揭示滑动窗口优化与迭代扩展卡尔曼滤波的理论等价性
Degeneration of Sliding-Window Factor Graph Optimization into Iterated Extended Kalman Filtering
- 提出递归因子图优化，通过两阶段边缘化实现理论降维
- 在单状态窗口下证明其与迭代扩展卡尔曼滤波完全等价
- 适用于需要统一平滑与滤波框架的定位系统研究者
滑动窗口因子图优化（SW-FGO）以其鲁棒性广受认可，但其与扩展卡尔曼滤波（EKF）的理论关系仍存争议。本文确立了将SW-FGO退化为迭代扩展卡尔曼滤波（IEKF）的充分条件。提出递归因子图优化（Re-FGO），采用两阶段边缘化流程，数学上将因子图优化退化为IEKF递归更新。在强马尔可夫假设和单状态窗口条件下，证明了IEKF与Re-FGO的理论等价性。仿真及真实城市环境下GNSS与INS紧耦合融合实验验证了结果：Re-FGO精确复现IEKF估计行为。表明两阶段边缘化是保证结构一致性的基础，成功在统一优化原则下融合基于图的平滑与滤波范式。
原文摘要 · Abstract (English)
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.
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