Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning

The BeiDou Navigation Satellite System (BDS) has completed third phase construction and currently provides global services, with a mixed constellation of BDS-2 and BDS-3. The newly launched BDS-3 satellites are equipped with rubidium and passive hydrogen maser (PHM) atomic clocks. The performance of atomic clocks is one of the cores of satellite navigation system, which will affect the performance of positioning, navigation and timing (PNT). In this paper, we systematically analyze the characteristics of BDS-2 and BDS-3 atomic clocks, based on more than one year of precise satellite clock products and broadcast ephemeris. Firstly, the results of overlapping Allan variations demonstrate that BDS-3 Rb and PHM clocks improve better in stability than BDS-2 Rb clock and are comparable to GPS IIF Rb and Galileo PHM clocks. Accordingly, the STDs of BDS-3 broadcast satellite clock are better than GPS and BDS-2, which are at the same level with that of Galileo. Secondly, the inter-system bias (ISB) between BDS-2 and BDS-3 is analyzed by satellite clock datum comparison and precise point positioning (PPP). Surprisingly, the discrepancy between BDS-2 and BDS-3 satellite clock datum has a great difference between products that could reach up to about 10 ns for WHU satellite clock products and broadcast ephemeris. Moreover, the ISBs between BDS-2 and BDS-3 satellite clocks are quite stable over one-year periods. Thirdly, due to the improved stability of BDS-3 atomic clock, the 68% positioning accuracy is better than 0.65 m at 10 min for BDS-3 PPP, based on broadcast ephemeris. Besides, the non-negligible bias between BDS-2 and BDS-3 will greatly affect the BDS precise data processing. The accuracy of positioning is greatly improved when considering the ISB.

Initial Results of Modeling and Improvement of BDS-2/GPS Broadcast Ephemeris Satellite Orbit Based on BP and PSO-BP Neural Networks

With the rapid development and gradual perfection of GNSS in recent years, improving the real-time service performance of GNSS has become a research hotspot. In GNSS single-point positioning, broadcast ephemeris is used to provide a space–time reference. However, the orbit parameters of broadcast ephemeris have meter-level errors, and no mathematical model can simulate the variation of this, which restricts the real-time positioning accuracy of GNSS. Based on this research background, this paper uses a BP (Back Propagation) neural network and a PSO (Particle Swarm Optimization)–BP neural network to model the variation in the orbit error of GPS and BDS broadcast ephemeris to improve the accuracy of broadcast ephemeris. The experimental results showed that the two neural network models in GPS can model the broadcast ephemeris orbit errors, and the results of the two models were roughly the same. The one-day and three-day improvement rates of RMS(3D) were 30–50%, but the PSO–BP neural network model was better able to model the trend of errors and effectively improve the broadcast ephemeris orbit accuracy. In BDS, both of the neural network models were able to model the broadcast ephemeris orbit errors; however, the PSO–BP neural network model results were better than those of the BP neural network. In the GEO satellite outcome of the PSO–BP neural network, the STD and RMS of the orbit error in three directions were reduced by 20–70%, with a 20–30% improvement over the BP neural network results. The IGSO satellite results showed that the PSO–BP neural network model output accuracy of the along- and radial-track directions experienced a 70–80% improvement in one and three days. The one- and three-day RMS(3D) of the MEO satellites showed that the PSO–BP neural network has a greater ability to resist gross errors than that of the BP neural network for modeling the changing trend of the broadcast ephemeris orbit errors. These results demonstrate that using neural networks to model the orbit error of broadcast ephemeris is of great significance to improving the orbit accuracy of broadcast ephemeris.

Rapid Earthquake Source Description Using Variometric-Derived GPS Displacements toward Application to the 2019 Mw 7.1 Ridgecrest Earthquake

Using near-field high-rate Global Positioning System (GPS) displacements to invert for earthquake fault slips in real time has the potential to improve the accuracy of earthquake early warning or tsunami early warning. For such applications, real-time retrieval of high-accuracy GPS displacements is essential. Here, we report on rapid modeling of the 2019 Mw 7.1 Ridgecrest earthquake with real-time GPS displacements derived from a variometric approach with readily available broadcast ephemeris. This method calculates station variations in real time by differencing continuous phase observations and does not rely on precise orbit and clock information. The phase ambiguity is also removed, and thus the method does not suffer from a relatively long convergence time. To improve the accuracy of variometric displacements, we use a local spatial filter to decrease the influence of residual errors that cannot be removed completely by the time difference. We invert for the centroid moment tensor, static fault slips, and fault rupture process from the derived displacements. Our results show that all inverted models are available within about 65 s after the origin time of the earthquake and are comparable with models inverted by real-time precise point positioning displacements. This study highlights the great value of variometric displacements for the rapid earthquake source description with only broadcast ephemeris.

Accuracy Evaluation of Broadcast Ephemeris for BDS-2 and BDS-3

The BDS-3 system was completed in July 2020 and began to provide services to users around the world. The inspection of its operation, especially the detailed evaluation of the orbit, clock error, TGD and other indicators, plays an important role in the subsequent positioning. This study conducts an investigation of the satellite broadcast ephemeris of the BDS-2 and BDS-3. The difference between the satellite orbit position calculated by the broadcast ephemeris and the position calculated by the precise ephemeris is used for analysis. First, the ephemeris form January 2020 to February 2020 are investigated. The results show that the broadcast ephemeris accuracy of the BDS-2 MEO satellite is the highest, while the GEO satellite broadcast ephemeris accuracy is the lowest. And their three-dimensional orbit difference is 3m and 7.5m, respectively. Second, the BDS-3 MEO satellite broadcast ephemeris accuracy is higher than the BDS-2, its three-dimensional orbit accuracy is about 0.39m, while its clock error is slightly smaller than the BDS-2. The result of ephemeris calculation is basically equivalent to the clock error of satellite-to-earth observation, which is related to the addition of the clock error of the inter-satellite link in the BDS-3. Finally, the clock error of the BDS-3 MEO satellite with the H clock is basically the same as that of the MEO satellite with the Rb clock.