发表机构
School of Surveying and Geo-Informatics, Tongji University; School of Automation and Intelligent Sensing, Shanghai Jiao Tong University; School of Robotics, Wuhan University（同济大学测绘与地理信息学院; 上海交通大学自动化与智能感知学院; 武汉大学机器人学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文评估了基于不同几何误差定义的INS/ZUPT滤波方法，推导了多种几何滤波器模型，并通过实验证明其与传统EKF精度相当，但一致性优势有限。
AI 中文摘要
近年来，几何滤波器被引入以提高基于惯性的组合导航系统的精度和一致性。误差状态通过特定的群操作进行定义，在误差定义中引入了状态相关性，而传统间接卡尔曼滤波器所使用的加性误差则缺乏这种相关性。基于特定的几何误差，可以获得理想的一致性滤波模型。对于在参考坐标系中表示的零速测量，本文从不变滤波、双框架群滤波和等变滤波中推导出左误差过程模型和测量模型。重要的是，为左切群等变误差引入了一种新的群操作。分析表明，双框架群不变扩展卡尔曼滤波器（TFG-IEKF）和切群等变滤波器（TG-EqF）相比不变扩展卡尔曼滤波器（IEKF）并未提供显著的一致性优势。使用INS/ZUPT测量系统的实验表明，在较小的初始姿态误差下，传统间接扩展卡尔曼滤波器（EKF）实现了低于行进距离0.1%的闭环位置误差，而三种几何滤波器达到了相当的定位精度。
英文摘要
Geometric filters have recently been introduced to improve the accuracy and consistency of inertial-based integrated navigation systems. Error states were defined through specific group operations, introducing state correlations in error definition, which were lacked in the additive error used by a conventional indirect Kalman filter. The desirable consistent filtering models can be obtained based on specific geometric errors. For zero-velocity measurements expressed in the reference frame, this paper derives left-error process and measurement models from invariant filtering, two-frame-group filtering, and equivariant filtering. Importantly, a new group operation is introduced for the left tangent-group equivariant error. The analysis shows that the two-frame-group invariant extended Kalman filter (TFG-IEKF) and the tangent-group equivariant filter (TG-EqF) do not offer a significant consistency advantage over the invariant extended Kalman filter (IEKF). Experiments with an INS/ZUPT measurement system show that, under small initial attitude errors, the conventional indirect extended Kalman filter (EKF) achieves loop-closure position errors below $0.1\%$ of the traveled distance, while the three geometric filters achieve comparable positioning accuracy.
