# Weighting of Multi-GNSS Observations in Real-Time Precise Point Positioning
## 1 Introduction  
A dynamic development of Global Navigational Satellite Systems (GNSS), namely GPS, GLONASS, Galileo, and BeiDou, constantly increases the number of operational spacecraft and the amount of provided frequencies. The main idea of all GNSS is uniform. Nevertheless, currently available systems are different in many aspects. Satellite constructions and on-board equipment vary not only between systems but also between satellite blocks. Besides commonly used medium earth-orbit (MEO) satellites, geostationary satellites (GEO), and inclined geosynchronous orbit (IGSO) satellites are encountered in the BeiDou constellation. There are also two Galileo satellites launched into incorrect, elliptical orbits [1]. Receiver Independent Exchange Format (RINEX) 3.03 supports 11 unique frequencies, and only some of them are shared between systems. World Geodetic System (WGS) 84, Paramety Zemli 1990 (PZ-90), Galileo Terrestrial Reference Frame (GTRF), and China Geodetic Coordinate System (CGCS) 2000 are reference frames of GPS, GLONASS, Galileo, and BeiDou, respectively. Each system has its unique time scale, as well. In order to benefit from multi-GNSS and multi-frequency observations, all the system-dependent calibration parameters must be delivered to the user [2]. Therefore, a great effort is being made by scientific community and industry to improve GNSS processing algorithms, techniques, and related models. The International GNSS Service (IGS) established a multi-GNSS experiment (MGEX) to track, collate, and analyze all of the available GNSS signals [3]. Currently, MGEX analysis centers (ACsprovide precise satellites products, including satellite orbits and clock corrections, for all GNSS. MGEX triggered an update of data formats and improvements in hardware development. It also provided many valuable models, such as satellite phase center offsets, code, and phase biases [4]. IGS products are currently expressed in IGS14, which is the latest in a series of GNSS reference frames adopted by the IGS, thus IGS14 aligns orbit products with the International Terrestrial Reference Frame 2014 [5]. Recent developments in GNSS and a common access to GNSS data stimulate a growth of GNSS-based applications. In addition to positioning, navigation, and timing (PNT) based applications, a wide scope of scientific and sophisticated applications can be found, e.g., space weather modeling [6], water vapor monitoring [7; 8], radio-occultation [9], soil moisture determination [10], and snow height measurements [11]. In many areas, such as geodynamics or see level climatology, the latency of results reaching even tens of days is highly acceptable and does not decrease its usefulness. On the other hand, there are more and more applications demanding precise positioning in real-time, e.g., unmanned aerial vehicle photogrammetry [12], tsunami warning systems [13], precision agriculture [14], and monitoring performance of athletes [15]. For many years real-time precise PNT applications were dominated by differential techniques such as real-time kinematics (RTK). In RTK, by forming between-satellite differences of between-receiver single differences, the following error sources are eliminated: satellite orbit and clock errors, ionosphere and troposphere signal delays, and hardware biases. The serious drawback of RTK is that it is area limited because a GNSS reference station nearby the rover receiver is required [16]. The distance to the reference station can be extended up to 100 km when supported by ionosphere corrections [17] and in network RTK (RTN) [18], or up to hundreds of kilometres in Wide Area RTK (WARTK) concept [19], but it is still far away from a global technique. The dependence on the reference station can be overcome by Precise Point Positioning (PPP) technique [20]. PPP is a single-receiver, autonomous technique that takes advantage of precise clocks and orbits, so the obtained results are strongly related to the quality of used products.