satellite systems that already provide position, navigation, and timing services include American GPS, Russian GLONASS, European Galileo, Chinese BDS, Japanese Quasi-Zenith Satellite System (QZSS), and so on. [PERSON] et al. have also analyzed the signal-in-space ranging errors of the broadcast ephemeris messages of these five navigation satellite systems [2]. By the end of January 2018, the GPS/GLONASS/BDS/Galileo/QZSS constellation was composed of 31/24/14/15/3 satellites, respectively, with operational capability. Each navigation satellite system also has its own future constellation construction plan. For users, there will be more satellites available in the future, and these satellites will also have better performance (e.g., in 2020, the Chinese global BeiDou navigation satellite system (BDS-3) will be composed of five geostationary earth orbit (GEO), three inclined geosynchronous orbit (IGSO), and twenty-seven medium earth orbit (MEO) satellites). Recently, BDS-3 has entered the intensive launch phase, and two BDS-3 satellites were launched on October 15, 2018. At the end of October 2018, there are 18 BDS-3 satellites being tested ([[http://www.csno-tarc.cn/system/constellation](http://www.csno-tarc.cn/system/constellation)]([http://www.csno-tarc.cn/system/constellation](http://www.csno-tarc.cn/system/constellation))). The construction and in-orbit operation of multiple navigation satellite systems can provide more reliable and accurate results for global navigation satellite system (GNSS) applications (e.g., atmospheric remote sensing [3; 4; 5], precise point positioning [6; 7; 8], precise relative positioning [9; 10], and the calculation of Earth rotation parameters [11]). At the same time, the multiple constellations also bring great challenges to the data processing of multi-GNSS. In order to promote the scientific and engineering applications of multi-GNSS in high-precision fields, the International GNSS Service (IGS) initiated the multi-GNSS experiment (MGEX) in 2011 ([[ftp://igs.org/pub/resource/pubs/IGSM-GEXVF.pdf](ftp://igs.org/pub/resource/pubs/IGSM-GEXVF.pdf)]([ftp://igs.org/pub/resource/pubs/IGSM-GEXVF.pdf](ftp://igs.org/pub/resource/pubs/IGSM-GEXVF.pdf))). Generally, seven MGEX analysis centers (ACs) provide special multi-GNSS precise orbit products to MGEX. These ACs are the Centre National d'Etudes Spatiales (CNES) and Collecte Localisation Satellites (CLS) in France; the Center for Orbit Determination in Europe (CODE) in Switzerland; the Deutsches GeoForschungsZentrum (GFZ), the Technische Universitat Munchen (TUM), and the European Space Agency (ESA) in Germany; Wuhan University (WU) in China, and the Japan Aerospace Exploration Agency (JAXA) in Japan. Among them, CODE, GFZ, and WU can provide five-system final precise orbit products, and ESA have only provided two-week final precise orbit products in the past. Because the accuracy of satellite orbits directly affects the accuracy of GNSS user position, navigation, and timing applications, GNSS precise orbit determination (POD) technology has become one of the key technologies in some GNSS research institutes (e.g., MGEX ACs). The techniques for the precise orbit determination of GNSS satellites are mainly based on microwave GNSS observations and satellite laser ranging (SLR) data [12]. For these reasons, these institutes have independently developed or redeveloped corresponding GNSS POD software platforms. In general, the GNSS POD software platforms used by CNES/CLS, CODE, GFZ, TUM, ESA, WU, and JAXA are POD GINS [13], Bernese v5.3 [14], EPOS.P8 [15], Bernese v5.0 [16], NAPEOS 3.8 [17], PANDA [18], and MADOCA [19], respectively. In this paper, we mainly consider the processing method of microwave GNSS observations, and the process of GNSS POD; the error equations are established by using non-difference observations in all MGEX ACs, except for the double-difference observations used by Bernese v5.3.