Inter-system PPP ambiguity resolution between GPS and BeiDou for rapid initialization

Rapid ambiguity resolution in precise point positioning (PPP-AR) has constantly been a difficulty preventing efficient initializations of user solutions. A successful initialization normally requires a few tens of minutes if only GPS data are processed, but can be accelerated significantly by integrating a second GNSS to both enhance the satellite geometry for faster ambiguity convergence and double the ambiguity quantity for higher partial-AR success rates. However, each GNSS asks for its own reference satellite to form resolvable ambiguities, namely intra-system PPP-AR. We propose to estimate station-specific inter-system phase biases (ISPBs) and then form resolvable ambiguities between, instead of within, GNSS (i.e., inter-system PPP-AR) aiming at providing one more ambiguity candidate for more efficient partial AR. We use 24 days of 5-s GPS/BeiDou data from 47 stations in China spanning an area of roughly 2000x2000km to carry out both intra- and inter-GPS/BeiDou PPP-AR. We find that about 85% of ISPBs vary minimally within 0.05cycles from day to day, favoring precise predictions for real-time PPP-AR, despite the rare subdaily ISPB anomalies of up to 0.1cycles and abrupt jumps of up to 0.3cycles at a few stations. From hourly kinematic solutions, we find that 42.3% of them can be initialized successfully within 5min in case of inter-GPS/BeiDou PPP-AR in contrast to only 29.7% in case of intra-GPS/BeiDou. The mean initialization time is therefore reduced appreciably from 649 to 586s. This 10% improvement, though minor, is reasonable and still encouraging on account of the fact that only one extra resolvable ambiguity is contributed during the transition from intra- to inter-GPS/BeiDou PPP-AR, while both actually have the same model strength. Moreover, we provide a preliminary theoretical framework to implement inter-GNSS or tightly coupled GNSS models which can be extended to other multi-GNSS analysis.