An improved GNSS tropospheric tomographic model with an extended region and combining virtual signals.

Global Navigation Satellite Systems (GNSS) water vapor tomography has been proved to be an effective method for retrieving three-dimensional (3D) water vapor distribution. Currently, due to the limitation on the availability and the poor distribution of observations, the ill-posed problem of the tomographic system still needs to be solved. In this study, a refined extended tomographic model with combining virtual signals is proposed to address the observational geometry defect and improve the performance of tomographic solutions. The new refined model was generated by adding auxiliary voxels of the same size as the original voxels around the original tomographic model and its tomographic body is with an inverted cone shape. Then, "virtual" signals that pass through the sides of the original tomographic body and the top boundary of the extended region are introduced. The slant wet delays (SWDs) of these virtual rays were obtained from the tropospheric parameters estimated from GNSS data processing and pre-defined elevation and azimuth angles. Three experimental schemes based on GNSS data from the Hong Kong reference network during the 30-day period in July 2019 were implemented to evaluate the proposed tomographic model. Statistical results showed that, compared with the tomographic models of other schemes, the new model shows strong robustness in terms of observational geometry and the accuracy of the 3D water vapor field inferred. The mean value of the root-mean-square errors (RMSEs) of the tomographic solutions during the period studied obtained from the proposed method was improved by 12% and 11% compared with Schemes I and II, when radiosonde data were used as the reference. Furthermore, compared to other schemes, the condition number of the design matrix reduced after the side-crossing virtual signals were added, implying improvements in the ill-condition of a tomographic system for the proposed method. All these results suggest the good performance of the proposed method. • An improved tomographic model is proposed to address the observational geometry defect and improve the performance. • The virtual signals penetrating from the side-faces of the tomographic model are incorporated into the observation eqs. • The new model with an inverted cone shape is built to utilize these virtual signals. [ABSTRACT FROM AUTHOR]