FCB estimation with three different PPP models: equivalence analysis and experiment tests

Precise and reliable fractional cycle bias (FCB) products are critical for ambiguity resolution of precise point positioning (PPP). Three PPP models are usually adopted to generate the FCB products, i.e., the traditional ionospheric-free combined PPP (IF-PPP) model, the uncombined and unconstrained PPP model (UU-PPP) as well as the ionospheric-constrained PPP (IC-PPP) model. Considering that different observation models and ionospheric delay constraints are used, the applicability and interoperability of the obtained FCB products are assessed. We presented the equivalent conversion formulas of different FCB products obtained with different PPP models, which are then converted and compared. The root mean square (RMS) of the wide-lane (WL) FCB differences for IF-UU, IF-IC and UU-IC is 0.021, 0.024 and 0.010 cycles, while the RMS of the narrow-lane FCB differences is 0.028, 0.018 and 0.021 cycles. The precision of the WL FCBs based on the uncombined PPP models is higher than that based on the IF-PPP model since the new WL ambiguities derived from the uncombined ambiguities are free of the pseudorange noise. The equivalence of the FCB products estimated from the three different PPP models is confirmed in theory and by experiment results. To further evaluate the performance of the three PPP models, the positioning accuracy, the convergence time and the ambiguity fixing success rate are calculated using IGS data. The maximum positioning difference is less than 0.9mm among the three PPP models. Compared to the float solutions of the IF-PPP, UU-PPP, IC-PPP with GIM model or with re-injected ionospheric delay corrections, the convergence time is shortened by 38.5%, 46.2%, 50.0% and 87.8% and the positioning accuracy improved by 27.1%, 38.9%, 41.1% and 25.7%, respectively. The ambiguity fixing success rate of the uncombined PPP models is slightly higher than that of the combined model, and fast ambiguity-fixed solution can proceed with high-precise ionospheric delay corrections.