FGO MythBusters: Explaining how Kalman Filter variants achieve the same performance as FGO in navigation applications

2025-10-31

AI Summary

Sliding-window factor graph optimization (SW-FGO) and Kalman filter variants (EKF, IEKF, REKF, RIEKF) are widely used in sequential state estimation, yet their theoretical relationships remain unclear. Method: This paper establishes rigorous equivalence conditions between SW-FGO and these Kalman filter variants under recursive estimation by introducing the Markov assumption, Gaussian noise modeling, and L2-loss constraints. It proposes a unified Recursive Factor Graph Optimization (Re-FGO) framework, which subsumes all aforementioned Kalman filter variants as special cases under specific assumptions. Contribution/Results: We prove that SW-FGO not only subsumes the estimation capabilities of Kalman filter variants but also achieves superior robustness and accuracy in nonlinear, non-Gaussian settings. Moreover, Re-FGO natively supports end-to-end integration with deep learning models. All algorithms and experimental data are publicly released to ensure full reproducibility.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Explaining theoretical relationship between sliding window FGO and Kalman filters
• Proposing recursive FGO framework to represent Kalman filter variants
• Highlighting SW-FGO advantages in nonlinear non-Gaussian navigation scenarios

Innovation

• Recursive FGO framework representing Kalman filter variants
• Sliding window FGO handling nonlinear non-Gaussian regimes
• Explicit conditions enabling exact regeneration of Kalman filters