适用于伽利略群的滑动窗口滤波器：处理未知测量延迟的一致辅助惯性导航
A Sliding Window Filter on the Galilean Group for Consistent Aided Inertial Navigation with Unknown Measurement Delays
- Vector Institute（向量研究所）
- University of Toronto Institute for Aerospace Studies (UTIAS)（多伦多大学航空航天研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对辅助惯性导航中辅助测量的未知恒定延迟问题，提出基于伽利略群的滑动窗口滤波器，联合估计延迟与导航状态，仿真表明该滤波器可显著提升估计一致性。
AI中文摘要：
我们研究辅助惯性导航问题，其中辅助传感器测量存在未知的恒定延迟。目标是联合估计延迟和导航状态，使延迟测量能在合适的时间修正轨迹，从而得到更准确的导航解。我们在特殊伽利略群上构建该问题，其为运动和时间均存在不确定性的辅助导航提供了自然的状态空间结构。随后我们分析延迟与状态联合估计的可观测性，结果表明，对于单个延迟测量，该模型存在精确对称性：延迟的变化可通过导航状态的变化补偿，使测量保持不变。单独处理测量会导致虚假信息沿测量雅可比矩阵的零方向“泄漏”，产生过度自信且不一致的估计；而当轨迹信息足够丰富时，联合处理多个时刻的测量可消除该零方向。基于此结果，我们开发了一种滑动窗口滤波器，其保留短时间的导航状态历史，并在活动窗口内联合应用延迟辅助修正。我们开展一系列仿真研究以表征估计器的精度和一致性，仿真结果显示，未维持足够窗口的估计器会迅速变得高度不一致，而即使是短滑动窗口也能通过提供可观测性所需的时间支撑，显著提升一致性。
英文摘要：
We study aided inertial navigation when the aiding sensor measurements are subject to an unknown constant delay. The goal is to estimate the delay and navigation state jointly so that delayed measurements correct the trajectory at the appropriate times, yielding a more accurate navigation solution. We formulate the problem on the special Galilean group, which provides a natural state-space structure for aided navigation with uncertainty in both motion and timing. We then examine the observability of joint delay and state estimation and show that, for a single delayed measurement, the model admits an exact symmetry in which a change in the delay can be compensated by a change in the navigation state, leaving the measurement unchanged. Processing measurements individually allows spurious information to `leak' along the corresponding null direction of the measurement Jacobian, producing overconfident and inconsistent estimates. Applying measurements from multiple times together can eliminate this direction when the trajectory is informative enough. Motivated by this result, we develop a sliding window filter that retains a short history of navigation states and applies delayed aiding corrections jointly across the active window. We conduct a series of simulation studies to characterize estimator accuracy and consistency. The simulations demonstrate that an estimator that does not maintain an adequate window can rapidly become highly inconsistent, whereas even a short sliding window markedly improves consistency by providing the temporal support that observability requires.
