This paper investigates the estimation problem of the pose (orientation and position) and linear velocity of a rigid body, as well as the landmark positions, using an inertial measurement unit (IMU) and a monocular camera. First, we propose a globally exponentially stable (GES) linear time-varying (LTV) observer for the estimation of body-frame landmark positions and velocity, using IMU and monocular bearing measurements. Thereafter, using the gyro measurements, some landmarks known in the inertial frame and the estimates from the LTV observer, we propose a nonlinear pose observer on $\SO(3)\times \mathbb{R}^3$. The overall estimation system is shown to be almost globally asymptotically stable (AGAS) using the notion of almost global input-to-state stability (ISS). Interestingly, we show that with the knowledge (in the inertial frame) of a small number of landmarks, we can recover (under some conditions) the unknown positions (in the inertial frame) of a large number of landmarks. Numerical simulation results are presented to illustrate the performance of the proposed estimation scheme.

翻译：本文研究了利用惯性测量单元（IMU）与单目相机对刚体姿态（朝向与位置）、线速度以及路标位置进行估计的问题。首先，我们提出了一种全局指数稳定（GES）的线性时变（LTV）观测器，该观测器利用IMU与单目方位测量数据来估计机体坐标系下的路标位置与速度。随后，结合陀螺仪测量值、惯性坐标系中已知的若干路标信息以及LTV观测器的估计结果，我们在$\SO(3)\times \mathbb{R}^3$上设计了一种非线性姿态观测器。通过引入几乎全局输入到状态稳定性（ISS）概念，证明了整个估计系统具有几乎全局渐近稳定性（AGAS）。值得注意的是，我们证明在已知惯性坐标系中少量路标信息的条件下，能够在特定情况下恢复惯性坐标系中大量未知路标的位置。数值仿真结果展示了所提估计方案的性能。