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Constrained simultaneous algebraic reconstruction technique (C-SART) —a new and simple algorithm applied to ionospheric tomography
Earth, Planets and Space volume 60, pages727–735(2008)
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.
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.
Andreeva, E. S., V. E. Kunitsyn, and E. D. Tereshchenko, Phase-difference radio tomography of the ionosphere, Ann. Geophys., 10, 849–855, 1992.
Bhuyan, K., S. B. Singh, and P. K. Bhuyan, Application of generalized singular value decomposition to ionospheric tomography, Ann. Geophys., 22, 3437–3444, 2004.
Bilitza, D., International Reference Ionosphere 2000, Radio Sci., 36(2), 261–275, 2001.
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.
Dagum, L. and R. Menon, OpenMP: an industry-standard API for shared-memory programming, IEEE Comput. Sci. Eng., 5(1), 46–55, 1998.
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.
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.
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.
Hargreaves, J. K., The solar-terrestrial environment, Cambridge University Press, Cambridge, 1992.
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.
Horvath, I. and S. Crozie, Software developed for obtaining GPS-derived total electron content values, Radio Sci., 42, RS2002, doi:10.1029/2006RS003452, 2007.
Ivansson, S., Seismic borehole tomography—theory and computational methods, Proc. IEEE, 76(2), 328–338, 1986.
Jiang, M. and G. Wang, Convergence of the simultaneous algebraic reconstruction technique (SART), IEEE Trans. Image Proc., 12(8), 957–961, 2003.
Kalman, R. E., A new approach to linear filtering and prediction problems, Trans. ASME—J. Basic Eng., 82(D), 35–45, 1960.
Koch, K. R., Parameter estimation and hypothesis testing in linear models, Springer, Berlin, 1988.
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.
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.
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.
Moore, G. E., Cramming more components onto integrated circuits, Electronics, 38, 114–117, 1965.
Ray, J. and K. Senior, Geodetic techniques for time and frequency comparisons using GPS phase and code measurements, Metrologia, 42, 215–232, 2005.
Raymund, T. D., Comparison of several ionospheric tomography algorithms, Ann. Geophys., 13, 1254–1262, 1995.
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.
Schaer, S., Mapping and predicting the Earth’s ionosphere using the Global Positioning System, PhD thesis, Astronomical Institute, University of Bern, 1999.
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.
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.
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.
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.
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.
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.
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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
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