Abstract
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.
Highlights
Precise point positioning (PPP) utilizes dual-frequency pseudorange and carrier-phase observations in single receiver to generate high-accuracy positioning solutions by using precise satellite orbits, clock corrections and other error models [1], [2]
Satisfiability Modulo Theories (SMT)-BASED SEARCHING ALGORITHM According to the above constraints, Traversal searching algorithm (TSA) obtains the feasible set by searching the whole range of coefficients i, j, and k
The results show that the combination (-2, 7, -4) has the largest inter frequency bias (IFB) amplification factor w, but its wavelength is so long that the influence of w can be ignored
Summary
Precise point positioning (PPP) utilizes dual-frequency pseudorange and carrier-phase observations in single receiver to generate high-accuracy positioning solutions by using precise satellite orbits, clock corrections and other error models [1], [2]. H. Qin et al.: Optimal Carrier-Phase Integer Combinations for Modernized Triple-Frequency BDS known as the LAMBDA method [7]. Qin et al.: Optimal Carrier-Phase Integer Combinations for Modernized Triple-Frequency BDS known as the LAMBDA method [7] It is characterized by a linear transformation based on the variance-covariance matrix which best decorrelates the unknown ambiguity parameters. Geng used a method of ionospheric prediction using ambiguity-fixed parameters from the PPP solution to correct the wide-lane carrier-phase observation [26]. Aiming at four problems about ambiguity-fixing in PPPAR, we fast select all feasible carrier-phase integer combinations which contain extra-wide-lane, wide-lane and narrowlane.
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