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With the modernization of Global Navigation Satellite System (GNSS), triple- or multi-frequency signals have become available from more and more GNSS satellites. The additional signals are expected to enhance the performance of precise point positioning (PPP) with ambiguity resolution (AR). To deal with the additional signals, we propose a unified modeling strategy for multi-frequency PPP AR based on raw uncombined observations. Based on the unified model, the fractional cycle biases (FCBs) generated from multi-frequency observations can be flexibly used, such as for dual- or triple- frequency PPP AR. Its efficiency is verified with Galileo and BeiDou triple-frequency observations collected from globally distributed MGEX stations. The estimated FCB are assessed with respect to residual distributions and standard deviations. The obtained results indicate good consistency between the input float ambiguities and the generated FCBs. To assess the performance of the triple-frequency PPP AR, 11 days of MGEX data are processed in three-hour sessions. The positional biases in the ambiguity-fixed solutions are significantly reduced compared with the float solutions. The improvements are 49.2%, 38.3%, and 29.6%, respectively, in east/north/up components for positioning with BDS, while the corresponding improvements are 60.0%, 29.0%, and 21.1% for positioning with Galileo. These results confirm the efficiency of the proposed approach, and that the triple-frequency PPP AR can bring an obvious benefit to the ambiguity-float PPP solution.

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The basic system of the BeiDou global navigation satellite system (BDS-3) with 18 satellites has been deployed since December 2018. As the primary frequency standard, BDS-3 satellites include two clock types with the passive hydrogen maser (PHM) and the rubidium atomic frequency standard (RAFS). Based on the final precise orbit and clock product from Xi’an Research Institute of Surveying and Mapping (XRS), the atomic clock performance of BDS-3 satellites is evaluated, including the frequency accuracy, frequency drift rate, and frequency stability, and compared with GPS block IIF satellites with RAFS, Galileo satellites with PHM, and BDS-2 satellites. A data auto-editing procedure to preprocess clock data and assess the clock performance is developed, where the assessed results are derived at each continuous data arc and the outliers are excluded properly. The stability of XRS product noise is given by using some stations equipped with high-precision active hydrogen masers (AHM). The best stability is 8.93 × 10−15 and 1.85 × 10−15 for the averaging time of 10,000 s and 1 day, which is basically comparable to one-third of the in-orbit PHM frequency stability. The assessed results show the average frequency accuracy and drift rate of BDS-3 with RAFS are slightly worse while the stability is better than BDS-2 medium earth orbit (MEO) satellites. The 10,000 s stability is better but the 1-day stability is worse than GPS, which may be related to the performance of the BDS-3 RAFS clock. As for BDS-3 with PHM, the frequency accuracy is slightly worse than Galileo PHM satellites; the drift rate, when excluding C34 and C35, is basically comparable to Galileo and significantly better than GPS satellites; the stability is comparable to Galileo, where the 10,000 s stability is slightly worse than Galileo and better than GPS. The 1-day stability among BDS-3 PHM, GPS IIF RAFS, and Galileo PHM satellites is basically comparable.