Multi-frequency phase-only PPP-RTK model applied to BeiDou data

Typically, navigation software processes global navigation satellite system (GNSS) phase observables along with the code observables to achieve high-precision positioning. However, the unmodeled code-related errors, typically multipath effects, may deteriorate the positioning performance. Such effects are well known for the second generation BeiDou navigation satellite system (BDS-2). To prevent this adverse effect on the state-of-the-art positioning technique, namely integer ambiguity resolution-enabled precise point positioning (PPP-RTK), we propose a multi-frequency phase-only PPP-RTK model. This model excludes the code observables and addresses the rank deficiency problem underlying the phase observation equations at the undifferenced and uncombined level. To verify the model, we collect five-day triple-frequency BDS 30-s data from a network of seven reference stations (about 112 km apart) to estimate the products on the network side. Based on these products, we conduct simulated dynamic positioning at a user station to test the phase-only PPP-RTK model and compare it with the customary code-plus-phase (CPP) model. The results show that the satellite phase biases, existing only at the third frequency, have a precision of better than two centimeters, while the precision of the satellite clock and ionospheric delay is better than eight centimeters. Due to the strong correlation between individual corrections, it is necessary to assess the quality of combined products, including the satellite clock, satellite phase bias and ionospheric delay, the precision of which is several millimeters to two centimeters, which is sufficiently precise for user positioning. Regarding BDS-2 positioning, the time-to-first-fix (TTFF) of the CPP PPP-RTK is 12 epochs, while it is only three epochs for the phase-only PPP-RTK. The reason why the CPP model underperforms the phase-only model is that the BDS-2 data collected are subject to notable code multipath. We show that the code multipath in the third-generation BDS (BDS-3) data is mild, so the CPP PPP-RTK achieves instantaneous centimeter-level positioning with a TTFF of one epoch. The BDS-3 phase-only PPP-RTK obtains virtually the same positioning results, but the TTFF is two epochs. When combining BDS-2 with BDS-3, the TTFF of both models remains unchanged compared to that of the BDS-3 solutions, implying that ambiguity resolution based on the stronger dual-system CPP model is robust to the BDS-2 code multipath. However, the ambiguity-float solution of the CPP PPP-RTK is adversely affected by the code multipath and requires 43 epochs to convergence, while its phase-only counterpart needs 36 epochs.