Robust Geometric Filtering via Linear Constraint

yuqiangjin; Shaoqing Xu; Xusheng Yang; Minglei Fu; Wen-An Zhang; Boris Sokolov; Vladislav Alekseevich Sobolevskii; Valerii Zakharov

yuqiangjin Zhejiang University of Technology
Shaoqing Xu Zhejiang University of Technology
Xusheng Yang Zhejiang University of Technology
Minglei Fu Zhejiang University of Technology
Wen-An Zhang Zhejiang University of Technology
Boris Sokolov St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences
Vladislav Alekseevich Sobolevskii St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences
Valerii Zakharov St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences

Keywords: Geometric Filtering, Model Mismatch, Robust Estimation, Kalman Filtering, Lie Groups and Lie Algebras

Abstract

Geometric filters are known to be highly sensitive to model mismatch — a critical limitation in real-world applications. To address this issue, this paper introduces a novel filtering framework grounded in linear constraint enforcement. We begin by analyzing how model mismatch propagates through the filtering process in group-affine systems, revealing the fundamental mechanism behind error accumulation in conventional geometric filters such as the invariant extended Kalman filter (InEKF). Building on this insight, we design a constrained filtering strategy that actively regulates the gain matrix along the direction of model deviation, thereby suppressing error growth while preserving the intrinsic geometric structure of the underlying Lie group manifold. Notably, the proposed method achieves this enhanced robustness without sacrificing computational efficiency, making it suitable for real-time deployment. Finally, simulations and real-world experiments on INS/GNSS integrated navigation demonstrate that the proposed method consistently achieves substantially improved estimation accuracy compared to the standard InEKF, offering an effective solution for robust filtering in complex environments.