Abstract
The ionospheric total electron content (TEC) plays a major role in the estimation of positional accuracy of satellite-based navigation systems. TEC disturbs the transmission of the signal transmitted from the satellite to receiver, which leads to range error. Hence, the prediction of VTEC can rectify the range errors in advance. Navigation with Indian Constellation (NavIC) is a navigational satellite system that gives position of a user and time information in India. NavIC receiver is installed at ACSCE, Bangalore, and it is utilized to estimate vertical total electron content (VTEC). In this paper, VTEC estimated from ACSCE station and VTEC obtained from IISC station, Bangalore, are compared and also ordinary kriging-based surrogate model (OKSM) and cokriging-based surrogate model (COKSM) are developed for forecasting NavIC/GPS VTEC. In these models, input parameters comprise the time, Bt, SSN, Ap and F10.7. NavIC and GPS VTEC are predicted for quiet days, i.e. from 16/1/2018 to 26/1/2018 and from 7/8/2018 to 13/8/2018, by using previous one week of VTEC data, and input parameters belong to ACSCE (12.8914° N, 77.4657° E) and IISC (13.0219° N, 77.5671° E) stations, Bangalore. The VTEC prediction results from OKSM and COKSM are compared. It shows that OKSM results are comparatively better than COKSM. In order to validate our developed models, OKSM and COKSM prediction results are compared with the SWIF model during storm days. Based on the comparison, it is observed that RMSE of OKSM is 3.5202 TECU, COKSM gives RMSE as 4.7126 TECU, and the SWIF model’s RMSE is 4.6804. From the comparison results, it is evident that OKSM yields better prediction results than COKSM and SWIF. These results indicate that the proposed model will be useful for correcting range measurement data in advance.
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References
Abdelazeem M, Celik RN, El-Rabbany A (2018) An accurate kriging bases regional ionospheric model using combined GPS/BeiDou observations. J Appl Geod 12(1):65–76. https://doi.org/10.1515/jag-2017-0023
Acharya R, Roy B, Sivaraman MR (2009) Kalman Filter approach for prediction of Ionospheric Total Electron Content. In: International conference on computers and devices for communication (CODEC). IEEE. https://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22First%2520Name%22:%22Ashish%22&searchWithin=%22Last%2520Name%22:%22Dasgupta%22&newsearch=true&sortType=newest
Ahmadi SH, Sedghamiz A (2008) Application and evaluation of kriging and Cokriging methods on groundwater depth mapping. Environ Monit Assess 138(1–3):357–368. https://doi.org/10.1007/s10661-007-9803-2
Arikan F, Arikan O, Erol CB (2007) Regularized estimation of TEC from GPS data for certain mid latitude stations and comparisons with IRI model. Adv Space Res 39(5):867–874. https://doi.org/10.1016/j.asr.2007.01.082
Box G, Jenkins G. 1970. Time series analysis: forecasting and control. J Time Series Anal
Brown RG (1956) Exponential smoothing for predicting demand. Arthur D. Little Inc, Cambridge
Chatfield (1978) Statistics for technology: a course in applied statistics. Chapman and Hall publishers, London
Durga Rao K, Dr VBS, Dutt SI (2017) An assessment of mapping functions for VTEC estimation using measurements of low latitude dual frequency GPS receiver. Int J Appl Eng Res 12(4):422–427
Dyson PL, Bennett JA (1988) A model of the vertical distribution of the electron concentration in the ionosphere and its application to oblique propagation studies. J Atmos Terr Phys 50(3):251–262. https://doi.org/10.1016/0021-9169(88)90074-8
Geng W, Huang W, Liu G, Aa E, Liu S, Chen Y, Luo B (2020) Generation of Ionospheric scintillation maps over southern china based on kriging method. Adv Space Res 65(12):2808–2820. https://doi.org/10.1016/j.asr.2020.03.035
Huang L, Zhang H, Peiliang Xu, Geng J, Wang C (2017) Kriging with unknown variance components for regional ionospheric reconstruction. Sensors 17(468):1–23. https://doi.org/10.3390/s17030468
Klobuchar JA (1987) Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Trans Aerosp Electron Syst 23(3):325–331. https://doi.org/10.1109/TAES.1987.310829
Lanyi GE, Roth T (1988) A comparison of mapped and measured total ionospheric electron content using global positioning system and beacon satellite observations. Radio Sci 23(4):483–492. https://doi.org/10.1029/RS023i004p00483
Mukesh R, Lingadurai K, Selvakumar U (2014) Kriging methodology for surrogate-based airfoil shape optimization. Arab J Sci Eng 39(10):7363–7373. https://doi.org/10.1007/s13369-014-1327-9
Nayir H, Arikan F, Arikan O, Erol CB (2007a) Total electron content estimation with Reg-Est. J Geophys Res. https://doi.org/10.1029/2007JA012459
Nayir H, Arikan F, Arikan O, Erol CB (2007b) GPS/TEC estimation with IONOLAB method. In: 3rd International conference on recent advances in space technologies. IEEE Xplore. https://doi.org/10.1109/RAST.2007.4283998
Oliver MA, Webster R (1990) Kriging: a method of interpolation for geographical information systems. Int J Geogr Inform Syst 4(3):313–332. https://doi.org/10.1080/02693799008941549
Orus R, Hernandez-Pajares M, Juan JM, Sanz J (2005) Improvement of global ionospheric VTEC maps by using kriging interpolation technique. J Atmos Solar Terr Phys 67:1598–1609. https://doi.org/10.1016/j.jastp.2005.07.017
Pignalberi A, Pezzopane M, Rizzi R, Galkin I (2018) Effective solar indices for ionospheric modeling: a review and a proposal for real time regional IRI. Surv Geophys 39:125–167. https://doi.org/10.1007/s10712-017-9438-y
Rathore VS, Kumar S (2015) A statistical comparison of IRI VTEC prediction with GPS VTEC measurement over Varanasi India. J Atmos Solar Terr Phys 124:1–9. https://doi.org/10.1016/j.jastp.2015.01.006
Razin MRG, Voosogh B (2016) Wavelet neural networks using particle swarm optimization training in modeling regional Ionospheric total electron content. J Atmos Solar Terr Phys 149:21–30. https://doi.org/10.1016/j.jastp.2016.09.005
Rui-Yuan L, Liu Guo-Hua WU, Jina Z-C (2008) Ionospheric foF2 reconstruction and its application to the short-term forecasting in china region. Chin J Geophys 51(2):206–213. https://doi.org/10.1002/cjg2.1212
Samardjiev T, Bradley PA, Cander LR, Dick MI (1993) Ionospheric mapping by computer contouring techniques. Electron Lett 29(20):1794–1795. https://doi.org/10.1049/el:19931194
Sarma AD, Venkata Ratnam D, Krishna Reddy D (2009) Modelling of low latitude ionosphere using modified planar fit method for GAGAN. IET Radar Sonar Navig 3(6):609–619. https://doi.org/10.1049/iet-rsn.2009.0022
Sayin I, Arikan F, Arikan O (2008) Regional TEC mapping with random field priors and Kriging. Radio Science 43(5):1–14. https://doi.org/10.1029/2007RS003786
Srilatha VBS, Dutt I, Gowsuddin S (2013) Ionospheric delay estimation using Klobuchar Algorithm for single frequency GPS receivers. Int J Adv Res Electron Commun Eng 2(2):202–207
Stanislawska I, Juchnikowski G, Cander L (1996) The kriging method of ionospheric parameter foF2 instantaneous mapping. Annals of Geophysics 39(4):845–852. https://doi.org/10.4401/ag-4007
Stanislawska I, Juchnikowski G, Cander LJR, Ciraolo L, Bradley PA, Zbyszynski Z, Swiatek A (2002) The Kriging method of TEC instantaneous mapping. Adv Space Res 29(6):945–948. https://doi.org/10.1016/S0273-1177(02)00050-9
Sun S, Egerstedt MB, Martin CF (2000) Control theoretic smoothing splines. IEEE Trans Autom Control 45(12):2271–2279. https://doi.org/10.1109/9.895563
Takka E, Belhadj-Aissa A, Kimouche H (2018) An end-to-end approach for near real time ionosphere monitoring over mid-latitudes from GPS data using kriging interpolation and IGS products. In: 2018 IEEE/ION position, location and navigation symposium (PLANS), Monterey, pp 1173–1180. https://doi.org/10.1109/PLANS.2018.8373502
Tsagouri I, Koutroumbas K, Elias P (2018) A new short-term forecasting model for the total electron content storm time disturbances. J Space Weather Space Clim. https://doi.org/10.1051/swsc/2018019
Wu W-C, Wang T-H, Chiu C-T (2013) Edge curve scaling and smoothing with cubic spline interpolation for image upscaling. IEEE Workshop Signal Process Syst, IEEE Xplore. https://doi.org/10.1109/SiPS.2013.6674482
Ya’acob N, Abdullah M, Ismail M (2010) GPS total electron content (TEC) prediction at ionosphere layer over the equatorial region. Trends in Telecommun Technol. https://doi.org/10.5772/8474
Acknowledgment
The research work presented in this paper has been carried out under the project entitled “Surrogate model for Ionospheric studies using NavIC/GPS Data”, funded by SAC, ISRO, Ahmedabad.
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Mukesh, R., Karthikeyan, V., Soma, P. et al. Ordinary kriging - and cokriging - based surrogate model for ionospheric TEC prediction using NavIC/GPS data. Acta Geophys. 68, 1529–1547 (2020). https://doi.org/10.1007/s11600-020-00473-6
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DOI: https://doi.org/10.1007/s11600-020-00473-6