用几何方法统一处理惯性导航中的姿态与速度估计，提升稳定性与鲁棒性。
A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements
- 基于李群SE(5)重构状态空间，解耦平移误差动态
- 在均匀可观测条件下实现几乎全局渐近稳定
- 适用于双目与GPS辅助惯导系统，设计更简洁
本文针对刚体的精确位姿（位置、速度、姿态）估计问题，结合通用惯性系和/或机体坐标系测量及惯性测量单元（IMU），提出一种基于几何框架的方法。通过将原始状态空间$ o imes R^3 imes R^3$嵌入更高维李群$ ext{SE}(5)$，重构车辆动力学与观测模型。该嵌入使几何误差动态解耦：平移误差动态呈现类似连续时间卡尔曼滤波器的结构，支持基于里卡蒂方程的时间变增益设计。在均匀可观测条件下，证明了在$ ext{SE}(5)$上设计的观测器具有几乎全局渐近稳定性。通过两个实际场景的仿真验证：双目辅助惯性导航系统（INS）与GPS辅助INS。所提方法显著简化了非线性几何观测器的设计，为惯性导航状态估计提供了一种通用且鲁棒的解决方案。
原文摘要 · Abstract (English)
This paper addresses accurate pose estimation (position, velocity, and orientation) for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space, $\so \times \R^3 \times \R^3$, within the higher-dimensional Lie group $\sefive$, we reformulate the vehicle dynamics and outputs within a structured, geometric framework. In particular, this embedding enables a decoupling of the resulting geometric error dynamics: the translational error dynamics follow a structure similar to the error dynamics of a continuous-time Kalman filter, which allows for a time-varying gain design using the Riccati equation. Under the condition of uniform observability, we establish that the proposed observer design on $\sefive$ guarantees almost global asymptotic stability. We validate the approach in simulations for two practical scenarios: stereo-aided inertial navigation systems (INS) and GPS-aided INS. The proposed method significantly simplifies the design of nonlinear geometric observers for INS, providing a generalized and robust approach to state estimation.
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