Abstract
An unwritten rule to resolve GNSS ambiguities in precise point positioning (PPP-AR) is that users should follow faithfully the frequency choices and observable combinations mandated by satellite clock and phase bias providers. Switching to other frequencies of measurements requires that the satellite clocks be converted, albeit in a roundabout way, to agree with the new frequencies of code biases. Satellite phase biases, on the other hand, are prescribed conventionally as wide-lane and narrow-lane combinations, which prevents users from resolving other phase combinations in the case of multi-frequency observables. We therefore develop an approach to compute observable-specific phase biases (phase OSBs) in concert with the legacy, but ambiguity-fixed, satellite clocks to enable PPP-AR over any frequency choices and observable combinations at the user end, i.e., all-frequency PPP-AR. In particular, the phase OSBs on the baseline frequencies (e.g., L1/L2 for GPS and E1/E5a for Galileo) are estimated by decoupling the code OSBs pre-aligned with the satellite clocks; then satellite clocks are re-estimated by holding pre-resolved undifferenced ambiguities and phase OSBs on the baseline frequencies; finally, all third-frequency phase OSBs are determined by introducing the ambiguity-fixed satellite clocks above. We used a global network of multi-frequency GPS/Galileo data over a month to verify this approach. In dual-frequency PPP-AR using GPS L1/L2, L1/L5, Galileo E1/E5a, E1/E5b, E1/E5 and E1/E6 signals, over 95% of wide-lane and narrow-lane ambiguity residuals were within ±0.25 and ±0.15 cycles, respectively, after the code and phase OSB corrections on raw GNSS measurements. As a result, the ambiguity fixing rates reached around 95% in all PPP-AR tests, though it was only the satellite clocks aligned with the GPS L1/L2 and Galileo E1/E5a pseudorange that were applied throughout. We stress that the key to computing such phase OSBs for all-frequency PPP-AR is that the code OSBs have the same bias datum as that of the satellite clocks.
Highlights
Undifferenced ambiguities of GNSS precise point positioning (PPP) are contaminated by various biases originating from both satellites and receivers (Zumberge et al 1997)
The phase OSBs in panels c) and g) are computed using the DLR (Deutsches Zentrum für Luft- und Raumfahrt) daily differential code biases (DCBs). These DCBs are converted into code OSBs which are plotted in panels d) and h) (Villiger et al 2019)
OSBs in panels a and e are computed using the WUM code OSBs, whereas those in panels (c) and (g) are based on the DLR DCBs. “p2p” stands for “peak-to-peak” which shows the mean peak-to-peak OSB variation during the 30 days for all GPS/Galileo satellites the better performance of DLR based OSBs, it is the phase OSBs in panels a) and e) that are used throughout this study for all-frequency PPP to enable undifferenced ambiguity resolution (PPP-AR)
Summary
Undifferenced ambiguities of GNSS precise point positioning (PPP) are contaminated by various biases originating from both satellites and receivers (Zumberge et al 1997) These biases are observable-specific which depend on tracking channels and observation frequencies, and divided into the code biases within pseudorange and the phase biases within carrier-phase measurements. A dilemma is that if one prefers GPS C1W/C5Q pseudorange and L1W/L5Q carrier-phase for PPP, for example, bias providers would be advised to recompute their satellite clocks and phase biases using the new four observables, or adapt their legacy satellite products using a clumsy chain of differential code biases (DCBs) to fit the wide-lane, narrow-lane and ionosphere-free combinations (e.g., Elmezayen and El-Rabbany 2019; Wen et al 2020). Liu et al (2020) extended phase OSBs to Galileo and BDS-2 triplefrequency signals They showed that phase OSBs could be estimated using uncombined triple-frequency PPP corrected for both pre-determined GPS IFCBs and code biases.
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