y, Wang N, Hernandez-Pajares M, Huo X (2015) SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions. J Geod 89(4):331–345. https://doi.org/10.1007/s00190-014-0778-9

    Article  Google Scholar 

  • Loyer S, Perosanz F, Mercier F, Capdeville H, Marty J-C (2012) Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center. J Geod 86(11):991–1003. https://doi.org/10.1007/s00190-012-0559-2

    Article  Google Scholar 

  • Melbourne W (1985) The case for ranging in GPS-based geodetic systems. In: Proceedings of 1st international symposium on precise positioning with GPS, pp 373–386

  • Mervart L, Beutler G, Rothacher M, Wild U (1994) Ambiguity resolution strategies using the results of the International GPS Geodynamics Service (IGS). Bull Géod 68(1):29–38. https://doi.org/10.1007/BF00806750

    Article  Google Scholar 

  • Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen PJ (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. J Geodesy 90(1):15–44

    Article  Google Scholar 

  • Raquet J, Lachapelle G, Fortes LPS (1998) Use of a covariance analysis technique for predicting performance of regional area differential code and carrier-phase, pp 1345–1354

  • Saastamoinen J (1972) Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. In: The use of artificial satellites for geodesy. American Geophysical Union (AGU), pp 247–251

  • Shi J, Gao Y (2014) A comparison of three PPP integer ambiguity resolution methods. GPS Solut 18(4):519–528. https://doi.org/10.1007/s10291-013-0348-2

    Article  Google Scholar 

  • Shi C, Gu S, Lou Y, Ge M (2012) An improved approach to model ionospheric delays for single-frequency Precise Point Positioning. Adv Space Res 49(12):1698–1708. https://doi.org/10.1016/j.asr.2012.03.016

    Article  Google Scholar 

  • Shu Y, Shi Y, Xu P, Niu X, Liu J (2017) Error analysis of high-rate GNSS precise point positioning for seismic wave measurement. Adv Space Res 59(11):2691–2713. https://doi.org/10.1016/j.asr.2017.02.006

    Article  Google Scholar 

  • Teunissen P (1985) Zero order design: generalized inverses, adjustment, the datum problem and s-transformations. In: Grafarend EW, Sansò F (eds) Optimization and design of geodetic networks. Springer, Berlin, pp 11–55

    Chapter  Google Scholar 

  • Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP-RTK methods. J Geod 89(3):217–240

    Article  Google Scholar 

  • Teunissen P, Joosten P, Tiberius CCJM (1999) Geometry-free ambiguity success rates in case of partial fixing. In: Proceedings of ION-NTM 1999

  • Teunissen PJ, Odijk D, Zhang B (2010) PPP-RTK: results of CORS network-based PPP with integer ambiguity resolution. J Aeronaut Astronaut Aviat Ser A 42(4):223–230

    Google Scholar 

  • Wabbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks, pp 2584–2594

  • Wang J, Huang G, Yang Y, Zhang Q, Gao Y, Xiao G (2019) FCB estimation with three different PPP models: equivalence analysis and experiment tests. GPS Solut 23(4):93. https://doi.org/10.1007/s10291-019-0887-2

    Article  Google Scholar 

  • Wanninger L (1995) Improved ambiguity resolution by regional differential modelling of the ionosphere, pp 55–62

  • Wübbena G, Bagge A, Seeber G, Böder V, Hankemeier P (1996) Reducing distance dependent errors for real-time precise DGPS applications by establishing reference station networks. In: PROCEEDINGS OF ION GPS. Institute of Navigation, pp 1845–1852

  • Wubbena G (1985) Software developments for geodetic positioning with GPS using TI 4100 code and carrier measurements. In: Proceedings 1st international symposium on precise positioning with the global positioning system. US Department of Commerce, pp 403–412

  • Xiang Y, Gao Y (2017) Improving DCB estimation using uncombined PPP. NAVIG J Inst Navig 64(4):463–473. https://doi.org/10.1002/navi.207

    Article  Google Scholar 

  • Xu P, Shi C, Liu J (2012) Integer estimation methods for GPS ambiguity resolution: an applications oriented review and improvement. Surv Rev 44(324):59–71. https://doi.org/10.1179/1752270611Y.0000000004

    Article  Google Scholar 

  • Xu P, Shi C, Fang R, Liu J, Niu X, Zhang Q, Yanagidani T (2013) High-rate precise point positioning (PPP) to measure seismic wave motions: an experimental comparison of GPS PPP with inertial measurement units. J Geod 87(4):361–372. https://doi.org/10.1007/s00190-012-0606-z

    Article  Google Scholar 

  • Yao YB, He CY, Zhang B, Xu CQ (2013) A new global zenith tropospheric delay model GZTD. Chin J Geophys 56(7):2218–2227. https://doi.org/10.6038/cjg20130709

    Article  Google Scholar 

  • Yao Y, Hu Y, Yu C, Zhang B, Guo J (2016) An improved global zenith tropospheric delay model GZTD2 considering diurnal variations. Nonlinear Process Geophys 23(3):127–136. https://doi.org/10.5194/npg-23-127-2016

    Article  Google Scholar 

  • Yigit CO, Gurlek E (2017) Experimental testing of high-rate GNSS precise point positioning (PPP) method for detecting dynamic vertical displacement response of engineering structures. Geomat Nat Haz Risk 8(2):893–904. https://doi.org/10.1080/19475705.2017.1284160

    Article  Google Scholar 

  • Zhang B, Teunissen PJG, Odijk D (2011) A novel un-differenced PPP-RTK concept. J Navig 64(S1):S180–S191. https://doi.org/10.1017/S0373463311000361

    Article  Google Scholar 

  • Zhang B, Ou J, Yuan Y, Li Z (2012) Extraction of line-of-sight ionospheric observables from GPS data using precise point positioning. Sci China Earth Sci 55(11):1919–1928

    Article  Google Scholar 

  • Zhang X, He X, Liu W (2017) Characteristics of systematic errors in the BDS Hatch–Melbourne–Wübbena combination and its influence on wide-lane ambiguity resolution. GPS Solut 21(1):265–277. https://doi.org/10.1007/s10291-016-0520-6

    Article  Google Scholar 

  • Zhang B, Chen Y, Yuan Y (2019) PPP-RTK based on undifferenced and uncombined observations: theoretical and practical aspects. J Geod 93(7):1011–1024. https://doi.org/10.1007/s00190-018-1220-5

    Article  Google Scholar 

  • Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102(B3):5005–5017. https://doi.org/10.1029/96JB03860

    Article  Google Scholar 

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Acknowledgements

The authors wish to acknowledge the financial supports from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Centre National d’Etudes Spatiales (GFZ) for providing open access real-time orbit/clock and ionosphere corrections products, and the International GNSS Service (IGS) for providing the public access GNSS observation data.

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ZL designed the research, processed and analyzed the data and prepared the paper draft; YG supervised the research and revised the manuscript.

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Correspondence to Zhitao Lyu.

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Lyu, Z., Gao, Y. PPP-RTK with augmentation from a single reference station. J Geod 96, 40 (2022). https://doi.org/10.1007/s00190-022-01627-8

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