Kalman Filtering-Enhanced Factor Graph Optimization for GNSS RTK in Complex Environment

The factor graph optimization (FGO) approach is increasingly utilized in Global Navigation Satellite System (GNSS) due to the global optimization capability and incremental computation paradigm. However, existing methods remain challenged by carrier phase ambiguity resolution (AR) and exhibit limited robustness in complex environments. This difficulty primarily arises from limited satellite visibility and frequent cycle slips in such environments, which cause repeated re-initialization and large float solution errors, making AR less reliable. Under these conditions, positioning accuracy largely depends on the effective use of historical information, where the efficiency and consistency of the marginalization process in FGO play a critical role. To mitigate potential inconsistency caused by time-varying measurement noise, robust modeling and adaptive weighting strategies are introduced. This paper proposes a Kalman Filtering-enhanced marginalization strategy of FGO-based GNSS Real Time Kinematic (RTK) to propagate the carrier phase ambiguity. The innovation lies in an adaptive weighting of historical information. We incorporate the marginalization process into the Kalman filter. The marginalized double differenced ambiguities serve as state predictions, while the current observations within the sliding window form the measurement equations. In this way, a recursive marginalization chain for carrier phase ambiguities is constructed using the Kalman filter. Experimental results in urban canyons demonstrate that the proposed Kalman filtering-enhanced FGO-RTK (KF-FGO-RTK) framework achieves 60.1% and 26.2% improvements of RMS over conventional Extended Kalman Filter (EKF)-based and standard FGO-based solutions, respectively.