On the Identifiability of Aided Inertial Navigation Under Measurement Delays: A Geometric Approach

2026-06-27

AI Summary

This study addresses the non-identifiability of unknown constant time delay and initial states in aided inertial navigation systems. By integrating differential geometry with system identifiability theory, the authors formulate a delayed observation model and analyze its inherent symmetry structure. The work reveals a broader class of degenerate trajectories than previously recognized, along which the system exhibits continuous symmetries that render the time delay and initial states unrecoverable in a unique manner. The paper precisely characterizes the trajectory conditions leading to such non-identifiability, thereby establishing theoretical limits and offering principled guidance for the design of multi-sensor fusion navigation systems.

Abstract

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 that parameterizes the trajectory. Identifiability depends on both the temporal structure of the aiding measurements and the form of the trajectory itself. Our geometric analysis shows that, for a larger class of uninformative (i.e., degenerate) trajectories than has previously been reported, the delayed measurement model admits a continuous symmetry that prevents unique delay-and-state recovery.

Problem

• identifiability
• inertial navigation
• measurement delays
• sensor fusion
• trajectory

Innovation

• identifiability
• inertial navigation
• measurement delay
• geometric approach
• degenerate trajectories