An improved ridge estimation (IRE) method for troposphere water vapor tomography

Abstract

Water vapor tomography technique is a research point in global navigation satellite system (GNSS) meteorology. However, GNSS tomography technique has an inherent issue of design matrix sparsity, which leads to the ill-posed problem in the inversion of normal equation. Singular value decomposition (SVD) method is commonly used to resolve this problem but performs poorly due to the large fluctuation in tomographic results caused by the small singular values. To overcome the above issue, this study proposes an improved ridge estimation (IRE) method, which only revises the relatively small singular values and retains the large singular values unchanged on the basis of the minimum deviation principle in the processing of regularization matrix. An adjustment coefficient is introduced to determine the node of small singular value with large influence on the tomographic result. Twelve GNSS stations from Hong Kong Satellite Positioning Reference Station Network (SatRef) were used to validate the performance of the proposed method over the period of day of year (Doy) 84–101, 2014. The established tomography model in SatRef was resolved using SVD and IRE methods, respectively. Statistical results show that the accuracy of average root mean square error (RMSE) of IRE method is improved by 16.7% compared with that of SVD method when the corresponding radiosonde is considered as the reference. Additionally, the comparisons of water vapor profile, relative error (RE) and the reconstructed SWV derived from IRE and SVD methods were also carried out and the numerical result indicates a good performance of the proposed IRE method. Such results verify that the applicability of proposed IRE method in this paper for GNSS water vapor tomography.