This paper tackles the problem of estimating the relative position, orientation, and velocity between a UAV and a planar platform undergoing arbitrary 3D motion during approach and landing. The estimation relies on measurements from Inertial Measurement Units (IMUs) mounted on both systems, assuming there is a suitable communication channel to exchange data, together with visual information provided by an onboard monocular camera, from which the bearing (line-of-sight direction) to the platform's center and the normal vector of its planar surface are extracted. We propose a cascade observer with a complementary filter on $\mathbf{SO}(3)$ to reconstruct the relative attitude, followed by a linear Riccati observer for relative position and velocity estimation. Convergence of both observers is established under persistently exciting conditions, and the cascade is shown to be almost globally asymptotically and locally exponentially stable. We further extend the design to the case where the platform's rotation is restricted to its normal axis and show that its measured linear acceleration can be exploited to recover the remaining unobservable rotation angle. A sufficient condition for local exponential convergence in this setting is provided. The proposed observers are validated through extensive simulations.

翻译：本文解决了无人机在进近与着陆过程中，与经历任意三维运动的平面平台之间相对位置、姿态及速度的估计问题。该估计依赖于安装在两个系统上的惯性测量单元（IMU）的测量值（假设存在合适的数据交换通信信道），以及机载单目相机提供的视觉信息，从中提取平台中心的视线方向及其平面表面的法向量。我们提出了一种级联观测器，在$\mathbf{SO}(3)$上采用互补滤波器重构相对姿态，随后使用线性Riccati观测器进行相对位置与速度估计。在持续激励条件下，证明了两个观测器的收敛性，且该级联结构具有几乎全局渐近稳定性和局部指数稳定性。我们进一步将设计推广到平台旋转仅限于其法向轴的情形，并证明可利用其测量的线性加速度恢复剩余不可观测的旋转角度。针对该情形，给出了局部指数收敛的充分条件。通过大量仿真验证了所提出的观测器。