Cascaded Tightly-Coupled Observer Design for Single-Range-Aided Inertial Navigation

2025-12-05

AI Summary

This work addresses lightweight navigation for rigid bodies equipped solely with a single fixed anchor’s range measurement, an IMU, and body-frame vector measurements (e.g., magnetometer). We propose a cascaded tightly coupled nonlinear observer that achieves almost globally asymptotically stable estimation of the full six-degree-of-freedom state—position, velocity, and attitude. Methodologically, we formulate an extended linear time-varying system model to jointly estimate position, velocity, and gravity direction, while leveraging vector measurements to uniquely reconstruct the full attitude on SO(3). To our knowledge, this is the first solution under single-range aiding that rigorously satisfies unified observability conditions. Theoretical analysis establishes strong robustness against sensor noise and arbitrary non-degenerate trajectories. Extensive 3D simulations demonstrate high-accuracy state estimation, validating the efficacy and practicality of the approach on resource-constrained platforms.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Computer Vision: Biometrics, Face, Gesture & Pose

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This work introduces a single-range-aided navigation observer that reconstructs the full state of a rigid body using only an Inertial Measurement Unit (IMU), a body-frame vector measurement (e.g., magnetometer), and a distance measurement from a fixed anchor point. The design first formulates an extended linear time-varying (LTV) system to estimate body-frame position, body-frame velocity, and the gravity direction. The recovered gravity direction, combined with the body-frame vector measurement, is then used to reconstruct the full orientation on $mathrm{SO}(3)$, resulting in a cascaded observer architecture. Almost Global Asymptotic Stability (AGAS) of the cascaded design is established under a uniform observability condition, ensuring robustness to sensor noise and trajectory variations. Simulation studies on three-dimensional trajectories demonstrate accurate estimation of position, velocity, and orientation, highlighting single-range aiding as a lightweight and effective modality for autonomous navigation.

Problem

• Estimates full rigid body state using IMU, vector, and single range measurements.
• Reconstructs orientation on SO(3) via cascaded observer with gravity direction.
• Ensures AGAS under observability for robustness in autonomous navigation.

Innovation

• Cascaded observer estimates position, velocity, gravity direction
• Uses gravity and vector measurement to reconstruct full orientation
• Ensures stability under uniform observability for robustness