Journal of Geodesy

, Volume 92, Issue 4, pp 401–413 | Cite as

Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers

  • Baocheng ZhangEmail author
  • Peter J. G. TeunissenEmail author
  • Yunbin Yuan
  • Hongxing Zhang
  • Min Li
Original Article


Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.


Global navigation satellite system (GNSS) Vertical total electron content (VTEC) Satellite differential code biases (SDCBs) Carrier-to-code leveling (CCL) Precise point positioning (PPP) Thin-layer ionospheric model 



This work was partially funded by the National key Research Program of China “Collaborative Precision Positioning Project” (No. 2016YFB0501900), the National Natural Science Foundation of China (Nos. 41604031, 41774042) and Natural Science Foundation of Jiangxi Province (No. 20161BAB213087). The first author is supported by the CAS Pioneer Hundred Talents Program. All this support is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and GeophysicsChinese Academy of SciencesWuhanChina
  2. 2.Global Navigation Satellite System (GNSS) Research CentreCurtin UniversityPerthAustralia
  3. 3.Geoscience and Remote SensingDelft University of TechnologyDelftThe Netherlands

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