Abstract
PPP–RTK, a synthesis of precise point positioning (PPP) and real-time kinematic (RTK) techniques, achieves fast integer ambiguity resolution-enabled positioning using, among others, satellite clocks, biases, and ionospheric corrections generated in a reference network. When formulating a network model to estimate these products, one usually considers a receiver as the pivot and selects its receiver-related parameters as the datum to address the rank deficiency problem. This work demonstrates that the precision of ambiguity-float combined PPP–RTK products relates to the pivot receiver selection. The combined product encompasses the summation of satellite clocks, satellite phase biases, and ionospheric delays at a certain station. Specifically, we find that the precision of ambiguity-float combined products at the pivot receiver surpasses that at non-pivot receivers by a significant margin. Consequently, user positioning becomes inhomogeneous in the network, as users far away from the pivot receiver perform worse than those close to the pivot receiver. To relieve this pivot receiver dependency, we emphasize the necessity of network integer ambiguity resolution, which improves the precision of products and ensures the homogeneity of user positioning. For verification purposes, we performed a one-week experiment involving 12 global positioning system (GPS) receivers to generate network products and 23 receivers to perform user positioning. The results showed that the precision of ambiguity-float combined products at the pivot receiver was better than 2 cm, whereas that at non-pivot receivers reached several decimeters. With these ambiguity-float products employed on the user side, the time-to-first-fix (TTFF) of the positioning near the pivot receiver was less than 5 epochs, but that away from the pivot receiver exceeded 15 epochs. Network integer ambiguity resolution improved the quality of PPP–RTK products, as the precision of combined products at an arbitrary receiver reached several millimeters. User positioning with ambiguity-fixed products became homogeneous with an average three-dimensional root-mean-square (3D RMS) of 1.5 cm, and the mean TTFF decreased to 4 epochs.
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Data availability
The data used in this study are available from the National Geodetic Survey (NGS) network (https://geodesy.noaa.gov/CORS/).
References
Baarda W (1973) S-transformations and criterion matrices. In: Publications on geodesy, 18, vol 5, no 1. Netherlands Geodetic Commission, Delft
Banville S et al (2021) Enabling ambiguity resolution in CSRS–PPP. Navig J Inst Navig 68(2):433–451. https://doi.org/10.1002/navi.423
Collins P, Bisnath S, Lahaye F, Héroux P (2010) Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. Navigation 57(2):123–135. https://doi.org/10.1002/j.2161-4296.2010.tb01772.x
Demyanov VV, Yasyukevich YV (2021) Space weather: risk factors for global navigation satellite systems. Sol Terr Phys 7(2):28–47. https://doi.org/10.12737/stp-72202104
Ge M, Gendt G, Ma R, 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
Geng J, Zhang Q, Li G, Liu J, Liu D (2022) Observable-specific phase biases of Wuhan multi-GNSS experiment analysis center’s rapid satellite products. Satel Navig 3(1):1–15
Hou P, Zhang B, Yasyukevich YV, Liu T, Zha J (2022) Multi-frequency phase-only PPP–RTK model applied to BeiDou data. GPS Solut 26(3):1–14. https://doi.org/10.1007/s10291-022-01263-x
Hu J, Zhang X, Li P, Ma F, Pan L (2020) Multi-GNSS fractional cycle bias products generation for GNSS ambiguity-fixed PPP at Wuhan University. GPS Solut 24(1):1–13. https://doi.org/10.1007/s10291-019-0929-9
Khodabandeh A (2021) Single-station PPP-RTK: correction latency and ambiguity resolution performance. J Geod 95(4):1–24. https://doi.org/10.1007/s00190-021-01490-z
Khodabandeh A, Teunissen P (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
Khodabandeh A, Teunissen P (2018) On the impact of GNSS ambiguity resolution: geometry, ionosphere, time and biases. J Geodesy 92(6):637–658. https://doi.org/10.1007/s00190-017-1084-0
Khodabandeh A, Teunissen PJG (2019) Integer estimability in GNSS networks. J Geod 93:1805–1819. https://doi.org/10.1007/s00190-019-01282-6
Koch K-R (1999) Parameter estimation and hypothesis testing in linear models. Springer, Berlin
Lannes A, Prieur J-L (2013) Calibration of the clock-phase biases of GNSS networks: the closure-ambiguity approach. J Geod 87(8):709–731. https://doi.org/10.1007/s00190-013-0641-4
Laurichesse D, Mercier F, Berthias JP, Broca P, Cerri L (2009) Integer ambiguity resolution on undifferenced gps phase measurements and its application to PPP and satellite precise orbit determination. Navigation 56(2):135–149. https://doi.org/10.1002/j.2161-4296.2009.tb01750.x
Naciri N, Bisnath S (2021) An uncombined triple-frequency user implementation of the decoupled clock model for PPP-AR. J Geod 95(5):60. https://doi.org/10.1007/s00190-021-01510-y
Odijk D, Teunissen PJ, Zhang B (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, Teunissen PJG, Khodabandeh A (2014) Single-frequency PPP–RTK: theory and experimental results. Earth on the edge: science for a sustainable planet. Springer, pp 571–578
Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen PJG (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP–RTK user models by means of S-system theory. J Geod 90(1):15–44. https://doi.org/10.1007/s00190-015-0854-9
Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. In: Publications on geodesy, 52, Netherlands Geodetic Commission, Delft
Odolinski R, Teunissen PJG, Odijk D (2015) Combined GPS + BDS for short to long baseline RTK positioning. Meas Sci Technol 26(4):045801. https://doi.org/10.1088/0957-0233/26/4/045801
Psychas D, Verhagen S, Liu X, Memarzadeh Y, Visser H (2018) Assessment of ionospheric corrections for PPP–RTK using regional ionosphere modelling. Meas Sci Technol 30(1):014001. https://doi.org/10.1088/1361-6501/aaefe5
Psychas D, Verhagen S, Teunissen P (2020) Precision analysis of partial ambiguity resolution-enabled PPP using multi-GNSS and multi-frequency signals. Adv Space Res 66(9):2075–2093
Psychas D, Khodabandeh A, Teunissen PJG (2022) Impact and mitigation of neglecting PPP–RTK correctional uncertainty. GPS Solut 26(1):1–15. https://doi.org/10.1007/s10291-021-01214-y
Schaer S, Villiger A, Arnold D, Dach R, Prange L, Jäggi A (2021) The CODE ambiguity-fixed clock and phase bias analysis products: generation, properties, and performance. J Geod 95:1–25
Schönemann E, Becker M, Springer T (2011) A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. J Geod Sci 1(3):204–214. https://doi.org/10.2478/v10156-010-0023-2
Teunissen PJG (1985) Generalized inverses, adjustment, the datum problem and S-transformations. In: Grafarend EW, Sanso F (eds) Optimization of geodetic networks. Springer, Berlin
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1):65–82
Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593. https://doi.org/10.1007/s001900050269
Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP–RTK methods. J Geod 89(3):217–240. https://doi.org/10.1007/s00190-014-0771-3
Teunissen PJG, Montenbruck O (2017) Springer handbook of global navigation satellite systems. Springer, Berlin
Teunissen PJG, 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
Verhagen S, Teunissen PJG (2013) The ratio test for future GNSS ambiguity resolution. GPS solutions 17(4):535–548. https://doi.org/10.1007/s10291-012-0299-z
Wübbena G, Schmitz M, Bagge A (2005) PPP–RTK: precise point positioning using state-space representation in RTK networks. In: Paper presented at the proceedings of ION GNSS 2005. The Institute of Navigation, Long Beach, pp 13–16
Zha J, Zhang B, Liu T, Hou P (2021) Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results. GPS Solutions. 25(4):1-12. https://doi.org/10.1007/s10291-021-01169-0
Zhang B, Teunissen PJ, Odijk D (2011) A novel un-differenced PPP–RTK concept. J Navig 64(S1):S180–S191. https://doi.org/10.1017/S0373463311000361
Zhang B, Hou P, Zha J, Liu T (2021) Integer-estimable FDMA model as an enabler of GLONASS PPP–RTK. J Geod 95(8):1–21. https://doi.org/10.1007/s00190-021-01546-0
Zhang B, Hou P, Zha J, Liu T (2022) PPP–RTK functional models formulated with undifferenced and uncombined GNSS observations. Satel Navig 3(1):1–15. https://doi.org/10.1186/s43020-022-00064-4
Acknowledgements
The authors would like to thank Prof. Peter Teunissen, Dr. Amir Khodabandeh, and two anonymous reviewers for their insightful and constructive comments. Yu.Yasyukevich acknowledges the Ministry of Science and Higher Education of the Russian Federation. This work was funded by the National Natural Science Foundation of China (Grant No. 42022025). The corresponding author is supported by the CAS Pioneer Hundred Talents Program.
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BZ initiated the idea, designed the research, and revised the manuscript. PH processed the data, analyzed the results, and drafted the manuscript. YVY revised the manuscript and provided suggestions for improvements.
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Hou, P., Zhang, B. & Yasyukevich, Y.V. Homogeneous PPP–RTK user positioning performance as a consequence of network integer ambiguity resolution. GPS Solut 28, 60 (2024). https://doi.org/10.1007/s10291-023-01600-8
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DOI: https://doi.org/10.1007/s10291-023-01600-8