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A study of smoothed TEC precision inferred from GPS measurements


The availability of a large amount of TEC data derived from dual frequency GPS measurements observed by GPS reference networks provides a great opportunity for ionosphere studies. In order to obtain better accuracy for the derived TEC, a data smoothing technique is usually employed to take advantage of both code pseudorange and carrier phase GPS measurements. The precision of TEC data therefore is dependent on the smoothing approach. However little work has been done to evaluate the precision of the smoothed TEC data obtained from different smoothing approaches. This investigation examines the properties of two popularly used smoothing approaches and develops the closed-form formulas for estimating the precision of the smoothed TEC data. In addition, a previously proposed approximate formula for estimating TEC precision is also evaluated against its closed-form formula developed in this paper. The TEC precisions derived from the closed-form precision estimation formulas for approaches I and II are analyzed in a numerical test. The results suggest that approach II outperforms approach I and the precision of TEC data smoothed by approach II is higher than approach I. For approach I, a numerical test is also conducted to compare the precision difference between the closed-form and approximate formulas for estimating TEC precision. The comparison indicates that TEC derived from the closed-form formula have better precisions than the approximate formula. Analysis also reminds users that extra cautions should be taken when using the approximate formula in order to avoid the precision divergence phenomenon.


  • Cheng, P., Remarks on Doppler-aided smoothing of code ranges, Journal of Geodesy, 73, 23–28, 1999.

    Article  Google Scholar 

  • Hajj, G. A., R. Ibañez-Meier, E. R. Kursinski, and L. J. Romans, Imaging the ionosphere with the Global Positioning System, International Journal of Imaging Systems and Technology, 5(2), 174–184, 1994.

    Article  Google Scholar 

  • Hatch, R., Synergism of GPS code and carrier measurements, Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning, 2, 1213–1231, New Mexico State University, NM, USA, Feb. 8–12, 1982.

    Google Scholar 

  • Hatch, R., Dynamic differential GPS at the centimeter level, Proceedings of the 4th International Geodetic Symposium on Satellite Positioning, 2, 1287–1298, Austin, TX, USA, Apr. 28–May 2, 1986.

    Google Scholar 

  • Hernández-Pajares, M., J. M. Juan, and J. Sanz, New approaches in global ionospheric determination using ground GPS data, Journal of Atmospheric and Solar-Terrestrial Physics, 61, 1237–1247, 1999.

    Article  Google Scholar 

  • Hernández-Pajares, M., J. M. Juan, J. Sanz, and D. Bilitza, Combining GPS measurements and IRI model values for space weather specification, Advances in Space Research, 29(6), 949–958, 2002.

    Article  Google Scholar 

  • Jin, X. X., Theory of carrier adjusted DGPS positioning approach and some experimental results, PhD thesis, Delft University Press, Delft, 1996.

    Google Scholar 

  • Lachapelle, G., J. Hagglund, W. Falkenberg, P. Bellemare, M. Casey, and M. Eaton, GPS land kinematic positioning experiments, Proceedings of the 4th International Geodetic Symposium on Satellite Positioning, 2, 1327–1344, Austin, TX, USA, Apr. 28–May 2, 1986.

    Google Scholar 

  • Langley, R., M. Fedrizzi, E. de Paula, I. Kantor, M. Santos, and A. Komjathy, Mapping the low-latitude ionosphere with GPS, GPS World, 13(2), 41–47, 2002.

    Google Scholar 

  • Leick, A., GPS Satellite Surveying, 560 pp., John Wiley, New York, 1995.

    Google Scholar 

  • Liu, Z. Z., Ionosphere tomographic modeling and applications using Global Positioning System (GPS) measurements, Ph.D thesis, 304 pp., Department of Geomatics Engineering, The University of Calgary, Calgary, Alberta, Canada, 2004.

    Google Scholar 

  • Liu, Z. Z. and Y. Gao, Ionospheric tomography using GPS measurements, Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, 111–120, Banff, Alberta, Canada, Jun. 5–8, 2001.

    Google Scholar 

  • Liu, Z. Z., S. Skone, Y. Gao, and A. Komjathy, Ionospheric modeling using GPS data, GPS Solutions, 9(1), DOI: 10.1007/s10291-004-0129-z, 2005.

    Google Scholar 

  • Sardon, E., A. Rius, and N. Zarraoa, Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from Global Positioning System observations, Radio Science, 29, 577–586, 1994.

    Article  Google Scholar 

  • Sekido, M., T. Kondo, E. Kawai, and M. Imae, Evaluation of GPS-based ionospheric TEC map by comparing with VLBI data, Radio Science, 38(4), 1069, doi:10.1029/2000RS002620, 2003.

    Article  Google Scholar 

  • Skone, S., Wide area ionosphere grid modeling in the auroral region, Ph.D thesis, Department of Geomatics Engineering, The University of Calgary, Calgary, Alberta, Canada, 1998.

    Google Scholar 

  • Skone, S., V. Hoyle, S. Lee, and S. Poon, Variations in point positioning accuracies for single frequency GPS users during solar maximum, Geomatica, 56(2), 131–140, 2002.

    Google Scholar 

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Correspondence to Zhizhao Liu.

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Liu, Z., Gao, Y. & Skone, S. A study of smoothed TEC precision inferred from GPS measurements. Earth Planet Sp 57, 999–1007 (2005).

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Key words

  • Global Positioning System
  • total electron content
  • data smoothing
  • precision estimation