New GNSS signals have significantly augmented positioning service and promoted algorithmic innovations such as rapid PPP convergence. With the emerging of multifrequency signals, it becomes essential to thoroughly explore the contribution of third frequency pseudorange and carrier phase toward PPP. In this study, we research the role of the third frequency observations on accelerating PPP convergence, commencing from both stochastic and functional models. We first constructed the stochastic model depending on the observation noise and then introduced two uncombined functional models with respect to different inter-frequency bias (IFB) estimation strategies. The double-differenced residuals based on a zero baseline were used to evaluate the signal noises, which were 0.09, 0.07, 0.11, 0.01 and 0.09 m for Galileo E1/E5a/E5b/E5/E6 pseudorange and 0.24, 0.31 and 0.05 m for BeiDou B1/B2/B3. Besides, carrier phase observations E5a/E5/E6/B1I/B3I shared a comparable signal noise of 0.002 m, while the signal noises of E1/E5b/B2I were 0.003 m. Both BeiDou-2/Galileo and Galileo-only float PPP were implemented based on the dataset collected from 25 stations, spanning 30 days. Triple-frequency Galileo PPP achieved convergence successfully in 19.9 min if observations were weighted according to observation precision, showing a comparable performance of dual-frequency PPP. Meanwhile, the convergence time of triple-frequency float PPP was further shortened to 19.2 min when satellite pair IFBs were eliminated by estimating a second satellite clock. While the improvement of triple-frequency float PPP was marginal, triple-frequency PPP-AR using signals E1/E5a/E6 shortened the initialization time of the dual-frequency counterpart by 38%. Moreover, the performance of triple-frequency PPP-AR kept almost unchanged after we excluded the third frequency pseudorange observations. We thus suggest that the contribution of the third frequency to PPP mainly rests on ambiguity resolution, favored by the additional carrier phase observations.

新的GNSS信号显着增强了定位服务，并促进了算法创新，例如快速PPP收敛。随着多频信号的出现，有必要彻底探索第三频率伪距和载波相位对PPP的贡献。在本研究中，我们从随机模型和功能模型开始研究第三频率观测值在加速PPP收敛中的作用。我们首先根据观察噪声构建随机模型，然后针对不同的频率间偏差（IFB）估计策略引入两个未组合的功能模型。基于零基线的双差分残差用于评估信号噪声，其中Galileo E1 / E5a / E5b / E5 / E6伪距为0.09、0.07、0.11、0.01和0.09 m，伪距为0.24，北斗B1 / B2 / B3分别为0.31和0.05 m。此外，载波相位观测值E5a / E5 / E6 / B1I / B3I的可比信号噪声为0.002 m，而E1 / E5b / B2I的信号噪声为0.003 m。BeiDou-2 / Galileo和仅Galileo的浮动PPP都是基于从25个站点收集的30天的数据集而实现的。如果根据观测精度对观测值进行加权，则三频伽利略PPP会在19.9分钟内成功收敛，这表明双频PPP具有可比的性能。同时，通过估算第二个卫星时钟消除了卫星对IFB时，三频浮点PPP的收敛时间进一步缩短至19.2分钟。虽然三频浮点PPP的改善是微不足道的，使用信号E1 / E5a / E6的三频PPP-AR将双频对应物的初始化时间缩短了38％。此外，在排除第三频率伪距观测值之后，三频PPP-AR的性能几乎保持不变。因此，我们建议第三频率对PPP的贡献主要取决于歧义分辨率，这受到附加载波相位观测的支持。