# A Parallel Approach for Multi-GNSS Ultra-Rapid Orbit Determination
## 1 Introduction  
Global Navigation Satellite System (GNSS) ultra-rapid orbit is the basis of geodetic research and real-time applications, such as real-time atmosphere monitoring [1, 2], real-time PPP [3, 4, 5], real-time satellite clock estimation [6], and real-time orbit determination of LEO satellite [7]. With the development of Galileo and implementation of BDS global service plan, the number of satellites in the constellation has increased dramatically to more than 130 [8]. Currently, the International GNSS Service (IGS), the Multi-GNSS Experiment and Pilot Project (MGEX) and the International GNSS Monitoring and Assessment System (iGMAS) have provided more than 500 global distributed stations. A combined multi-GNSS solution can effectively reduce systematic errors and improve the accuracy and reliability of satellite orbit. However, on the other hand, the increase in the number of satellite constellations and stations makes the processing model more complicated and results in larger computational burden [9], which decrease the computational efficiency ofmulti-GNSS ultra-rapid orbit determination [10]. Real-time or quasi-real-time users have higher requirements for the accuracy, stability, and update frequency of GNSS ultra-rapid orbits. Therefore, further research on the rapid determination of multi-GNSS predicted orbits is critical for its high-precision applications. GNSS orbit products that have been widely used are gradually developing toward multi-system, higher accuracy and higher update frequency. Since its establishment in 1994, IGS has vigorously carried out research on GNSS precise orbit determination, and the accuracy and reliability of the products have been continuously improved [11; 12]. At present, the accuracy of the ultra-rapid orbit is better than 5 cm, which is provided for real-time users. The details of the accuracy and latency of orbit products are shown in Table 1 ([[http://www.igs.org/products](http://www.igs.org/products)]([http://www.igs.org/products](http://www.igs.org/products)), accessed January 2019). IGS also generates experimental final combined multi-GNSS orbits, which include GPS, GLONASS, Galileo, BDS-2, BDS-3, and QZSS [13]. The IGS called for participation in MGEX in 2012 ([[http://mgex.igs.org](http://mgex.igs.org)]([http://mgex.igs.org](http://mgex.igs.org)), accessed January 2019). Subsequently, five analysis centers (ACs) provided multi-system orbit products, including CNES, TUM, GFZ, CODE and WUH. The later three ACs can provide the orbit product of GPS, GLONASS, Galileo and BDS, as well as QZSS. In recent years, ACs have increased the update frequency of ultra-rapid orbit for real-time applications ([[ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex/](ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex/)]([ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex/](ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex/)), accessed January 2019). IGS increased the update frequency from 12-h to 6-h. The frequency of ultra-rapid orbit has been further improved to 3-h by the German Research Centre for Geosciences (GFZ) (ftp.gfz-potadam.de, accessed January 2019). The analysis center at Wuhan university is the first to provide a 1-h update frequency ultra-rapid orbit product. The algorithm of precise orbit determination (POD) mainly uses dynamics and reduced dynamics methods [14; 15; 16; 17; 18]. The methods above are first applied to GPS satellite orbit determination and are widely used in GLONASS, Galileo, BDS and other satellite systems, as well as the combination of them with the development of GNSS [19; 20; 21; 22; 23; 24]. Based on this, the predicted orbit of ultra-rapid products is generally obtained by integration of initial orbit and force model parameters [25]. The accuracy of orbit for real-time applications is directly related to the accuracy of satellite orbit initial values and the length of extrapolation time.