B-spline function-based approach for GPS tropospheric tomography

Saeid Haji-Aghajany, Yazdan Amerian*, Sandra Verhagen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)
18 Downloads (Pure)


Tropospheric tomography is one of the most important techniques to reconstruct three-dimensional (3D) images of the tropospheric water vapor fields using a local GNSS network. In the conventional tropospheric tomography method, called voxel-based tropospheric tomography, the 3D space is divided into many voxels and the amount of water vapor is estimated for each voxel. This method suffers from three disadvantages. First, it needs empirical constraints in order to fix the rank deficiency of the coefficient matrix. Second, the amount of water vapor is assumed to be constant in the 3D space of a voxel despite the large spatial variations of this parameter. Third, the number of unknown parameters is high compared to the number of observations. Therefore, an approach based on mathematical functions, called function-based tropospheric tomography, is presented to overcome these problems. The tropospheric tomography using the voxel-based and function-based approaches is performed using 17 GPS stations. Radiosonde observations and precise point positioning results are used to validate the obtained results. A comparison of the results with the radiosonde data indicates that using the function-based method reduces the mean RMSE by about 0.3 gr/m3. Validation using positioning under different wet conditions shows that in wet weather conditions the difference between the RMSE of the two tropospheric tomography approaches is significant. All the validations show the ability and applicability of the function-based tropospheric tomography approach.

Original languageEnglish
Article number88
Number of pages12
JournalGPS Solutions
Issue number3
Publication statusPublished - 2020

Bibliographical note

Accepted Author Manuscript


  • B-spline
  • Function-based
  • GPS
  • Tropospheric tomography
  • Voxel-based


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