# A Parallel Approach for Multi-GNSS Ultra-Rapid Orbit Determination
## 4 Conclusions  
A parallel ultra-rapid POD approach has been proposed in this study. The parallel approach properly makes use of parallel computing to improve the efficiency of multi-GNSS orbit determination. The construction of normal equations, parameter elimination and orbit extrapolation in the GNSS POD algorithm are optimized based on MPI/OpenMP. The following conclusions can be drawn:  
(1) The precision loss and feasibility of parallel POD are verified. The results show that 1D mean RMS of GPS, GLONASS, Galileo and BDS orbit in non-parallel mode are 1.3 cm, 2.7 cm, 2.7 cm, and 5.4 cm, respectively. Moreover, the precision loss of using the parallel approach is at the sub-millimeter level, which can be ignored, thus verifying the feasibility of the parallel method. (2) The improvement of efficiency by the parallel approach is analyzed in detail, including multiple factors such as the number of processes, the number of threads, the number of stations and the number of satellite systems. The results show that with the increase of the number of threads and processes, the efficiency of the parallel approach increases more obviously. The approach is more applicable to large reference networks and multiple satellite systems. (3) The superiority of the parallel approach used in multi-GNSS ultra-rapid POD is verified. The improvement of accuracy of predicted orbit with an increased update frequency of 1-h is analyzed in detail. The 1-h updated orbit determined by the parallel approach is compared with the 6-h updated orbit determined by the non-parallel approach, and the results show that the accuracy of GPS, GLONASS, Galileo and BDS are 33.4%, 31.4%, 40.1% and 32.8% higher than the 6-h results of the non-parallel approach, respectively. Additionally, the accuracy of the 1-h updated orbit is evaluated by comparing with IGS and CODE precise orbit products. The 1-h orbit product of Wuhan University is selected for comparison. The results show that the orbit with 1-h update frequency by the parallel approach has higher accuracy and stability. Further, statistical results show that the 1D mean RMS of the ultra-rapid predicted orbit of GPS, GLONASS, Galileo, and BDS with the proposed parallel algorithm is 3.2 cm, 5.1 cm, 5.6 cm and 11.8 cm, respectively. In summary, the proposed parallel approach can greatly improve the efficiency of multi-GNSS ultra-rapid orbit determination and enhance the update frequency from 6-h to 1-h, which can help for the improvement of the ultra-rapid orbit accuracy and stability. The proposed parallel approach makes it possible to use a denser network of reference stations for multi-GNSS ultra-rapid POD with high update frequency for real-time users. It should be noted that we adopted the ECOM1 SRP model for the one-step orbit determination of the GPS, GLONASS, Galileo and BDS in this study. For the specific elongated shape of Galileo satellites, orbit accuracy will be improved by using a prior model. In addition, clock determination is not related in this study, making it difficult to get the Signal In Space Range Error (SISRE). In the next studies, we will use an a priori model to reduce the orbit perturbations for Galileo, and we will combine the orbit and clocks through the processing in order to calculate clocks and orbital SISRE for the analysis of the algorithm. All authors contributed to the design of the study. [PERSON] and [PERSON] came up with the idea of the study. [PERSON] carried out the experiments and performed the data analysis. [PERSON], [PERSON], [PERSON] and [PERSON] discussed the results. [PERSON] wrote the manuscript with support of [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript. This research was founded by the National Key Research Program and Development of China (2020 YFB0505800, 2016 YFB0501900, and 2016 YFC0803102), the National Natural Science Foundation of China (41874032,42074012 and 42030109), the Liaoning Key Research and Development Program (2020 JH2/10100044).