Sliding window factor graph optimization (SW-FGO) is widely recognized for its robustness, yet its theoretical relationship with the extended Kalman filter (EKF) remains a subject of debate. This paper establishes the sufficient conditions to bridge SW-FGO with the iterated extended Kalman filter (IEKF). We introduce recursive FGO (Re-FGO), a conceptual perspective that employs a two-stage marginalization pipeline to mathematically degenerate the factor graph optimization to the IEKF recursive update. By enforcing the Markov assumption and a single-state window, we prove the theoretical equivalence between the IEKF and Re-FGO. This degeneration is validated through simulations and real-world urban GNSS and INS tightly coupled fusion experiments. The results confirm that Re-FGO exactly reproduces IEKF estimation behavior, demonstrating that the two-stage marginalization pipeline is foundational to enforce structural consistency, thereby successfully uniting graph-based smoothing and filtering paradigms under unified optimization principles.

翻译：滑动窗口因子图优化（SW-FGO）因其鲁棒性广受认可，但其与扩展卡尔曼滤波（EKF）的理论关系仍存争议。本文建立了将滑动窗口因子图优化与迭代扩展卡尔曼滤波（IEKF）桥接的充分条件。我们提出递归因子图优化（Re-FGO）这一概念框架，通过采用两阶段边缘化流程，从数学上实现因子图优化向迭代扩展卡尔曼滤波递归更新的退化。通过施加马尔可夫假设与单状态窗口，我们证明了IEKF与Re-FGO的理论等价性。该退化过程通过仿真实验和真实场景城市GNSS与INS紧耦合融合实验得到验证。结果表明，Re-FGO能够精确复现IEKF的估计行为，证明两阶段边缘化流程是强化结构一致性的基础，从而在统一优化准则下成功联合图优化平滑与滤波范式。