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. 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. Crucially, the proposed method achieves this enhanced robustness without sacrificing computational efficiency, making it suitable for real-time deployment. Finally, simulations and experiments on an integrated inertial navigation and global navigation satellite system (INS/GNSS) demonstrate that the proposed approach achieves substantial improvements in estimation accuracy compared to the standard InEKF, offering an effective solution for robust filtering in complex environments.

Key words: Geometric filtering, model mismatch, robust estimation, Kalman filter, Lie groups and Lie algebras