Skip to main content
Log in

On the optimal height of ionospheric shell for single-site TEC estimation

  • Original Article
  • Published:
GPS Solutions Aims and scope Submit manuscript

Abstract

The ionospheric shell height has an impact on the estimated differential code bias (DCB) and total electron content (TEC) obtained by global navigation satellite system (GNSS) data, especially for a single site. However, the shell height is generally considered as a fixed value. Based on data from the international GNSS service (IGS), we propose the concept of optimal ionospheric shell height, which minimizes |ΔDCB| when compared to the DCB provided by Center for Orbit Determination in Europe (CODE). Based on the data from five IGS stations at high, middle, and low latitudes during the time 2003–2013, we investigate the variation in the optimal ionospheric shell height and its relation with the solar activity. Results indicate that the relation between the mean of the optimal ionospheric shell height and the latitude is N-shaped. At the three stations at midlatitude, the mean value almost increases linearly with the latitude. The optimal ionospheric shell heights show 11-year and 1-year periods. The influences of the solar activity are related to the means of the optimal ionospheric shell height during the time 2003–2013. The slope of the linear fitting decreases with the mean value. Using the data from 2003 to 2013, we estimate the daily optimal ionospheric shell heights for 2014 by using the Fourier fitting method and then calculate the daily average of ΔDCB of the observed satellites by comparing to CODE results. The statistical results of the daily average in 2014 show that the optimal ionospheric shell height is much better than the fixed one. From the high-latitude station to the low-latitude station, the improvements in the mean value are about 75, 92, 96, 50, and 88% and the root-mean-squares are reduced by about 0.16, 2.09, 2.01, 1.01, and 0.02 TECu, respectively.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Alizadeh MM, Schuh H, Todorova S, Schmidt M (2011) Global ionosphere maps of VTEC from GNSS, satellite altimetry, and Formosat-3/COSMIC data. J Geod 85(12):975–987

    Article  Google Scholar 

  • Anghel A, Carrano C, Komjathy A, Astilean A, Leita T (2009) Kalman filter-based algorithms for monitoring the ionosphere and plasmasphere with GPS in near real-time. J Atmos Sol Terr Phys 71(1):158–174

    Article  Google Scholar 

  • Arikan F, Nayir H, Sezen U, Arikan O (2008) Estimation of single station interfrequency receiver bias using GPS-TEC. Radio Sci 43(4):RS4004. https://doi.org/10.1029/2007RS003785

    Article  Google Scholar 

  • Birch MJ, Hargreaves JK, Bailey GJ (2002) On the use of an effective ionospheric height in electron content measurement by GPS reception. Radio Sci 37(1):1015. https://doi.org/10.1029/2000RS002601

    Article  Google Scholar 

  • Brunini C, Camilion E, Azpilicueta F (2011) Simulation study of the influence of the ionospheric layer height in the thin layer ionospheric model. J Geod 85(9):637–645

    Article  Google Scholar 

  • Carrano C, Anghel A, Quinn R, Groves K (2009) Kalman filter estimation of plasmaspheric total electron content using GPS. Radio Sci 44(1):RS0A10. https://doi.org/10.1029/2008RS004070

    Google Scholar 

  • Chen P, Yao Y, Yao W (2017) Global ionosphere maps based on GNSS, satellite altimetry, radio occultation and DORIS. GPS Solut 21(2):639–650

    Article  Google Scholar 

  • Ciraolo L, Azpilicueta F, Brunini C, Meza A, Radicela SM (2007) Calibration errors on experimental slant total electron content determined with GPS. J Geod 81(2):111–120. https://doi.org/10.1007/s00190-006-0093-1

    Article  Google Scholar 

  • Coco DS, Coker C, Dahlke SR, Clynch JR (1991) Variability of GPS satellite differential group delay biases. IEEE Tran Aerosp Electron Syst 27(6):931–938. https://doi.org/10.1109/7.104264

    Article  Google Scholar 

  • Coster A, Williams J, Weatherwax A, Rideout W, Herne D (2013) Accuracy of GPS total electron content: GPS receiver bias temperature dependence. Radio Sci 48(2):190–196. https://doi.org/10.1002/rds.20011

    Article  Google Scholar 

  • Davies K (1990) Ionospheric radio. Peter Peregrinus Ltd, London, pp 70–73

    Book  Google Scholar 

  • Dyrud L, Jovancevic A, Brown A, Wilson D, Ganguly S (2008) Ionospheric measurement with GPS: receiver techniques and methods. Radio Sci 43(6):RS6002. https://doi.org/10.1029/2007rs003770

    Article  Google Scholar 

  • Horvath I, Crozier S (2007) Software developed for obtaining GPS-derived total electron content values. Radio Sci 42(2):RS2002

    Article  Google Scholar 

  • Huang Z, Yuan H (2014) Ionospheric single-station TEC short-term forecast using RBF neural network. Radio Sci 49(4):283–292

    Article  Google Scholar 

  • Iijima BA, Harris IL, Ho CM, Lindqwister UJ, Mannucci AJ, Pi X, Reyes MJ, Sparks LC, Wilson BD (1999) Automated daily process for global ionospheric total electron content maps and satellite ocean ionospheric calibration based on Global Positioning System. J Atmos Solar Terr Phys 61(16):1205–1218

    Article  Google Scholar 

  • Kao S, Tu Y, Chen W, Weng D, Ji S (2013) Factors affecting the estimation of GPS receiver instrumental bias. Surv Rev 45(328):59–67

    Article  Google Scholar 

  • Komjathy A, Langley RB (1996) The effect of shell height on high precision ionospheric modelling using GPS. In: Proceedings of the international GPS service for geodynamics (IGS) workshop in Silver Spring, MD, 19–21 March 1996, pp 193–203

  • Lanyi GE, Roth T (1988) A comparison of mapped and measured total ionospheric electron content using Global Positioning System and beacon satellite observations. Radio Sci 23(4):483–492

    Article  Google Scholar 

  • Li Z, Yuan Y, Li H, Ou J, Huo X (2012) Two-step method for the determination of the differential code biases of COMPASS satellites. J Geod 86(11):1059–1076. https://doi.org/10.1007/s00190-012-0565-4

    Article  Google Scholar 

  • Li M, Yuan Y, Wang N, Li Z, Li Y, Huo X (2017a) Estimation and analysis of Galileo differential code biases. J Geod 91(3):279–293

    Article  Google Scholar 

  • Li M, Yuan Y, Zhang B, Wang N, Li Z, Liu X, Zhang X (2017b) Determination of the optimized single-layer ionospheric height for electron content measurements over China. J Geod. https://doi.org/10.1007/s00190-017-1054-6

    Google Scholar 

  • Lomb NR (1976) Least-squares frequency analysis of unequally spaced data. Astrophys Space Sci 39(2):447–462

    Article  Google Scholar 

  • Lu W, Ma G, Wang X, Wan Q, Li J (2017) Evaluation of ionospheric height assumption for single station GPS-TEC derivation. Adv Space Res 60(2):286–294

    Article  Google Scholar 

  • Ma G, Maruyama T (2003) Derivation of TEC and estimation of instrumental biases from GEONET in Japan. Ann Geophys 21(10):2083–2093

    Article  Google Scholar 

  • Ma XF, Maruyama T, Ma G, Takeda T (2005) Determination of GPS receiver differential biases by neural network parameter estimation method. Radio Sci 40(1):RS1002. https://doi.org/10.1029/2004RS003072

    Article  Google Scholar 

  • Mannucci AJ, Wilson BD, Yuan DN, Ho CH, Lindqwister UJ, Runge TF (1998) A global mapping technique for GPS-derived ionospheric total electron content measurements. Radio Sci 33(3):565–583

    Article  Google Scholar 

  • Niranjan K, Srivani B, Gopikrishna B, Rama Rao PVS (2007) Spatial distribution of ionization in the equatorial and low-latitude ionosphere of the Indian sector and its effect on the pierce point altitude for GPS applications during low solar activity periods. J Geophys Res. https://doi.org/10.1029/2006JA011989

    Google Scholar 

  • Rao PVS, Niranjan K (2006) Prasad DSVVD, Krishna SG, Uma G (2006) On the validity of the ionospheric pierce point (IPP) altitude of 350 km in the Indian equatorial and low-latitude sector. Ann Geophys 24(8):2159–2168

    Article  Google Scholar 

  • Sardón E, Zarraoa N (1997) Estimation of total electron content using GPS data: how stable are the differential satellite and receiver instrumental biases? Radio Sci 32(5):1899–1910. https://doi.org/10.1029/97RS01457

    Article  Google Scholar 

  • Sardón E, Rius A, Zarraoa N (1994) Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from global positioning system observations. Radio Sci 29(3):577–586

    Article  Google Scholar 

  • Scargle JD (1982) Studies in astronomical time series analysis. II-Statistical aspects of spectral analysis of unevenly spaced data. Astrophys J 263:835–853

    Article  Google Scholar 

  • Schaer S, Beutler G, Mervart L, Rothacher M, Wild U (1995) Global and regional ionosphere models using the GPS double difference phase observable. In: Proceedings of the IGS workshop on special topics and new directions, Potsdam, Germany, May 15–17, pp 77–92

  • Sekido M, Kondo T, Kawai E, Imae M (2003) Evaluation of GPS-based Ionospheric TEC Map by Comparing with VLBI Data. Radio Sci 38(4):1069. https://doi.org/10.1029/2000RS002620

    Article  Google Scholar 

  • Shukla AK, Das S, Nagori N, Sivaraman MR, Bandyopadhyay K (2009) Two-shell ionospheric model for Indian region: a novel approach. IEEE Trans Geosci Remote Sens 47(8):2407–2412

    Article  Google Scholar 

  • Wang N, Yuan Y, Li Z, Montenbruck O, Tan B (2016) Determination of differential code biases with multi-GNSS observations. J Geod 90(3):209–228

    Article  Google Scholar 

  • Warnant R (1997) Reliability of the TEC computed using GPS measurements—the problem of hardware biases. Acta Geod Geophys Hung 32(3–4):451–459. https://doi.org/10.1007/BF03325514

    Google Scholar 

  • Yuan Y, Ou J (2002) Differential areas for differential stations (DADS): a new method of establishing grid ionospheric model. Chin Sci Bull 47(12):1033–1036. https://doi.org/10.1007/BF02907577

    Article  Google Scholar 

  • Yuan YB, Ou JK (2004) A generalized trigonometric series function model for determining ionospheric delay. Prog Nat Sci 14(11):1010–1014

    Article  Google Scholar 

Download references

Acknowledgements

This study is based on data services provided by the IGS (International GNSS Service) and CODE (the Center for Orbit Determination in Europe). This work is supported by the National Natural Science Foundation of China (NSFC Grant 41574146 and 41774162).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chen Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, J., Zhou, C. On the optimal height of ionospheric shell for single-site TEC estimation. GPS Solut 22, 48 (2018). https://doi.org/10.1007/s10291-018-0715-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10291-018-0715-0

Keywords

Navigation