解决惯性导航中传感器延迟导致状态无法唯一识别的问题
On the Identifiability of Aided Inertial Navigation Under Measurement Delays: A Geometric Approach
- 基于伽利略群几何方法分析延迟与初始状态的可辨识性
- 揭示特定轨迹下延迟和状态无法唯一恢复的本质原因
- 适用于需要高精度时间对齐的导航系统设计与故障诊断
在辅助惯性导航中，不同传感器的测量常存在未知的相对时间延迟。考虑一个辅助传感器，其测量相对于惯性数据流存在未知但恒定的延迟。本文研究该延迟及参数化轨迹的初始导航状态的可辨识性。可辨识性取决于辅助测量的时间结构和轨迹形式。利用特殊伽利略群，确定了恢复延迟与导航状态所需的最少测量数量及类型。同时，刻画了一类信息缺失的轨迹，其延迟测量模型具有连续对称性，导致延迟与状态无法唯一恢复。我们证明每类此类轨迹均由伽利略李代数中的常量生成，并将其结果与经典的线性化雅可比分析相联系。
原文摘要 · Abstract (English)
In aided inertial navigation, measurements from different sensors are often subject to unknown relative time delays. Consider a single aiding sensor whose measurements have an unknown but constant delay relative to the inertial-measurement data stream. We study the identifiability of the delay and the initial navigation state parameterizing the trajectory. Identifiability depends on both the temporal structure of the aiding measurements and the form of the trajectory. Using the special Galilean group, we determine the minimal number and type of aiding measurements needed to recover the delay and the navigation state. We also characterize a class of uninformative trajectories, for which the delayed measurement model admits a continuous symmetry that prevents unique delay-and-state recovery. We show that each such trajectory is generated by a constant element of the Galilean Lie algebra, and connect this result to the familiar linearized, Jacobian-based analysis.
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