Skip to main content
SpringerLink
Log in

The effect of function-based and voxel-based tropospheric tomography techniques on the GNSS positioning accuracy

  • Original Article
  • Published:
Journal of Geodesy Aims and scope Submit manuscript

Abstract

Tropospheric wet delay, the main source of which is water vapor, is one of the major factors affecting the accuracy of positioning techniques using microwave. Tropospheric tomography is a powerful method to reconstruct the water vapor content in four-dimensional (4D) space. This paper studies the effect of using function-based and voxel-based tropospheric tomography methods on the positioning accuracy. This examination is performed on the static and kinematic positioning modes using Global Navigation Satellite Systems (GNSS) stations under different weather conditions. After validating the results of tomography methods using radiosonde observations, the tomography-based positioning solutions, including function-based and voxel-based approaches, are compared with the positions obtained using tropospheric models. The results of two GPS stations show that the accuracy increases when applying tomography approaches. The function-based tomography is able to increase the accuracy of the up component of the static and kinematic modes by about 0.42 and 0.79 cm, respectively, compared to the voxel-based method. In addition, the use of the function-based tropospheric tomography can decrease the convergence time of the kinematic Precise Point Positioning (PPP) solution.

Highlights

  • The first attempt to evaluate the efficiency of troposphere tomography in different positioning techniques including static and kinematic.

  • Comparison of the accuracy of the voxel-based and function-based tomography techniques.

  • Comparison of the effect of using tomography approaches with conventional and traditional tropospheric correction methods in increasing the accuracy of positioning.

  • Study of the effect of using voxel-based and function-based troposphere tomography and other approaches in increasing the convergence speed of kinematic positioning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability statement

All the GPS data used in this paper are publicly available in the UNAVCO data portal (https://www.unavco.org/data/gps-gnss/data-access-methods/dai2/app/dai2.html). The reanalysis data, ERA-Interim product, are released by ECMWF at https://www.ecmwf.int/.

References

  • Adavi Z, Weber R (2019) Evaluation of virtual reference station constraints for gnss tropospheric tomography in Austria region. Adv Geosci 50:39–48. https://doi.org/10.5194/adgeo-50-39-2019

    Article  Google Scholar 

  • Amerian Y, Hossainali MM, Voosoghi B (2013a) Regional improvement of IRI extracted ionospheric electron density by compactly supported base functions using GPS observations. J Atmos Sol Terr Phys 92:23–30. https://doi.org/10.1016/j.jastp.2012.09.011

    Article  Google Scholar 

  • Amerian Y, Voosoghi B, Mashhadi Hossainali M (2013b) Regional ionosphere modeling in support of IRI and wavelet using GPS observations. Acta Geophys 61(5):1246–1261. https://doi.org/10.2478/s11600-013-0121-5

    Article  Google Scholar 

  • Bender M, Stosius R, Zus F et al (2011) GNSS water vapour tomography – Expected improvements by combining GPS, GLONASS and Galileo observations. Adv Space Res 47:886–897

    Article  Google Scholar 

  • Bevis M, Businger S, Herring TA, Rocken C, Anthes RA, Ware RH (1992) GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System. Journal of Geophysical Research: Atmospheres 97(D14):15787–15801

    Article  Google Scholar 

  • Brenot H, Rohm W, Kačmařík M, Möller G, Sá A, Tondaś D, Champollion C (2020) Cross-comparison and methodological improvement in GPS tomography. Remote Sensing 12(1):30

    Article  Google Scholar 

  • Böhm 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 33(7):L07304. https://doi.org/10.1029/2005GL025546

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Böhm J, Kouba J, Schuh H (2008) Forecast Vienna Mapping Functions 1 for real-time analysis of space geodetic observations. J Geodesy 83:397–401

    Article  Google Scholar 

  • Chen G, Herring TA (1997) Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data. J Geophys Res 102(B9):20489–20502. https://doi.org/10.1029/97JB01739

    Article  Google Scholar 

  • Chen BY, Liu ZZ (2014) Voxel-optimized regional water vapor tomography and comparison with radiosonde and numerical weather model. J Geod 88:391–703. https://doi.org/10.1007/s00190-014-0715-y

    Article  Google Scholar 

  • Dach R, S Lutz, P Walser, P. Fridez (2015) Bernese GNSS Software Version 5.2. User manual, Astronomical Institute, University of Bern, Bern Open Publishing. DOI: https://doi.org/10.7892/boris.72297; ISBN: 978–3–906813–05–9.

  • Dahmen W, DeVore R, Scherer K (1980) Multi-Dimensional spline approximation. SIAM J Numer Analy 17(3):380–402

    Article  Google Scholar 

  • Davis J, Elgered G, Niell AE, Kuehn CE (1993) Ground-based measurement of gradients in the wet radio refractivity of air. Radio Sci 28:1003–1038

    Article  Google Scholar 

  • Dee DP et al (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137(656):553–597. https://doi.org/10.1002/qj.828

    Article  Google Scholar 

  • Douša J, Eliaš M (2014) An improved model for calculating tropospheric wet delay. Geophys Res Lett. https://doi.org/10.1002/2014GL060271

    Article  Google Scholar 

  • Flores A, Ruffini G, Rius A (2000) 4D tropospheric tomography using GPS slant wet delays. Ann Geophys Ger 18:223–234

    Article  Google Scholar 

  • Gao Y, Chen K (2005) Performance analysis of precise point positioning using real-time orbit and clock products. J Glob Position Syst 3:95–100

    Article  Google Scholar 

  • Gao Y (2006) GNSS solutions: Precise point positioning and its challenges. Inside GNSS November/December, 16–18.

  • Hadas T, Kaplon J, Bosy J, Sierny J, Wilgan K (2013) Near-real-time regional troposphere models for the GNSS precise point positioning technique. Meas Sci Technol 24:055003

    Article  Google Scholar 

  • Haji-Aghajany S, Voosoghi B, Yazdian A (2017) Estimation of north Tabriz fault parameters using neural networks and 3D tropospherically corrected surface displacement field. Geomat Nat Hazards Risk 8:918–932

    Article  Google Scholar 

  • Haji-Aghajany S, Amerian Y (2017) Three dimensional ray tracing technique for tropospheric water vapor tomography using GPS measurements. J Atmos Solar Terr Phys 164:81–88. https://doi.org/10.1016/j.jastp.2017.08.003

    Article  Google Scholar 

  • Haji-Aghajany S, Amerian Y (2018) Hybrid regularized GPS tropospheric sensing using 3-D Ray tracing technique. IEEE Geosci Remote Sens Lett 15:1475–1479. https://doi.org/10.1109/LGRS.2018.2853183

    Article  Google Scholar 

  • Haji-Aghajany S, Amerian Y (2020a) Atmospheric phase screen estimation for land subsidence evaluation by InSAR time series analysis in Kurdistan, Iran. J Atmos Solar-Terr Physi. https://doi.org/10.1016/j.jastp.2020.105314

    Article  Google Scholar 

  • Haji-Aghajany S, Amerian Y (2020b) Assessment of InSAR tropospheric signal correction methods. J Appl Remote Sens 14(4): 044503. https://doi.org/10.1117/1.JRS.14.044503

  • Haji-Aghajany S, Voosoghi B, Amerian Y (2019) Estimating the slip rate on the north Tabriz fault (Iran) from InSAR measurements with tropospheric correction using 3D ray tracing technique. Adv Space Res 64:2199–2208

    Article  Google Scholar 

  • Haji-Aghajany S, Amerian Y, Verhagen S, Rohm W, Ma H (2020a) an optimal troposphere tomography technique using the WRF model outputs and topography of the Area. Remote Sens 12:1442. https://doi.org/10.3390/rs12091442

    Article  Google Scholar 

  • Haji-Aghajany S, Amerian Y, Verhagen S (2020b) B-spline function-based approach for GPS tropospheric tomography. GPS Solut 24:88. https://doi.org/10.1007/s10291-020-01005-x

    Article  Google Scholar 

  • Hansen PC (1997) Rank-deficient and Discrete Ill-posed Problems. Numerical Aspects of Linear Inversion, Monographs on Mathematical Modeling and computation, Vol. 4, SIAM, Philadelphia.

  • Heroux P, Kouba J (2001) GPS precise point positioning using IGS orbit products. Phys Chem Earth 26:573–578

    Article  Google Scholar 

  • Herring TA, King RW, McClusky SC (2010) GPS Analysis at MIT, GAMIT Reference Manual, Release 10.5. (Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology, Cambridge MA, available on line at http://wwwgpsg.mit.edu/~simon/gtgk/GAMIT_Ref.pdf accessed 12 May 2015).

  • Heublein M, Alshawaf F, Ba E, Zhu X, Hinz S (2019) Compressive sensing reconstruction of 3D wet refractivity based on GNSS and InSAR observations. J Geodesy 93–2:197–217

    Article  Google Scholar 

  • Hirahara K (2000) Local GPS tropospheric tomography, earth planet. Space 52:935–939

    Google Scholar 

  • Hopfield HS (1969) Two-quartic tropospheric refractivity profile for correcting satellite data. J Geophys Res 74:4487–4499

    Article  Google Scholar 

  • Ibrahim HE, El-Rabbany A (2011) Performance analysis of NOAA tropospheric signal delay model. Meas Sci Technol 22:115107

    Article  Google Scholar 

  • Jolivet R, Agram PS, Lin NY, Simons M, Doin MP, Peltzer G, Li Z (2014) Improving InSAR geodesy using global atmospheric models. J Geophys Res Solid Earth 119:2324–2341. https://doi.org/10.1002/2013JB010588

    Article  Google Scholar 

  • Li X, Zhang X, Ge M (2011) Regional reference network augmented precise point positioning for instantaneous ambiguity resolution. J Geodesy 85:151–158

    Article  Google Scholar 

  • Lou Y, Huang J, Zhang W, Liang H, Zheng F, Liu J (2017) A New Zenith tropospheric delay grid product for real-time PPP applications over China. Sensors 18:65

    Article  Google Scholar 

  • Lu C, Zus F, Ge M, Heinkelmann R, Dick G, Wickert J, Schuh H (2016) Tropospheric delay parameters from numerical weather models for multi-GNSS precise positioning. Atmos Meas Tech 9:5965–5973

    Article  Google Scholar 

  • Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: modern insights from FES2004 Ocean Dyn, 56: 394–415, https://doi.org/10.1007/s10236-006-0086-x

  • Ma H, Verhagen S (2020) Precise point positioning on the reliable detection of tropospheric model errors. Sensors 20:1634

    Article  Google Scholar 

  • Mautz R, Ping J, Heki K, Schaffrin B, Shum CK, Potts L (2005) Efficient spatial and temporal representations of global ionosphere maps over Japan using B-spline wavelets. J Geodesy 78:660–667

    Article  Google Scholar 

  • Möller G, Landskron D (2019) Atmospheric bending effects in GNSS tomography. Atmos Meas Tech 12:23–34. https://doi.org/10.5194/amt-12-23-2019

    Article  Google Scholar 

  • Perler D, Geiger A, Hurter F (2011) 4D GPS water vapor tomography: new parameterized approaches. J Geodesy 85(8):539–550

    Article  Google Scholar 

  • Ray RD, Ponte RM (2003) Barometric tides from ECMWF operational analyses. Ann Geophys 21(8):1897–1910. https://doi.org/10.5194/angeo-21-1897-2003

    Article  Google Scholar 

  • Rohm W, Bosy J (2009) Local tomography troposphere model over mountains area. Atmos Res 93:777–783

    Article  Google Scholar 

  • Rohm W, Zhang K, Bosy J (2014) Limited constraint, robust Kalman filtering for GNSS troposphere tomography. Atmos Meas Tech 6:1475–1486

    Article  Google Scholar 

  • Saastamoinen J (1973) Contributions to the theory of atmospheric refraction. Part II: refraction corrections in satellite geodesy. Bull Geod 107:13–34

    Article  Google Scholar 

  • Sadikin R, Swardiana I and Wirahman T (2017). Cubic spline interpolation for large regular 3D grid in cylindrical coordinate: (Invited paper)," 2017 International Conference on Computer, Control, Informatics and its Applications (IC3INA), Jakarta, Indonesia, 2017, pp. 1–6 https://doi.org/10.1109/IC3INA.2017.8251730.

  • Shi J, Xu C, Guo J, Gao Y (2014) Local troposphere augmentation for real-time precise point positioning. Earth Planets Space 66:30

    Article  Google Scholar 

  • Wilgan K, Hadas T, Hordyniec P, Bosy J (2017) Real-time precise point positioning augmented with high-resolution numerical weather prediction model. GPS Solut 21(3):1341–1353

    Article  Google Scholar 

  • Yao Y, Yu C, Hu Y (2014) A new method to accelerate PPP convergence time by using a Global Zenith Troposphere delay estimate model. J Navig 67:899–910

    Article  Google Scholar 

  • Yao Y, Zhao Q (2016) Maximally using GPS observation for water vapor tomography. IEEE T Geosci Remote 54:7185–7196

    Article  Google Scholar 

  • Yu W, Chen B, Dai W, Luo X (2018) Real-time precise point positioning using tomographic wet refractivity fields. Remote Sens 10:928

    Article  Google Scholar 

  • Zhao Q, Yao Y, Yao W, Xia P (2018) An optimal tropospheric tomography approach with the support of an auxiliary area. Ann Geophys 36:1037–1046. https://doi.org/10.5194/angeo-36-1037-2018

    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 12:5005–5017

    Article  Google Scholar 

Download references

Acknowledgements

Authors would like to appreciate the UNAVCO for the GPS observations. We are also grateful to the ECMWF for publishing ERA-Interim data.

Author information

Authors and Affiliations

  1. Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Saeid Haji-Aghajany & Yazdan Amerian

  2. Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN, Delft, The Netherlands

    Saeid Haji-Aghajany & Sandra Verhagen

  3. Institute of Geodesy and Geoinformatics, Wroclaw University of Environmental and Life Sciences, Grunwaldzka 53, 50-357, Wroclaw, Poland

    Witold Rohm

  4. GFZ German Research Centre for Geosciences, 14473, Potsdam, Germany

    Harald Schuh

  5. Chair of Satellite Geodesy, Technische Universität Berlin, 10623, Berlin, Germany

    Harald Schuh

Authors
  1. Saeid Haji-Aghajany
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yazdan Amerian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sandra Verhagen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Witold Rohm
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Harald Schuh
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.H-A,Y.A and W.R conceptualized the study. S.H-A and Y.A processed data and prepared the paper draft. S.V, H.S and W.R substantially contributed to the interpretation of results and provided many useful suggestions in the internal review process. All authors were involved in result discussions throughout the development.

Corresponding author

Correspondence to Yazdan Amerian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haji-Aghajany, S., Amerian, Y., Verhagen, S. et al. The effect of function-based and voxel-based tropospheric tomography techniques on the GNSS positioning accuracy. J Geod 95, 78 (2021). https://doi.org/10.1007/s00190-021-01528-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00190-021-01528-2

Keywords

Search

Navigation