发表机构
Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil; Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia, Genova, Italy（里约热内卢天主教大学; 动态腿部系统实验室，意大利理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对经典SO(3)-EKF的虚假可观测性问题，提出迭代不变扩展卡尔曼滤波(IterIEKF)用于地标辅助惯性3D定位，通过数值仿真证明其在估计精度和一致性上优于现有方法。
AI 中文摘要
由三维地标测量辅助的惯性导航系统构成了机器人感知和状态估计中的一个基本问题。经典的基于SO(3)的扩展卡尔曼滤波(SO(3)-EKF)方法提供了实用的解决方案，但存在虚假可观测性问题，即滤波器在不可观测方向上变得过度自信，导致估计性能下降。不变扩展卡尔曼滤波(IEKF)通过将系统动力学重新表述为李群上的群仿射系统来解决这一局限性，尽管其测量更新并未完全满足某些状态兼容性属性。最近，提出了迭代不变扩展卡尔曼滤波(IterIEKF)以进一步改进IEKF，通过在低噪声条件下确保估计状态保持在观测状态流形上，同时不确定性被限制在其切空间中。在这项工作中，我们首次将IterIEKF公式化并应用于基于地标的惯性3D定位。通过数值仿真，我们表明所提出的方法在估计精度和一致性方面均优于经典的SO(3)-EKF、迭代SO(3)-EKF和IEKF。
英文摘要
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.
