Abstract
The performance of precise point positioning real-time kinematic (PPP-RTK) is closely tied to the accuracy of atmospheric corrections, with the ionospheric delay, including its uncertainty, being of particular importance. In this study, a grid-based slant ionospheric weighted method is proposed to enhance PPP-RTK performance across diverse network scales and ionospheric activity levels. First, the receiver-specific hardware delays are precisely calibrated for the maximum utilization of ionospheric corrections retrieved in PPP-RTK networks. Then, a grid-based polynomial fitting and residual interpolation model is developed with a stochastic model considering the distribution of reference stations, the elevation of satellites, and rate of total electron content index (ROTI). Three networks situated in different latitudes with the max inter-station distance of 26.7 km, 134.2 km, and 247.9 km, respectively, were employed to verify the enhancement to PPP-RTK. The proposed method presents a significant improvement in reducing the convergence time of PPP-RTK in all three networks, with the horizontal convergence time decreased from 5 to 14 s to less than 1 s in the small- and medium-scale networks, 44–25 s in the large-scale network compared to the modified linear combination method (MLCM). Besides, a vehicular experiment on an urban loop was conducted for further validation. The positioning accuracy of the PPP-RTK vehicular solutions with the newly proposed method is 2.74, 2.28 and 5.54 cm in the east, north and up components, respectively, with an improvement of 10, 11 and 40% over MLCM. The proportion of 3D positioning accuracy less than 5 cm also increased from 50.1 to 87.8%. Moreover, during the ionospheric active period, the average positioning accuracy is increased from decimeter- to centimeter-level horizontally, and the fixing rate can be increased from 80.6 to 90.0%.
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Data availability
The GNSS precise products are available in the IGS repository (https://cddis.nasa.gov/archive/gnss/products/). The GNSS observation data of Hong Kong is approved by the Hong Kong Geodetic Survey services (ftp://ftp.geodetic.gov.hk/), while the datasets collected in Wuhan and Hebei are available on reasonable request from the corresponding author.
References
Banville S, Collins P, Zhang W, Langley RB (2014) Global and regional ionospheric corrections for faster PPP convergence. Navigation 61:115–124. https://doi.org/10.1002/navi.57
Cabinet Office (2021) Quasi-zenith satellite system interface specification centimeter level augmentation service (IS-QZSS-L6-004). https://qzss.go.jp/en/technical/download/pdf/ps-is-qzss/is-qzss-l6-004.pdf
Ciraolo L, Azpilicueta F, Brunini C, Meza A, Radicella SM (2007) Calibration errors on experimental slant total electron content (TEC) determined with GPS. J Geod 81:111–120. https://doi.org/10.1007/s00190-006-0093-1
Gao J (1997) Resolution and accuracy of terrain representation by grid DEMs at a micro-scale. Int J Geogr Inf Sci 11:199–212. https://doi.org/10.1080/136588197242464
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 82:389–399. https://doi.org/10.1007/s00190-007-0187-4
Hatch R (1983) The synergism of GPS code and carrier measurements. In: International geodetic symposium on satellite Doppler positioning, vol 2
Héroux P, Kouba J (2001) GPS precise point positioning using IGS orbit products. Phys Chem Earth (a) 26:573–578. https://doi.org/10.1016/S1464-1895(01)00103-X
Khodabandeh A (2021) Single-station PPP-RTK: correction latency and ambiguity resolution performance. J Geod 95:42. https://doi.org/10.1007/s00190-021-01490-z
Khodabandeh A, Teunissen PJG (2019) Integer estimability in GNSS networks. J Geod 93:1805–1819. https://doi.org/10.1007/s00190-019-01282-6
Kuhn HW, Tucker AW (1951) Nonlinear programming. In: Proceedings of the 2nd Berkeley symposium on mathematical statistics and probability. University of California Press, pp 481–493
Li B, Li Z, Zhang Z, Ya T (2017) ERTK: extra-wide-lane RTK of triple-frequency GNSS signals. J Geod 91:1031–1047. https://doi.org/10.1007/s00190-017-1006-1
Li X, Li X, Yuan Y, Zhang K, Zhang X, Wickert J (2018) Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geod 92:579–608. https://doi.org/10.1007/s00190-017-1081-3
Li X, Han X, Li X, Liu G, Feng G, Wang B, Zheng H (2021a) GREAT-UPD: an open-source software for uncalibrated phase delay estimation based on multi-GNSS and multi-frequency observations. GPS Solut 25:66. https://doi.org/10.1007/s10291-020-01070-2
Li X, Huang J, Li X, Lyu H, Wang B, Xiong Y, Xie W (2021b) Multi-constellation GNSS PPP instantaneous ambiguity resolution with precise atmospheric corrections augmentation. GPS Solut 25:107. https://doi.org/10.1007/s10291-021-01123-0
Li P, Cui B, Hu J, Liu X, Zhang X, Ge M, Schuh H (2022) PPP-RTK considering the ionosphere uncertainty with cross-validation. Satell Navig 3:10. https://doi.org/10.1186/s43020-022-00071-5
Liu M, Yin X, Xiang M (2023) Improved PPP-RTK positioning performance by using the elevation-dependent weighting model for the atmospheric delay corrections. Meas Sci Technol 34:055003. https://doi.org/10.1088/1361-6501/acb168
Lyu S, Xiang Y, Zhang Y, Yang H, Pei L, Yu W, Turong T-K (2023) A consistent and grid-based regional slant ionospheric model with an increasing number of satellite corrections for PPP-RTK. GPS Solut 27:97. https://doi.org/10.1007/s10291-023-01439-z
Malys S, Jensen PA (1990) Geodetic point positioning with GPS carrier beat phase data from the CASA UNO Experiment. Geophys Res Lett 17:651–654. https://doi.org/10.1029/GL017i005p00651
Marques HAS, Monico JFG, Marques HA (2016) Performance of the L2C civil GPS signal under various ionospheric scintillation effects. GPS Solut 20:139–149. https://doi.org/10.1007/s10291-015-0472-2
Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. NCG, Nederlandse Commissie Voor Geodesie, Delft
Pi X, Mannucci AJ, Lindqwister UJ, Ho CM (1997) Monitoring of global ionospheric irregularities using the worldwide GPS network. Geophys Res Lett 24:2283–2286. https://doi.org/10.1029/97GL02273
Psychas D, Verhagen S (2020) Real-time PPP-RTK performance analysis using ionospheric corrections from multi-scale network configurations. Sensors 2020(20):3012. https://doi.org/10.3390/s20113012
Psychas D, Khodabandeh A, Teunissen PJG (2022) Impact and mitigation of neglecting PPP-RTK correctional uncertainty. GPS Solut 26:33. https://doi.org/10.1007/s10291-021-01214-y
Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42:59–66. https://doi.org/10.2307/2685263
Rovira-Garcia A, Juan JM, Sanz J, Gonzalez-Casado G (2015) A worldwide ionospheric model for fast precise point positioning. IEEE Trans Geosci Remote Sens 53:4596–4604. https://doi.org/10.1109/TGRS.2015.2402598
Takasu T, Yasuda A (2010) Kalman-filter-based integer ambiguity resolution strategy for long-baseline RTK with ionosphere and troposphere estimation. In: Proc. ION GNSS 2010, Institute of Navigation, Portland, OR, September, pp 161–171
Teunissen PJG (2000) Adjustment theory: an introduction. Delft University Press
Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP-RTK methods. J Geod 89:217–240. https://doi.org/10.1007/s00190-014-0771-3
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):223–229
Teunissen PJG, Joosten P, Tiberius CCJM (1999) Geometry-free ambiguity success rates in case of partial fixing. In: Proc. ION NTM 1999, Institute of Navigation, San Diego, CA, January, pp 201–207
Wang S, Li B, Gao Y, Gao Y, Guo H (2020) A comprehensive assessment of interpolation methods for regional augmented PPP using reference networks with different scales and terrains. Measurement 150:107067. https://doi.org/10.1016/j.measurement.2019.107067
Wielgosz P, Kashani I, Grejner-Brzezinska D (2005) Analysis of long-range network RTK during a severe ionospheric storm. J Geod 79:524–531. https://doi.org/10.1007/s00190-005-0003-y
Wübbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks. In: Proc. ION GNSS 2005, Institute of Navigation, Long Beach, CA, September 2005, pp 2584–2594
Yin X, Chai H, El-Mowafy A, Zhang Y, Zhang Y, Du Z (2022) Modeling and assessment of atmospheric delay for GPS/Galileo/BDS PPP-RTK in regional-scale. Measurement 194:111043. https://doi.org/10.1016/j.measurement.2022.111043
Yu S, Liu Z (2021) The ionospheric condition and GPS positioning performance during the 2013 tropical cyclone Usagi event in the Hong Kong region. Earth Planets Space 73:66. https://doi.org/10.1186/s40623-021-01388-2
Zha J, Zhang B, Liu T, Hou P (2021) Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results. GPS Solut 25:135. https://doi.org/10.1007/s10291-021-01169-0
Zhang B, Teunissen PJG, Odijk D (2011) A novel un-differenced PPP-RTK concept. J Navig 64:S180–S191. https://doi.org/10.1017/S0373463311000361
Zhang X, Guo F, Zhou P (2014) Improved precise point positioning in the presence of ionospheric scintillation. GPS Solut 18:51–60. https://doi.org/10.1007/s10291-012-0309-1
Zhang B, Hou P, Odolinski R (2022a) PPP-RTK: from common-view to all-in-view GNSS networks. J Geod 96:102. https://doi.org/10.1007/s00190-022-01693-y
Zhang X, Ren X, Chen J, Zuo X, Mei D, Liu W (2022b) Investigating GNSS PPP–RTK with external ionospheric constraints. Satell Navig 3:6. https://doi.org/10.1186/s43020-022-00067-1
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 102:5005–5017. https://doi.org/10.1029/96JB03860
Acknowledgments
This work has been supported by the National Natural Science Foundation of China (No. 42204017), the National Postdoctoral Program for Innovative Talents, China (No. BX20220239), the Fundamental Research Funds for the Central Universities (2042022kf1001), and the China Postdoctoral Science Foundation (No. 2022M712443). The algorithm implementation is based on the GNSS+ REsearch, Application and Teaching (GREAT) software developed by the GREAT Group, School of Geodesy and Geomatics, Wuhan University. The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
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Junjie Han and Xingxing Li provided the initial idea and designed the experiments for this study; Junjie Han, Xingxing Li and Xin Li analyzed the data and wrote the manuscript; Jiaxin Huang, Zhiheng Shen and Zongzhou Wu helped with the writing. All authors reviewed the manuscript.
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Li, X., Han, J., Li, X. et al. A grid-based ionospheric weighted method for PPP-RTK with diverse network scales and ionospheric activity levels. GPS Solut 27, 191 (2023). https://doi.org/10.1007/s10291-023-01522-5
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DOI: https://doi.org/10.1007/s10291-023-01522-5