An Optimal Weighting Method of Global Positioning System (GPS) Troposphere Tomography

The functional model of Global Positioning System (GPS) troposphere tomography consists of three types of equations including the observation equation, the horizontal constraint equation, and the vertical constraint equation. The prerequisite for ensuring the accuracy of troposphere tomography modeling is to determine the optimal weights for the three types of equations. In order to reasonably determine the weights among these equations, this paper proposes an optimal weighting method. Compared to the conventional equal weighting scheme and constant weighting scheme, the method proposed in this paper can adaptively adjust the weights for various equations and enable the posterior unit weight variances for the three types of equations that achieve statistically equal. Numerical results under various weather conditions showed that the proposed method can significantly improve the accuracy of GPS tomography modeling with the GPS PPP-estimated slant tropospheric delay as reference when compared to the other two conventional methods.