Study on the Relationship Between the Equivalent GDOP and the Convergence Time of LEO-Augmented BDS PPP

Abstract

Compared with BeiDou satellites, low earth orbit (LEO) satellites travel faster and show greater changes in spatial geometry within the same duration. When they are served as navigation satellites and assist BDS precise point positioning (PPP), fast initialization can be realized. Usually, the geometry of a constellation is represented by the geometric dilution of precision (GDOP). However, traditional GDOP metric can only reflect the instantaneous positioning accuracy of standard navigation and positioning service rather than the convergence performance of PPP, and cannot be calculated when the number of instantaneous visible satellites is less than 4. Considering that the coverage fold of future LEO navigation-augmentation constellation may be below 4 and meanwhile it is meaningful to comprehensively describe the continuous impacts of satellite numbers, moving velocity, moving direction and geometric change level on the convergence process of PPP, the concept of equivalent GDOP (EGDOP) based on accumulated time is proposed. Then, thousands of LEO constellations and their observation data are simulated and used for the analysis of the relationship between the EGDOP of LEO constellation and the convergence time of LEO-augmented BDS PPP. The results show that for 1-min sessions the smaller the EGDOP, the shorter the convergence time and the higher the probability that PPP converge within 1 min. Under ideal ephemeris conditions, the probabilities of realizing fast PPP with the horizontal positioning accuracy better than 10 cm and convergence time below 1 min are 100%, 95% and 65% when the corresponding EGDOP are below 0.29, 0.30 and 0.51, respectively. The relevant results can be used as an important basis for the optimization design of future LEO navigation-augmentation constellations.