Robust geometric filtering via linear constraint

To address the sensitivity of geometric filtering results to model mismatch, 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 model mismatch accumulation in conventional geometric filters such as the Invariant Extended Kalman Filter (InEKF). Second, we design a constrained filtering strategy that actively regulates the gain matrix along the direction of model deviation, thereby suppressing model mismatch 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 (Inertial Navigation System/Global Navigation Satellite System) 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.