Analysis of different weighting functions of observations for GPS and Galileo PPP

At present, significant development of the positioning methods using the Global Navigation Satellite System (GNSS) can be seen. One of the most developed methods is the absolute Precise Point Positioning (PPP) method. This can be particularly seen using multi-GNSS measurements. The development of multi-GNSS increases the number of satellites observed and increases the accuracy of the products, but also creates new requirements for observation modeling. Obtaining the correct values, ​​of the estimated parameters, requires the appropriate determination of the deterministic model as well as the stochastic model. Currently, the deterministic model is well known. In contrast, the stochastic model is not fully known and still requires a number of studies. Stochastic modeling is based on determining the covariance matrix and which can be modeled using a weighting function that takes into account the elevation angle of the observed satellite. ​

In our analysis, we focus on studies on the weighting functions of GNSS observations for the PPP method. Analysis was performed on the Multi-GNSS Pilot Project (MGEX) stations which were characterized by global distribution and various equipment in 2021. Studies were conducted for the GPS‑only, Galileo-only, and GPS+Galileo constellations, with particular emphasis on the Galileo observations, which has achieved significant progress in recent years. Eight different observation weighting models have been selected for analysis: one of them assumes that all observations have the same precision, without dependence on the elevation angle; for the other used functions, the observation precision value depends on the elevation angle. Parameters such as accuracy, convergence time, zenith path delay (ZPD), and inter-system bias (ISB) are analyzed.

Based on the tests performed, we show that, depending on the solutions adopted (i.e. GPS-only, Galileo-only, GPS+Galileo), the best results were obtained for different weighting functions. We have shown that using different weighting functions have no impact on the horizontal component but a visible impact on the vertical component,  the tropospheric delay, and the convergence time. Also, we choose the best functions for GPS-only and Galileo-only and used them for the GPS+Galileo solution. For this new approach obtained a shorter convergence time and higher accuracy of the ZPD. More information and results will be presented at the conference.