研究惯性导航中未知时间延迟下的状态可辨识性问题

In many multisensor systems, measurements from different sensors are subject to unknown relative time delays. Accurate state estimation requires that delays be accounted for and, when possible, calibrated online. We consider the case of aided inertial navigation, where measurements from a single aiding sensor are subject to an unknown but constant delay relative to the inertial measurement stream, and study the identifiability of the resulting system. Critically, identifiability depends not only on the temporal structure of the measurements, but also on the shape of the vehicle trajectory: some trajectories are sufficiently informative to support unique recovery of the delay and the navigation state, while others are not. Using the special Galilean Lie group, we characterize a broad family of uninformative trajectories, each generated by a constant element of the Galilean Lie algebra. We show that, along any such trajectory, the delayed measurement model admits a continuous symmetry that prevents unique recovery of the delay and the navigation state. We connect this symmetry-based characterization to the familiar linearized, Jacobian-based analysis. Although our development is motivated by aided navigation, the underlying ideas apply more generally to estimation problems on Lie groups with delayed measurements.