Journal of Geodesy

, Volume 89, Issue 4, pp 347–360 | Cite as

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

  • Murat DurmazEmail author
  • Mahmut Onur Karslioglu
Original Article


There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate B-splines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.


Ionosphere VTEC BMARS B-spline Regional modeling Semi-parametric SP-BMARS 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Geomatics Engineering Division, Civil Engineering DepartmentMiddle East Technical University (METU)AnkaraTurkey
  2. 2.Department of Geodetic and Geographic Information Technologies (GGIT), Institute of Applied and Natural SciencesMiddle East Technical University (METU)AnkaraTurkey

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