Abstract The real-time precise point positioning (RT PPP) with ambiguity resolution (AR) technique has attracted increasing attention due to its high accuracy and low cost. With the availability of RT precise orbits, clocks, and multi-frequency phase bias products for multi-GNSS constellations, which are provided freely by the Centre National d’Etudes Spatiales (CNES), it is possible now to investigate RT PPP AR based on undifferenced and uncombined PPP model. However, only a few studies described these phase bias model tersely, especially in the multi-frequency and multi-system PPP AR. Moreover, the impact on inter-frequency clock bias (IFCB) for triple-frequency GPS/Galileo RT PPP by using the phase bias products have not been investigated. In this paper, the transformation between multi-frequency phase bias model and integer recovery clock (IRC) model was formulated where IFCBs are well considered. Meanwhile, the convergence time, positioning accuracy, narrow-lane ambiguity N1 fixing rate of GPS/Galileo PPP AR were analyzed by using a modified version of the Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator (PPP-WIZARD). Experiments with GPS/Galileo observation from 50 stations over 32 days were performed in static and kinematic modes. Data were processed with four strategies: dual-frequency float and fixed PPP, triple-frequency float and fixed PPP. Results showed that the effect of the IFCB of GPS Block IIF could be mitigated by using the phase bias products from CNES. Among four solutions, the triple-frequency PPP AR achieved the fastest convergence time of 10.43 and 12.55 min in static and kinematic modes, respectively. The average RMS values are 1.2, 1.5, 3.1 cm in static mode while 2.0, 2.5, 3.8 cm in kinematic mode with the 3 h observation session by triple-frequency PPP AR in the east, north and up directions, respectively. Compared with dual-frequency PPP AR, triple-frequency PPP AR could contribute to improving the performance of convergence time and positioning accuracy, especially when few satellites can be observed.

中文翻译：

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使用基于 CNES 相位偏差的模糊分辨率评估 GPS/Galileo 实时精确点定位

摘要 具有模糊分辨率（AR）技术的实时精确点定位（RT PPP）因其高精度和低成本而受到越来越多的关注。随着国家空间研究中心 (CNES) 免费提供的用于多 GNSS 星座的 RT 精确轨道、时钟和多频相位偏置产品的可用性，现在可以研究基于 RT PPP AR无差异和无组合的 PPP 模型。然而，只有少数研究简洁地描述了这些相位偏置模型，特别是在多频率和多系统 PPP AR 中。此外，尚未研究使用相位偏置产品对三频 GPS/Galileo RT PPP 的频率间时钟偏置 (IFCB) 的影响。在本文中，在充分考虑 IFCB 的情况下，制定了多频相位偏置模型和整数恢复时钟 (IRC) 模型之间的转换。同时，利用改进版的整数零差模糊度分辨率演示器（PPP-WIZARD）对GPS/Galileo PPP AR的收敛时间、定位精度、窄线模​​糊度N1固定率进行了分析。在静态和动态模式下进行了 50 个站点超过 32 天的 GPS/伽利略观测实验。数据采用四种策略处理：双频浮动和固定 PPP、三频浮动和固定 PPP。结果表明，通过使用 CNES 的相位偏置产品，可以减轻 GPS Block IIF 的 IFCB 的影响。在四种解决方案中，三频 PPP AR 在静态和运动模式下分别实现了 10.43 和 12.55 分钟的最快收敛时间。平均 RMS 值在静态模式下为 1.2、1.5、3.1 厘米，而在运动模式下的平均 RMS 值分别为 2.0、2.5、3.8 厘米，通过三频 PPP AR 在东、北和向上方向进行 3 小时观测。与双频 PPP AR 相比，三频 PPP AR 有助于提高收敛时间和定位精度的性能，尤其是在可观测卫星较少的情况下。