# Weighting of Multi-GNSS Observations in Real-Time Precise Point Positioning
## 1 Introduction
GNSS products of the highest quality are obtained with combined solutions of contributing ACs, but they are obtained in a post-processing mode and are delivered with a latency of few weeks [21]. This eliminates their usefulness in real-time applications. Fortunately for real-time PPP users, in 2013, IGS established a Real-Time Service (RTS) that provides precise products for GPS and experimental products for GLONASS in real-time via Internet streams [22]. Currently, there is only one IGS AC, namely, Centre National d'Etudes Spatiales (CNES), which freely provides corrections to GPS, GLONASS, Galileo, and BeiDou [23], thus supporting all of the currently available systems. This allows for performing real-time multi-GNSS PPP. Moreover, ionosphere corrections, code, and phase biases are provided in CNES streams, which allows for ambiguity resolution in zero-differenced processing. With official IGS RTS corrections only float ambiguity solution is possible. Real-time float GPS PPP can provide sub-decimeter accuracy of positioning [24; 25] and improves the solution RMS by about 50% when compared with the solution obtained from the predicted part of the IGS ultra-rapid products [26]. The fusion of multiple GNSS results in more stable coordinate time series, thus, a few centimeter accuracy is possible even with 40 degrees cut-off elevation [27]. However, adding GLONASS to GPS has a negative or marginal effect on real-time static PPP [28], while kinematic PPP may be improved especially under reduced visibility scenarios [29]. It was also found that multi-GNSS solutions accelerate the initialization time by up to 27% and improve the positioning accuracy by up to 22% [30]. Unfortunately, the quality of real-time products is not homogenous among systems and it depends on many factors, such as satellite constellation, Sun elevation above the orbital plane (\(\beta\) angle), or orbit type [31]. Moreover, there are many deficiencies in satellite orbit models, especially for modernized blocks and emerging systems, which additionally deteriorate the quality of orbits and clocks. For these reasons, a special attention should be paid on the proper weighting of observations. Many weighting approaches have been proposed for observation weighting of the same type, e.g., carrier-to-noise ratio [32] and elevation-depending weight models [33]. For weighting different types of observations,which is the case of processing multi-GNSS data, the rigorous Helmert variance component estimation method is widely used [34], but it requires a postprocessing of high redundant observations [35]. For real-time multi-GNSS application both intra- and inter-system weights should be known in advance, which optimize the processing of a variety of observations. Therefore, the goal of this study is to develop and compare several observation weighting schemes that are suitable for real-time multi-GNSS PPP. The paper is structured as follows. After the introductory Section 1, GNSS data processing strategy and the development of stochastic models are described in detail in Section 2. Afterwards, results of multi-GNSS processing with different weighting schemes are analyzed by means of formal errors, coordinate repeatability, and convergence time. Section 4 provides the discussion and conclusions.