Analysis of Triple-Frequency PPP Ambiguity Resolution with Different Ambiguity Fixing Methods

Abstract

Accurate ambiguity resolution (AR) is critical for precise point positioning (PPP). Triple-frequency observations enable longer wavelength combinations, improving AR performance. This study evaluates four AR algorithms, Integer Least Squares (ILS), Partial Ambiguity Resolution (PAR), Best Integer Equivariants (BIEs), and Integer Aperture Bootstrapping (IAB), using triple-frequency observations from 275 MGEX stations and a kinematic vehicle. The results show that PAR achieves the fastest convergence, within 1.0 min at the 68th percentile and 3.0 min at the 84th percentile. Satellites excluded by PAR are typically 10–12° lower in elevation than retained ones, and their exclusion is driven more by ambiguity geometry and noise than by large fractional parts. In the kinematic vehicle test, BIE offers superior stability, with RMS errors of 0.042 m (east) and 0.059 m (north), while the ILS fixing rate drops below 6%, and PAR remains at 97%. A dual-frequency baseline further shows that the third frequency benefits all four methods: in terms of the station-averaged 86th-percentile convergence time, ILS and IAB gain the most (−43% and −42% horizontally), whereas its effect on positioning precision is modest (1–28% in all components), with PAR remaining the most precise method.