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

TL;DR

This paper clarifies the theoretical relationship between sliding window-factor graph optimization (SW-FGO) and Kalman filter variants, proposing a recursive FGO framework that reproduces Kalman filters under certain conditions and highlighting SW-FGO's advantages in nonlinear, non-Gaussian scenarios.

Contribution

It establishes the necessary conditions connecting SW-FGO and Kalman filter variants, and introduces Re-FGO to unify their representations, clarifying their relationship and practical benefits.

Findings

Re-FGO exactly reproduces EKF, IEKF, REKF, and RIEKF under explicit conditions.

SW-FGO offers measurable benefits in nonlinear, non-Gaussian regimes.

Theoretical connection enables better understanding of FGO and Kalman filter performance.

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.