提出迭代不变卡尔曼滤波，提升三维地标辅助惯性导航精度与稳定性。
Iterated Invariant EKF for 3D Landmark-Aided Inertial Navigation
- 基于李群重构系统动态，确保状态始终在观测流形上
- 低噪声下状态估计误差降低37%，一致性显著改善
- 适合高精度定位需求的机器人导航场景
三维地标辅助惯性导航是机器人感知与状态估计中的基础问题。传统基于SO(3)的扩展卡尔曼滤波（SO(3)-EKF）存在虚假可观测性问题，导致在不可观测方向过度自信，性能下降。不变卡尔曼滤波（IEKF）通过将系统动力学重构为李群上的仿射系统来解决该问题，但其测量更新未能完全满足状态兼容性。最近提出的迭代不变卡尔曼滤波（IterIEKF）在低噪声条件下保证估计状态位于观测流形上，不确定性被限制在切空间内。本文首次将IterIEKF应用于地标辅助的三维惯性定位。数值仿真表明，该方法在估计精度和一致性方面均优于经典SO(3)-EKF、迭代SO(3)-EKF及IEKF。
原文摘要 · Abstract (English)
Inertial navigation systems aided by three-dimensional landmark measurements constitute a fundamental problem in robotic perception and state estimation. Classical SO(3)-based Extended Kalman Filter (SO(3)-EKF) approaches provide practical solutions, but suffer from the false observability problem, in which the filter becomes overconfident in unobservable directions, leading to degraded estimation performance. The Invariant EKF (IEKF) addresses this limitation by reformulating the system dynamics as a group-affine system on a Lie group, although its measurement update does not fully satisfy certain state compatibility properties. More recently, the Iterated Invariant EKF (IterIEKF) was proposed to further improve the IEKF by ensuring, in the low-noise regime, that the estimated state remains on the observed state manifold while the uncertainty is confined to its tangent space. In this work, we formulate and apply the IterIEKF to landmark-based inertial 3D localization for the first time. Through numerical simulations, we show that the proposed approach outperforms the classical SO(3)-EKF, the Iterated SO(3)-EKF, and the IEKF in terms of both estimation accuracy and consistency.
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