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

TL;DR

This paper introduces an Equivariant Filter for accurately estimating the relative attitude and angular velocity between two rigid bodies, crucial for aerospace tasks like spacecraft rendezvous, using noisy sensor data and symmetry-based design.

Contribution

It presents a novel Equivariant Filter leveraging system symmetries for reliable estimation of relative attitude and angular velocity, validated through simulations and real-world experiments.

Findings

The filter achieves accurate estimates under noisy conditions.

Performance is robust even with low-rate measurements.

Experimental validation confirms practical effectiveness.

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 angular velocity using noisy observations of two known, non-collinear vectors fixed in the target frame. To 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. Experimental results, using fiducial markers and both conventional and event cameras for measurement acquisition, further validate the approach, confirming its effectiveness in a realistic setting.