Optimal Carrier-Phase Integer Combinations for Modernized Triple-Frequency BDS in Precise Point Positioning

The latest generation of Global Navigation Satellite System (GNSS) satellites are transmitting signals on three or more frequencies, it brings new opportunities and challenges for data integration in Multi-GNSS Experiment (MGEX). To reduce the convergence time, less computationally intensive method is three-carrier ambiguity resolution (TCAR). But the three combinaitons can not be found in precise point positioning (PPP) yet, especially for the third generation BeiDou Navigation Satellite System (BDS-3). This contribution concentrates on the multi-frequency carrier-phase integer combinations for BDS-3 in PPP. More specifically, the triple-frequency plane is degraded to two-dimensional plane for BDS-3 under the assumption of a low observation noise. And then third frequency coefficient should be limited as a constraint, considering that inter frequency bias (IFB) is dynamic quantity. Thereafter, a new searching algorithm based on the Satisfiability Modulo Theories (SMT) is presented to search the optimal integer combinations fast. Meanwhile, ionosphere-free combinations are exhibited and are not suitable for TCAR. Futhermore, the availability of the SMT-based searching algorithm (SMTSA) is verified. Finally, the most interesting carrier-phase combinations that can be used for PPP ambiguity resolution are screened out for later research. Meanwhile, in order to give a referenced comprehensive assessment of the integer combination, some valuable combinations for BDS-3 are displayed. It provides scientific support for the triple-frequency AR which has less convergence time than dual-frequency AR. Moreover, it also gives the important and valuable reference for future research on multi-frequency ambiguity-enabled PPP.