The PPP-RTK system, which is capable of providing a centimeter-level real-time positioning service for an unlimited number of users, is becoming a promising tool in mass-market applications such as smartphones, the Internet of Things (IoT), and the automotive industry. The extended Kalman filter (EKF) is the conventional method for parameter estimation in the existing PPP-RTK system. Recently, an alternative method known as factor graph optimization (FGO), which fully leverages the time correlation among current and historical measurements, has the potential to further improve the accuracy and robustness of PPP-RTK solutions. In this contribution, a factor graph optimization-based PPP-RTK framework is developed, where raw pseudorange, phase measurements, precise atmospheric corrections, and time-differenced carrier-phase (TDCP) measurements serve as factors in FGO estimators. The continuously tracked phase ambiguities are estimated as the time-invariant state node and propagated by marginalization while ambiguity resolution is conducted independently between epochs. A second optimization process with the utilization of ambiguity-resolved solutions and time-differenced carrier-phase (TDCP) measurements is conducted to further improve the reliability of positioning results. The effectiveness of the proposed method is evaluated by vehicular tests in urban environments. Results indicate that the FGO method could improve the performance of ambiguity resolution by reducing the ambiguity search space and increasing the ratio values, leading to a significant accuracy improvement of 55% in an open-sky environment compared to the traditional EKF-based method. Furthermore, in GNSS signal partly block scenes, the FGO-based PPP-RTK is capable of obtaining more robust and accurate positioning solutions with fewer outliers compared to the EKF method.

PPP-RTK系统能够为无限数量的用户提供厘米级实时定位服务，正在成为智能手机、物联网(IoT)和移动设备等大众市场应用的一个有前景的工具。汽车行业。扩展卡尔曼滤波器（EKF）是现有PPP-RTK系统中参数估计的常规方法。最近，一种称为因子图优化（FGO）的替代方法充分利用了当前和历史测量之间的时间相关性，有可能进一步提高 PPP-RTK 解决方案的准确性和鲁棒性。在本文中，开发了基于因子图优化的 PPP-RTK 框架，其中原始伪距、相位测量、精确大气校正和时差载波相位 (TDCP) 测量作为 FGO 估计器中的因子。连续跟踪的相位模糊度被估计为时不变状态节点，并通过边缘化进行传播，而模糊度解析在历元之间独立进行。利用模糊度解决方案和时差载波相位（TDCP）测量进行第二次优化过程，以进一步提高定位结果的可靠性。通过城市环境中的车辆测试评估了所提出方法的有效性。结果表明，FGO 方法可以通过减小模糊度搜索空间和增加比率值来提高模糊度解析性能，与传统的基于 EKF 的方法相比，在开放天空环境中精度显着提高 55%。此外，在GNSS信号部分遮挡的场景中，与EKF方法相比，基于FGO的PPP-RTK能够获得更鲁棒、更准确的定位解，且异常值更少。