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

TL;DR

This paper presents a cascaded observer architecture for inertial navigation that reconstructs full state using only IMU, a body-frame vector, and a single-range measurement, with proven stability and robust performance.

Contribution

It introduces a novel cascaded observer design that achieves full state estimation with minimal sensors and guarantees almost global stability under observability conditions.

Findings

Accurate estimation of position, velocity, and orientation demonstrated in simulations.

The observer design is robust to sensor noise and trajectory variations.

Single-range aiding is effective for lightweight autonomous navigation.

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.