Relative Pose-Velocity Estimation Using Dual IMU Measurements and Relative Position Sensing

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.