A Two-Step Projected Iterative Algorithm for Tropospheric Water Vapor Tomography

The tropospheric tomography is an ill-posed inversion problem due to the sparsity of global navigation satellite systems (GNSS) stations and the limitation on the projection angles of GNSS signals, which in turn affects the stability and robustness of the tomographic solution. To address this, a new tomographic algorithm, named two-step projected iterative algorithm (TSPIA), is proposed. The wet refractivity (WR) field was constructed in two steps: first, an iterative preprocessing for the initial input values was performed, and then its resultant solution was input into the projected iterative method, in which a hypothesis convex set was constructed to constrain the reconstruction based on the classical algebraic iterative reconstruction (AIR) methods. In addition, a two-dimensional normalized cumulative periodogram (2-D-NCP) termination criterion was investigated since the traditional criteria for judging the convergence of iterations use prefixed empirical thresholds, which may lead to excessive iterations and need complicated work. The TSPIA was tested using GNSS data in Hong Kong over a wet period and a dry period. Statistical results showed that, compared to the classical AIR methods, the accuracy of the reconstructed WR field of the TSPIA were improved by about 10% and 15% when radiosonde and ECMWF data were used as the reference, respectively. Moreover, experiments for the proposed 2-D-NCP criterion demonstrated noticeable computational efficiency. These results suggest that the new approaches proposed in this article can improve the performance of the iterative methods for GNSS tropospheric tomography.