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Effect of stochastic ionospheric delay modeling for GPS ambiguity resolution


The network-derived ionospheric delay can improve the fast and accurate determination of the long baseline in both the rapid-static and kinematic Global Positioning System (GPS) positioning mode. In this study, an interpolation of the undifferenced (UD) ionospheric delays is performed on a satellite-by-satellite and epoch-by-epoch basis, respectively, using the least-squares collocation (LSC) to provide not only ionospheric delays but also their variances. The developed method retains the simplicity of the two-dimensional (2-D) model, but it does not introduce errors due to the thin-shell assumption made in the single-layered model. Our method also provides flexibility in forming the predicted double-differenced (DD) ionospheric delays. Faster and more reliable positioning solutions can be obtained when the developed method is used to predict DD ionospheric delays. The numerical test applying the method to the Ohio Continuously Operating Reference Station network shows a 23% improvement in mean time-to-fix with the network-derived ionospheric delays.


  • Blanch, J., T. Walter, and P. Enge, Ionospheric estimation using extended Kriging for low latitude SBAS, ION GNSS17th International Technical Meeting of the Satellite Division, Long Beach, CA, pp. 387–391, 21–24 Sept., 2004.

    Google Scholar 

  • Cannon, M. E., G. Lachapelle, P. Alves, L. P. Fortes, and B. Townsend, GPS RTK positioning using a regional reference network, theory and results, Proceedings of the 5th GNSS International Symposium, Seville, 8-11 May, 2001.

    Google Scholar 

  • Grejner-Brzezinska, D. A., P. Wielgosz, I. Kashani, D. A. Smith, P. S. J. Spencer, D. S. Robertson, and G. L. Mader, An analysis of the effects of different network-based ionosphere estimation models on rover positioning accuracy, J. Global Position. Systems, 3(1–2), 115–131, 2004.

    Article  Google Scholar 

  • Grejner-Brzezinska, D. A., P. Wielgosz, and I. Kashani, Performance assessment of the new rapid-static module of the online positioning user service-OPUS-RS, Proceedings of the 18th ION GNSS International Technical Meeting of the Satellite Division, Long Beach, CA, pp. 2595–2605, 2005.

    Google Scholar 

  • Hong, C.-K., D. A. Grejner-Brzezinska, and J. H. Kwon, Efficient GPS receiver DCB estimation for ionosphere modeling using satellite-receiver geometry changes, Earth Planets Space, 60(11), e25–e28, 2008.

    Article  Google Scholar 

  • Moritz, H., Advanced Physical Geodesy (reprint), Dept. of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, OH, USA, 2001.

    Google Scholar 

  • Odijk, D., Weighting ionospheric corrections to improve fast GPS positioning over medium distances, Proceedings of ION GPS, Sept. 19-12, Salt Lake City, UT, pp. 1113–1123, 2000.

    Google Scholar 

  • Odijk, D., H. Marel, and I. Song, Precise GPS positioning by applying ionospheric corrections from an active control network, GPS Solutions, 3, 49–57, 2000.

    Article  Google Scholar 

  • Orus, R., M. Hernandez-Pajares, J. M. Juan, and J. Sanz, Improvement of global ionospheric VTEC maps by using the kriging interpolation technique, J. Atmos. Sol-Terr. Phys., 67, 1598–1609, 2005.

    Article  Google Scholar 

  • Serpas, J. G., Local and regional geoid determination from vector airborne gravimetry, OSU Report No. 468, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, USA, 2003.

    Google Scholar 

  • Shaer, S., Mapping and predicting the Earth’s ionosphere using global positioning system, PhD dissertation, Astronomical Institute, University of berne, Switzerland, 205 pp., 1999.

    Google Scholar 

  • Spencer, P. S. J., D. S. Robertson, and G. L. Mader, Ionospheric data assimilation methods for geodetic applications, Proceedings of the IEEE PLANS, Monterey, California, pp. 510–517, 2004.

    Google Scholar 

  • Teunissen, P. J. G., A new method for fast carrier phase ambiguity estimation, Proceedings of the IEEE PLANS, pp. 562–573, 1994.

    Google Scholar 

  • Wang, J., M. Stewart, and M. Tsakiri, A discrimination test procedure for ambiguity resolution on-the-fly, J. Geod., 72, 644–653, 1998.

    Article  Google Scholar 

  • Wielgosz, P., D. Grejner-Brzezinska, I. Kashani, and Y. Yi, Instantaneous regional ionosphere modeling, Proceedings of ION GPS/GNSS 2003, pp. 1750–1757, 2003.

    Google Scholar 

  • Yi, Y and D. A. Grejner-Brzezinska, Kinematic carrier phase GPS positioning aided by an instantaneous local ionospheric model based on multiple base stations using Kriging, Proceedings of the 59th ION Annual Meeting/22nd CIGTF Guidance Test Sypositium, Albuquerque, NM, pp. 387–396, 2003.

    Google Scholar 

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Correspondence to Chang-Ki Hong.

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Hong, CK., Grejner-Brzezinska, D.A., Kwon, J.H. et al. Effect of stochastic ionospheric delay modeling for GPS ambiguity resolution. Earth Planet Sp 61, e41–e44 (2009).

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