Impact analysis of arc length in multi-GNSS ultra-rapid orbit determination based on the one-step method

With the development of near real-time and real-time high-precision global navigation satellite system (GNSS) applications, users' requirements for the accuracy and stability of ultra-rapid orbits have increased, especially for multi-constellation orbits. Generally, several factors affect the accuracy and stability of multi-GNSS ultra-rapid orbit determination; however, this study is focused only on analyzing the orbit arc length of ultra-rapid orbits of the GPS, GLONASS, BeiDou-2, and Galileo satellites based on the one-step method. To realize nearly ideal conditions in the process of analysis, one full year's rapid orbit products during 2018 provided by the GeoForschungsZentrum multi-GNSS experiment analysis center were used as fitted observed orbits and also as a reference orbit for comparison to the predicted orbit. In terms of residual analysis of orbit difference and stability analysis of Helmert transformation parameters, the numerical results showed that the optimal orbit arc lengths of quad-constellation medium earth orbit (MEO) satellites for 6 h and 3 h predicted ultra-rapid orbits based on the one-step method were in the range of 44–45 h and 41–44 h, respectively. Overall, for both 6 h and 3 h predictions, when only considering the impact of the orbit arc length on the accuracy and stability of the orbit itself, 44 h can be considered as the overlapping optimal orbit arc length of quad-constellation MEO satellitesʼ ultra-rapid orbits generated by the one-step method. In addition, these ranges of orbit arc length can contribute to the multi-GNSS ultra-rapid orbit determination. (paper)