Degeneration of Sliding-Window Factor Graph Optimization into Iterated Extended Kalman Filtering

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.