FGO MythBusters: Explaining how Kalman Filter variants achieve the same performance as FGO in navigation applications
Baoshan Song, Ruijie Xu, Li-Ta Hsu
TL;DR
This paper analyzes when sliding window-factor graph optimization (SW-FGO) and Kalman filter variants (KFV) are theoretically equivalent in navigation state estimation. It introduces Re-FGO, a recursive FGO framework, and derives explicit conditions—the Markov property, Gaussian noise with $L_2$ loss, and a one-state window—under which EKF, IEKF, REKF, and RIEKF are exactly regenerated by SW-FGO. Empirically, FG‑KFV tracks KF performance under these conditions, while SW-FGO offers measurable advantages in nonlinear, non-Gaussian regimes at predictable compute costs, with longer windows yielding further gains. The work clarifies the relationship between filtering and optimization approaches, highlights SW-FGO’s numerical estimation and deep learning integration advantages, and provides open-source code for reproducibility and further research.
Abstract
Sliding window-factor graph optimization (SW-FGO) has gained more and more attention in navigation research due to its robust approximation to non-Gaussian noises and nonlinearity of measuring models. There are lots of works focusing on its application performance compared to extended Kalman filter (EKF) but there is still a myth at the theoretical relationship between the SW-FGO and EKF. In this paper, we find the necessarily fair condition to connect SW-FGO and Kalman filter variants (KFV) (e.g., EKF, iterative EKF (IEKF), robust EKF (REKF) and robust iterative EKF (RIEKF)). Based on the conditions, we propose a recursive FGO (Re-FGO) framework to represent KFV under SW-FGO formulation. Under explicit conditions (Markov assumption, Gaussian noise with L2 loss, and a one-state window), Re-FGO regenerates exactly to EKF/IEKF/REKF/RIEKF, while SW-FGO shows measurable benefits in nonlinear, non-Gaussian regimes at a predictable compute cost. Finally, after clarifying the connection between them, we highlight the unique advantages of SW-FGO in practical phases, especially on numerical estimation and deep learning integration. The code and data used in this work is open sourced at https://github.com/Baoshan-Song/KFV-FGO-Comparison.