A troposphere tomography method considering the weighting of input information

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.