Skip to main content
Earth, Planets and Space
Download PDF

Constrained simultaneous algebraic reconstruction technique (C-SART) —a new and simple algorithm applied to ionospheric tomography

Earth, Planets and Space volume 60, pages 727–735 (2008)Cite this article

Abstract

A simple and relatively fast method (C-SART) is presented for tomographic reconstruction of the electron density distribution in the ionosphere using smooth fields. Since it does not use matrix algebra, it can be implemented in a low-level programming language, which speeds up applications significantly. Compared with traditional simultaneous algebraic reconstruction, this method facilitates both estimation of instrumental offsets and consideration of physical principles (expressed in the form of finite differences). Testing using a 2D scenario and an artificial data set showed that C-SART can be used for radio tomographic reconstruction of the electron density distribution in the ionosphere using data collected by global navigation satellite system ground receivers and low Earth orbiting satellites. Its convergence speed is significantly higher than that of classical SART, but it needs to be speeded up by a factor of 100 or more to enable it to be used for (near) real-time 3D tomographic reconstruction of the ionosphere.

References

  • Andersen, A. H. and A. C. Kak, Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm, Ultrason. Img., 6, 81–94, 1984.

    Article  Google Scholar 

  • Andreeva, E. S., V. E. Kunitsyn, and E. D. Tereshchenko, Phase-difference radio tomography of the ionosphere, Ann. Geophys., 10, 849–855, 1992.

    Google Scholar 

  • Bhuyan, K., S. B. Singh, and P. K. Bhuyan, Application of generalized singular value decomposition to ionospheric tomography, Ann. Geophys., 22, 3437–3444, 2004.

    Article  Google Scholar 

  • Bilitza, D., International Reference Ionosphere 2000, Radio Sci., 36(2), 261–275, 2001.

    Article  Google Scholar 

  • Censor, Y. and T. Elfving, Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem, SIAM J. Matrix Anal. Appl., 24, 40–58, 2002.

    Article  Google Scholar 

  • Dagum, L. and R. Menon, OpenMP: an industry-standard API for shared-memory programming, IEEE Comput. Sci. Eng., 5(1), 46–55, 1998.

    Article  Google Scholar 

  • Feltens, J., The activities of the ionosphere working group of the International GPS Service (IGS), GPS Solutions, 7(1), 41–46, doi:0.1007/s10291-003-0051-9, 2003.

    Article  Google Scholar 

  • Gordon, R., R. Bender, and G. T. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, J. Theor. Biol., 29, 471–482, 1970.

    Article  Google Scholar 

  • Hajj, G. A., B. D. Wilson, C. Wang, X. Pi, and I. G. Rosen, Data assimilation of ground GPS total electron content into a physics-based ionospheric model by use of the Kalman filter, Radio Sci., 39, doi:10.1029/2002RS002859, 2004.

  • Hansen, P. C., The truncated SVD as a method for regularization, BIT, 27, 534–553, 1987.

    Article  Google Scholar 

  • Hargreaves, J. K., The solar-terrestrial environment, Cambridge University Press, Cambridge, 1992.

    Book  Google Scholar 

  • Hernandez-Pajares, M., J. M. Juan, and J. Sanz, New approaches in global ionospheric determination using ground GPS data, J. Atmos. Solar Terr. Phys., 61, 1237–1247, 1999.

    Article  Google Scholar 

  • Horvath, I. and S. Crozie, Software developed for obtaining GPS-derived total electron content values, Radio Sci., 42, RS2002, doi:10.1029/2006RS003452, 2007.

    Article  Google Scholar 

  • Ivansson, S., Seismic borehole tomography—theory and computational methods, Proc. IEEE, 76(2), 328–338, 1986.

    Article  Google Scholar 

  • Jiang, M. and G. Wang, Convergence of the simultaneous algebraic reconstruction technique (SART), IEEE Trans. Image Proc., 12(8), 957–961, 2003.

    Article  Google Scholar 

  • Kalman, R. E., A new approach to linear filtering and prediction problems, Trans. ASME—J. Basic Eng., 82(D), 35–45, 1960.

    Article  Google Scholar 

  • Koch, K. R., Parameter estimation and hypothesis testing in linear models, Springer, Berlin, 1988.

    Book  Google Scholar 

  • Lee, J. K., F. Kamalabadi, and J. J. Makela, Localized three-dimensional ionospheric tomography with GPS ground receiver measurements, Radio Sci., 42, RS4018, doi:10.1029/2006RS003543, 2007.

    Article  Google Scholar 

  • Ma, X. F., T. Murayama, G. Ma, and T. Takeda, Three-dimensional ionospheric tomography using observation data of GPS ground receivers and ionosonde by neural network, J. Geophys. Res., 110, A05308, doi:10.1029/2004JA010797, 2005.

    Google Scholar 

  • Mailloux, G. E., R. Noumeir, and R. Lemieux, Deriving the multiplicative algebraic reconstruction algorithm (MART) by the method of convex projections (POCS), Proc. IEEE Int. Conf. Acoustics, Speech Signal Proc, 5, 457–460, 1993.

    Google Scholar 

  • Moore, G. E., Cramming more components onto integrated circuits, Electronics, 38, 114–117, 1965.

    Google Scholar 

  • Ray, J. and K. Senior, Geodetic techniques for time and frequency comparisons using GPS phase and code measurements, Metrologia, 42, 215–232, 2005.

    Article  Google Scholar 

  • Raymund, T. D., Comparison of several ionospheric tomography algorithms, Ann. Geophys., 13, 1254–1262, 1995.

    Google Scholar 

  • Ruffini, G. A. Flores, and A. Rius, GPS tomography of the ionospheric electron content with a correlation functional, IEEE Trans. Geosci. Remote Sens., 36(1), 143–153, 1998.

    Article  Google Scholar 

  • Schaer, S., Mapping and predicting the Earth’s ionosphere using the Global Positioning System, PhD thesis, Astronomical Institute, University of Bern, 1999.

    Google Scholar 

  • Skjellum, A., N. E. Doss, and P. V. Bangalore, Writing libraries in MPI. Proceedings of the Scalable Parallel Libraries Conference, IEEE Computer Society Press, 166–173, 1993.

    Google Scholar 

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

    Google Scholar 

  • Wen, D. B., Imaging the ionospheric electron density using a combined to-mographic algorithm, Proceedings of the International Technique Meeting of the Satellite Devision, 25–28 September 2007, Fort Worth, Texas, 2337–2345, 2007.

    Google Scholar 

  • Wen, D. B., Y. B. Yuan, J. K. Ou, and X. L. Huo, Monitoring the three-dimensional ionospheric electron distribution using GPS observations over China, J. Earth Syst. Sci., 116(3), 235–244, 2007a.

    Article  Google Scholar 

  • Wen, D. B., Y. B. Yuan, J. K. Ou., X. L. Huo, and K. F. Zhang, Threedimensional ionospheric tomography by an improved algebraic reconstruction technique, GPS Solutions, 11(4), 251–258, 2007b.

    Article  Google Scholar 

  • Wen, D. B., Y. B. Yuan, J. K. Ou., X. L. Huo, and K. F. Zhang, Ionospheric temporal and spatial variations during the 18 August 2003 storm over China, Earth Planets Space, 59, 313–317, 2007c.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Space-Time Standards Group, Kashima Space Research Center, National Institute of Information and Communications Technology, 893-1 Hirai, Kashima, 314-0012, Japan

    Thomas Hobiger, Tetsuro Kondo & Yasuhiro Koyama

Authors
  1. Thomas Hobiger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tetsuro Kondo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yasuhiro Koyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Hobiger.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Hobiger, T., Kondo, T. & Koyama, Y. Constrained simultaneous algebraic reconstruction technique (C-SART) —a new and simple algorithm applied to ionospheric tomography. Earth Planet Sp 60, 727–735 (2008). https://doi.org/10.1186/BF03352821

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352821

Key words