A troposphere tomography method considering the weighting of input information

Abstract

Abstract. Troposphere tomography measurement using a global navigation satellite system (GNSS) generally consists of several types of input information including the observation equation, horizontal constraint equation, vertical constraint equation, and a priori constraint equation. The reasonable weightings of input information are a prerequisite for ensuring the reliability of the adjustment of the parameters. This forms the focus of this research, which tries to determine the weightings, including the observations, for the same type of equation and the optimal weightings for different types of equations. The optimal weightings of the proposed method are realized on the basis of the stable equilibrium relationship between different types of a posteriori unit weight variances, which are capable of adaptively adjusting the weightings for different types of equations and enables the ratio between the two arbitrary a posteriori unit weight variances to tend to unity. A troposphere tomography experiment, which was used to consider these weightings, was implemented using global positioning system (GPS) data from the Hong Kong Satellite Positioning Reference Station Network (SatRef). Numerical results show the applicability and stability of the proposed method for GPS troposphere tomography assessment under different weather conditions. In addition, the root mean square (RMS) error in the water vapor density differences between tomography-radiosonde and tomography-ECMWF (European Centre for Medium-Range Weather Forecasts) are 0.91 and 1.63 g m −3 , respectively, over a 21-day test.

Cross-Comparison and Methodological Improvement in GPS Tomography

“…Improvements of the tomographic method, with the aim to obtain the best convergence of retrievals, have been developed by [23] using singular value decomposition combined with a Kalman filter. Improvements have also been developed by Bender et al [13] with algebraic reconstruction, by Perler et al [14] with the use of new parametrised approaches, and more recently by Rohm [24] with an unconstrained approach and the use of a robust Kalman filter [25], and by Zhao et al [26] by considering various input observation weighting schemes. Note that for all these methods, the observation-a priori weighting scheme affects the inversion process, and the redundancy or the conflict of information from GPS slant observations crossing the same voxel are critical for good achievement of the tomography technique.…”