# Multipath Error Fusion Modeling Methods for Multi-GNSS
## 1 Introduction  
The multipath effect refers to the phenomenon where signals from satellites arrive at the receiver antenna through multiple paths due to reflection and scattering. Both pseudorange and carrier phase measurements are affected by it. Theoretically, the maximum value of multipath on phase measurements can reach 1/4 of the wavelength [1], so the influence should be considered when using global navigation satellite system (GNSS) technology to carry out high-precision data processing. In order to mitigate the multipath error, we can model it like some of the other errors in GNSS data processing. Sidereal filtering (SF) is a widely used multipath error mitigation method. Some scholars [2, 3] have found that the multipath error could be separated and modeled by using the periodic repetition characteristics of the satellite orbit, and then the observations of the following days couldbe corrected and the multipath error will be mitigated. With the deepening of research, [PERSON] et al. found that the repetition period of te global positioning system (GPS) satellites is not a simple sidereal day, and there are also differences between different satellites [4]. [PERSON] et al. compared the methods of using SF based on the coordinate domain and the observation domain, and showed that the former is more computationally efficient while the latter can achieve better improvements [5]. Compared with SF, the description of the multipath error in the space domain is also an effective solution to mitigate its influence. [PERSON] and [PERSON] established the lookup table for the antenna [6; 7], and [PERSON] et al. proposed the error correction method to establish the multipath hemispherical map by using a common receiver clock for the multiple antennas [8; 9]. In the past, multipath modeling methods have mainly focused on the GPS. However, with the gradual improvement of the BeiDou navigation satellite system (BDS), it has been a research focus in recent years, and many studies about its performance have been published. [PERSON] et al. used the SF method to carry out multipath modeling research for the regional BeiDou navigation satellite system (BDS2), and pointed out that the orbit repeat periods of satellites from different constellations are different [10]. The SF based on single-differenced residuals, which are mapped from double-differenced observation residuals, was used to mitigate the multipath error. [PERSON] et al. pointed out that the above additional constraint for double-differenced residuals is not appropriate, and new errors will be mixed into the positioning results [11]. They extended [PERSON]'s method based on the multipath hemispherical map to mitigate the multipath error of BDS in the double-differenced observation domain and obtained some useful achievements. When separating the multipath error of different constellations in BDS, a stationary geostationary earth orbit (GEO) satellite should be selected as the reference satellite, which reduces the application scope of the method. Besides BDS, the Galileo navigation satellite system in Europe is also developing rapidly [12]. In addition, with the recovery of the Russian economy in recent years, the Global Navigation Satellite System (GLONASS) realized full constellation operation again in 2011. According to the official statistics of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX), more than 120 satellites of the four major navigation satellite systems have been operating normally in orbit as of the end of November 2020 [13]. In order to solve the problem of the limited number of available satellites for a single navigation system in complex environments, the integration of multi-GNSS will be the development trend of GNSS high-precision data processing in the future. However, there is little research on the multipath error modeling for Galileo and GLONASS. At the same time, with the development of GNSS, the issue of compatibility and interoperability has gradually received attention.