用双惯导和相对位置信息，实现车辆对运动目标的位姿与速度精准估计。
Relative Pose-Velocity Estimation Using Dual IMU Measurements and Relative Position Sensing
- 在SE₂(3)上建模相对运动，转为ℝ¹⁵空间的时变线性系统。
- 相对位置测量下仅需目标加速度持续激励即可全局指数收敛。
- 设计了在SO(3)上的非线性互补滤波器，保证姿态估计稳定平滑。
本文研究车辆相对于运动目标的相对位姿（位置与姿态）及速度估计问题，双方均配备惯性测量单元（IMU），并假设有相对位置或方位测量。将体-目标相对动力学建模于$ℝ^2(3)$，并重构为环境空间$ℝ^{15}$中的线性时变（LTV）模型，进而设计确定性Riccati观测器。分析了两种测量情形下的均匀可观察性（UO）条件，确保估计误差在环境空间中全局指数收敛：相对位置测量下，仅需目标加速度满足持续激励条件；而方位测量则需额外条件。在此基础上，设计了定义在$ℝℝ(3)$上的非线性互补滤波器，实现状态中姿态分量的平滑估计，并具有几乎全局渐近稳定性。最后通过仿真验证了所提方法的有效性。
原文摘要 · Abstract (English)
This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability of relative position or bearing measurements. The body-target relative dynamics are formulated on $\mathbf{SE}_2(3)$ and recast into a linear time-varying (LTV) model in the ambient space $\mathbb{R}^{15}$, on which a deterministic Riccati observer is designed. We analyze the uniform observability (UO) conditions required to guarantee global exponential convergence of the estimation error in the ambient space for both measurement cases. In the case of relative position measurements, UO requires only a persistence-of-excitation condition on the target acceleration, whereas for bearing measurements, additional conditions are required. Building on this, a nonlinear complementary filter on $\mathbf{SO}(3)$ is designed to provide a smooth estimate of the orientation component of the state with almost global asymptotic stability. Finally, simulation results are provided to validate the proposed solution.
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