仅用惯性传感器和单个距离测量，实现高精度姿态与位置估计。
Cascaded Tightly-Coupled Observer Design for Single-Range-Aided Inertial Navigation
- 分步设计：先估位置速度与重力方向，再重构完整姿态。
- 在统一可观测条件下实现几乎全局渐近稳定，抗噪声强。
- 适合轻量化导航系统，尤其适用于无视觉或卫星信号场景。
本文提出一种仅依赖惯性测量单元（IMU）、机体坐标系矢量测量（如磁力计）及固定锚点的距离测量的单距离辅助导航观测器。首先构建扩展线性时变（LTV）系统，用于估计机体坐标系下的位置、速度和重力方向；随后利用恢复出的重力方向与机体矢量测量，重构完整的SO(3)姿态。在统一可观测性条件下，证明了该级联设计具有几乎全局渐近稳定性（AGAS），对传感器噪声和轨迹变化具有鲁棒性。三维轨迹仿真结果表明，该方法可精确估计位置、速度与姿态，验证了单距离辅助作为轻量高效自主导航模态的可行性。
原文摘要 · Abstract (English)
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.
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