Equivariant Filter for Relative Attitude and Target's Angular Velocity Estimation

Abstract-- Accurate estimation of the relative attitude and angular velocity between two rigid bodies is fundamental in aerospace applications such as spacecraft rendezvous and docking. In these scenarios, a chaser vehicle must determine the orientation and angular velocity of a target object using onboard sensors. This work addresses the challenge of designing an Equivariant Filter (EqF) that can reliably estimate both the relative attitude and the target's angular velocity using noisy observations of two known, non-collinear vectors fixed in the target frame. T o derive the EqF, a symmetry for the system is proposed and an equivariant lift onto the symmetry group is calculated. Observability and convergence properties are analyzed. Simulations demonstrate the filter's performance, with Monte Carlo runs yielding statistically significant results. The impact of low-rate measurements is also examined and a strategy to mitigate this effect is proposed. I. INTRODUCTION In the past decade, there has been a growing interest in the development and validation of On-Orbit Servicing (OOS) and Active Debris Removal (ADR) technologies [1], [2], [3], driven by the ever-increasing number of satellites deployed each year. In OOS and ADR missions, the chaser or servicer spacecraft will need to approach the target spacecraft and synchronize its motion before performing the planned operations. As such, the chaser must estimate the relative attitude and angular velocity of the target, as well as the relative position and linear velocity.