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A modified three-dimensional ionospheric tomography algorithm with side rays

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Abstract

The three-dimensional ionospheric tomography (3DCIT) algorithm based on Global Navigation Satellite System (GNSS) observations have been developed into an effective tool for ionospheric monitoring in recent years. However, because the rays that come into or come out from the side of the inversion region cannot be used, the distribution of the rays in the edge and bottom part of the inversion region is scarce and the electron density cannot be effectively improved in the inversion process. We present a three-dimensional tomography algorithm with side rays (3DCIT-SR) applying the side rays to the inversion. The partial slant total electron content (STEC) of side rays in the inversion region is obtained based on the NeQuick2 model and GNSS-STEC. The simulation experiment results show that the algorithm can effectively improve the distribution of GNSS rays in the inversion region. Meanwhile, the iteration accuracy has also been significantly improved. After the same number of iterations, the iterative results of 3DCIT-SR are closer to the truth than 3DCIT, in particular, the inversion of the edge regions is improved noticeably. The GNSS data of the International GNSS Service (IGS) stations in Europe are used to perform real data experiments, and the inversion results show that the electron density profiles of 3DCIT-SR are closer to the ionosonde measurements. The accuracy improvement of 3DCIT-SR is up to 56.3% while the improvement is more obvious during the magnetic storm compared to the case of a calm ionospheric state .

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References

  • Austen JR, Franke SJ, Liu CH, Yeh KC (1986) Application of computerized tomography techniques to ionospheric research. In: Proceedings of the international beacon satellite symposium on radio beacon contribution to the study of ionization and dynamics of the ionosphere and to corrections to geodesy and technical workshop, University of Oulu, Finland, pp 25–35. http://adsabs.harvard.edu/abs/1986ibs..symp...2A

  • Austen JR, Franke SJ, Liu CH (1988) Ionospheric imaging using computerized tomography. Radio Sci 23(3):299–307

    Article  Google Scholar 

  • Burrell AG, Bonito NA, Carrano CS (2009) Total electron content processing from GPS observations to facilitate ionospheric modeling. GPS Solut 13(2):83–95

    Article  Google Scholar 

  • Bust GS, Coco D, Makela JJ (2000) Combined ionospheric campaign 1: ionospheric tomography and GPS total electron count (TEC) depletions. Geophys Res Lett 27(18):2849–2852

    Article  Google Scholar 

  • Chen CH, Saito A, Lin CH, Yamamoto M, Suzuki S, Seemala GK (2016) Medium-scale traveling ionospheric disturbances by three-dimensional ionospheric GPS tomography. Earth Planets Space 68(32):1–9

    Google Scholar 

  • Das SK, Shukla AK (2011) Two-dimensional ionospheric tomography over the low-latitude Indian region: an intercomparison of ART and MART algorithms. Radio Sci. https://doi.org/10.1029/2010RS004350

    Article  Google Scholar 

  • Ezquer RG, Scidá LA, Orué YM, Lescano GE, Alazo-Cuartas K, Cabrera MA, Radicella SM (2017) NeQuick 2 total electron content predictions for middle latitudes of North American region during a deep solar minimum. J Atmos Sol Terr Phy 154(2):55–66

    Article  Google Scholar 

  • Farzaneh S, Forootan E (2018) Reconstructing regional ionospheric electron density: a combined spherical slepian function and empirical orthogonal function approach. Surv Geophys 39(2):289–309. https://doi.org/10.1007/s10712-017-9446-y

    Article  Google Scholar 

  • Fehmers GC, Kamp L, Sluijter FW, Spoelstra T (1998) A model-independent algorithm for ionospheric tomography: 2. Experimental results. Radio Sci 33(1):165–173

    Article  Google Scholar 

  • Gerzen T, Minkwitz D (2016) Simultaneous multiplicative column-normalized method (SMART) for 3-D ionosphere tomography in comparison to other algebraic methods. Ann Geophys Germ 34(1):97–115. https://doi.org/10.5194/angeo-34-97-2016

    Article  Google Scholar 

  • Han D, Kim D, Kee C (2018) Improving performance of GPS satellite DCB estimation for regional GPS networks using long-term stability. GPS Solut 22(1):13

    Article  Google Scholar 

  • Hansen AJ, Walter T, Enge P (1997) Ionospheric correction using tomography. In: Proc. ION GPS-97, Institute of Navigation, Kansas City, MO, USA, September 16–19, pp 249–260

  • Hernández-Pajares M, Juan JM, Sanz J, Sol Eacute JG (1998) Global observation of the ionospheric electronic response to solar events using ground and LEO GPS data. J Geophys Res-Space 103(A9):20789–20796

    Article  Google Scholar 

  • Hernández-Pajares M, Juan JM, Sanz J, Colombo OL (2000) Application of ionospheric tomography to real-time GPS carrier-phase ambiguities resolution, at scales of 400–1000 km and with high geomagnetic activity. Geophys Res Lett 27(13):2009–2012

    Article  Google Scholar 

  • Hirooka S, Hattori K (2016) Validation of Ionospheric Tomography Using Residual Minimization Training Neural Network. Electr Commun Jpn 99(4):50–57

    Article  Google Scholar 

  • Hirooka S, Hattori K, Takeda T (2011a) Numerical validations of neural-network-based ionospheric tomography for disturbed ionospheric conditions and sparse data. Radio Sci 46(5):RS0F05. https://doi.org/10.1029/2011RS004760

    Article  Google Scholar 

  • Hirooka S, Hattori K, Nishihashi M, Takeda T (2011b) Neural network based tomographic approach to detect earthquake-related ionospheric anomalies. Nat Hazard Earth Sys 11(8):2341–2353

    Article  Google Scholar 

  • Hobiger T, Kondo T, Koyama Y (2008) Constrained simultaneous algebraic reconstruction technique (C-SART)—a new and simple algorithm applied to ionospheric tomography. Earth Planets Space 60(7):727–735

    Article  Google Scholar 

  • Howe BM, Runciman K, Secan JA (1998) Tomography of the ionosphere: four-dimensional simulations. Radio Sci 33(1):109–128

    Article  Google Scholar 

  • Huang CR, Liu CH, Yeh KC, Lin KH, Tsai WH, Yeh HC, Liu JY (1999) A study of tomographically reconstructed ionospheric images during a solar eclipse. J Geophys Res Space 104(A1):79–94

    Article  Google Scholar 

  • Jin S, Li D (2018) 3-D ionospheric tomography from dense GNSS observations based on an improved two-step iterative algorithm. Adv Space Res 62(4):809–820

    Article  Google Scholar 

  • Jin R, Jin S, Feng G (2012) M_DCB: Matlab code for estimating GNSS satellite and receiver differential code biases. GPS Solut 16(4):541–548. https://doi.org/10.1007/s10291-012-0279-3

    Article  Google Scholar 

  • Kunitsyn VE, Andreeva ES, Razinkov OG (1997) Possibilities of the near-space environment radio tomography. Radio Sci 32(5):1953–1963

    Article  Google Scholar 

  • Lee JK, Kamalabadi F, Makela JJ (2007) Localized three-dimensional ionospheric tomography with GPS ground receiver measurements. Radio Sci 42(04):1–15

    Article  Google Scholar 

  • Ma XF, Maruyama T, Ma G, Takeda T (2005) Three-dimensional ionospheric tomography using observation data of GPS ground receivers and ionosonde by neural network. J Geophys Res Space 110(A5):A5308. https://doi.org/10.1029/2004JA010797

    Article  Google Scholar 

  • Macalalad FV, Jr JH, Apostol JV, Preston FW (1993) Experimental ionospheric tomography with ionosonde input and EISCAT verification. Ann Geophys Ger 11(11–12):1064–1074

    Google Scholar 

  • Markkanen M, Lehtinen M, Nygrén T, Pirttilä J, Henelius P, Vilenius E, Tereshchenko ED, Khudukon BZ (1995) Bayesian approach to satellite radiotomography with applications in the Scandinavian sector. ISME J 8(11):2280–2289

    Google Scholar 

  • Mitchell CN, Spencer PSJ (2003) A three-dimensional time-dependent algorithm for ionospheric imaging using GPS. Ann Geophys Italy 46(4):687–696

    Google Scholar 

  • Nava B, Coisson P, Radicella SM (2008) A new version of the NeQuick ionosphere electron density model. J Atmos Solar Terr Phys 70(15):1856–1862

    Article  Google Scholar 

  • Nava B, Radicella SM, Azpilicueta F (2011) Data ingestion into NeQuick 2. Radio Sci, 46(6):RS0D17. https://doi.org/10.1029/2010RS004635, 2011

    Article  Google Scholar 

  • Nigussie M, Radicella SM, Damtie B, Nava B, Yizengaw E, Groves K (2013) Validation of the NeQuick 2 and IRI-2007 models in East-African equatorial region. J Atmos Sol Terr Phy 102(9):26–33

    Article  Google Scholar 

  • Norberg J, Roininen L, Vierinen J, Amm O, Mckay-Bukowski D, Lehtinen M (2015) Ionospheric tomography in Bayesian framework with Gaussian Markov random field priors. Radio Sci 50(2):138–152

    Article  Google Scholar 

  • Nygrén T, Markkanen M, Lehtinen M, Tereshchenko ED, Khudukon BZ (1997) Stochastic inversion in ionospheric radiotomography. Radio Sci 32(6):2359–2372. https://doi.org/10.1029/97RS02915

    Article  Google Scholar 

  • Oladipo OA, Schüler T (2012) GNSS single frequency ionospheric range delay corrections: NeQuick data ingestion technique. Adv Space Res 50(9):1204–1212

    Article  Google Scholar 

  • Prol FS, Camargo PO, Muella MTAH (2017) Numerical simulations to assess ART and MART performance for ionospheric tomography of Chapman profiles. An Acad Bras Cienc 89(3):1531–1542. https://doi.org/10.1590/0001-3765201720170116

    Article  Google Scholar 

  • Pryse SE, Kersley L, Rice DL, Russell CD, Walker IK (1993) Tomographic imaging of the ionospheric mid-latitude trough. Ann Geophys 11(3):144–149

    Google Scholar 

  • Pryse SE, Kersley L, Williams MJ, Walker IK, Willson CA (1997) Tomographic imaging of the polar-cap ionosphere over svalbard. J Atmos Sol Terr Phy 59(15):1953–1959

    Article  Google Scholar 

  • Raymond TD, Franke SJ, Yeh KC (1994) Ionospheric tomography: its limitations and reconstruction methods. J Atmospheric Sol Terr Phys 56(5):637–653

    Article  Google Scholar 

  • Raymund TD, Austen JR, Franke SJ, Liu CH, Klobuchar JA, Stalker J (1990) Application of computerized tomography to the investigation of ionospheric structures. Radio Sci 25(05):771–789

    Article  Google Scholar 

  • Rideout W, Coster A (2006) Automated GPS processing for global total electron content data. GPS Solut 10(3):219–228

    Article  Google Scholar 

  • Rius A, Ruffini G, Cucurull L (1997) Improving the vertical resolution of ionospheric tomography with GPS occultations. Geophys Res Lett 24(18):2291–2294

    Article  Google Scholar 

  • Saito S, Suzuki S, Yamamoto M, Saito A, Chen CH (2017) Real-time ionosphere monitoring by three-dimensional tomography over Japan. Navig J Inst Navig 64(4):495–504

    Article  Google Scholar 

  • Schüler T, Oladipo OA (2014) Single-frequency single-site VTEC retrieval using the NeQuick2 ray tracer for obliquity factor determination. GPS Solut 18(1):115–122

    Article  Google Scholar 

  • Seemala GK, Yamamoto M, Saito A, Chen CH (2014) Three-dimensional GPS ionospheric tomography over Japan using constrained least squares. J Geophys Res Space 119(4):3044–3052

    Article  Google Scholar 

  • Ssessanga N, Kim YH, Kim E (2015) Vertical structure of medium-scale traveling ionospheric disturbances. Geophys Res Lett 42(21):9156–9165

    Article  Google Scholar 

  • Themens DR, Jayachandran PT, Langley RB, MacDougall JW, Nicolls MJ (2013) Determining receiver biases in GPS-derived total electron content in the auroral oval and polar cap region using ionosonde measurements. GPS Solut 17(3):357–369

    Article  Google Scholar 

  • Wang S, Huang S, Xiang J, Fang H, Feng J, Wang Y (2016) Three-dimensional ionospheric tomography reconstruction using the model function approach in Tikhonov regularization. J Geophys Res Space 121(12):104–112. https://doi.org/10.1002/2016JA023487 (115)

    Article  Google Scholar 

  • Wen D, Yuan Y, Ou J, Huo X, Zhang K (2007) Three-dimensional ionospheric tomography by an improved algebraic reconstruction technique. GPS Solut 11(4):251–258

    Article  Google Scholar 

  • Wen D, Yuan Y, Ou J, Zhang K, Liu K (2008) A hybrid reconstruction algorithm for 3-D ionospheric tomography. IEEE Trans Geosci Remote Sens 46(6):1733–1739

    Article  Google Scholar 

  • Wen D, Wang Y, Norman R (2012) A new two-step algorithm for ionospheric tomography solution. GPS Solut 16(1):89–94. https://doi.org/10.1007/s10291-011-0211-2

    Article  Google Scholar 

  • Yao Y, Kong J, Tang J (2015) A new ionosphere tomography algorithm with two-grid virtual observations constraints and three-dimensional velocity profile. IEEE Trans Geosci Remote 53(5):2373–2383. https://doi.org/10.1109/TGRS.2014.2359762

    Article  Google Scholar 

  • Yao YB, Zhao QZ, Zhang B (2016) A method to improve the utilization of GNSS observation for water vapor tomography. Ann Geophys Ger 34(1):143–152. https://doi.org/10.5194/angeo-34-143-2016

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the International Global Navigation Satellite System Service (IGS) for the data used in this work. The authors also thank the Global Ionosphere Radio Observatory for the ionosonde data. The ionosonde (PQ052) data were downloaded from ftp://ftp.ngdc.noaa.gov/ionosonde/data/.

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Authors and Affiliations

  1. School of Geodesy and Geomatics, Wuhan University, Wuhan, China

    Yibin Yao, Changzhi Zhai & Cunjie Zhao

  2. Chinese Antarctic Center of Surveying and Mapping, Wuhan University, Wuhan, China

    Jian Kong

  3. College of Geomatics, Xi’an University of Science and Technology, Xi’an, China

    Qingzhi Zhao

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  1. Yibin Yao
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  2. Changzhi Zhai
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  4. Qingzhi Zhao
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  5. Cunjie Zhao
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Correspondence to Yibin Yao.

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Yao, Y., Zhai, C., Kong, J. et al. A modified three-dimensional ionospheric tomography algorithm with side rays. GPS Solut 22, 107 (2018). https://doi.org/10.1007/s10291-018-0772-4

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