Weighting of Multi-GNSS Observations in Real-Time Precise Point Positioning

The combination of Global Navigation Satellite Systems (GNSS) may improve the accuracy and precision of estimated coordinates, as well as the convergence time of Precise Point Positioning (PPP) solutions. The key conditions are the correct functional model and the proper weighting of observations, for which different characteristics of multi-GNSS signals should be taken into account. In post-processing applications, the optimum stochastic model can be obtained through the analysis of post-fit residuals, but for real-time applications the stochastic model has to be defined in advanced. We propose five different weighting schemes for the GPS + GLONASS + Galileo + BeiDou combination, including two schemes with no intra-system differences, and three schemes that are based on signal noise and/or quality of satellite orbits. We perform GPS-only and five multi-GNSS solutions representing each weighting scheme. We analyze formal errors of coordinates, coordinate repeatability, and solution convergence time. We found that improper or equal weighting may improve formal errors but decreases coordinate repeatability when compared to the GPS-only solution. Intra-system weighting based on satellite orbit quality allows for a reduction of formal errors by 40%, for shortening convergence time by 40% and 47% for horizontal and vertical components, respectively, as well as for improving coordinate repeatability by 6%.