Equivariant Filter for Relative Attitude and Target Angular Velocity Estimation

2025-06-06

AI Summary

Simultaneous estimation of relative attitude and target angular velocity in spacecraft rendezvous and docking remains challenging, particularly under low-frequency, noisy measurements of only two non-collinear vectors observed in the target body frame. Method: This paper proposes a novel cooperative estimation algorithm based on Equivariant Filtering (EqF). We first construct a Lie-group equivariant system symmetry model tailored to this joint estimation problem; design an EqF architecture with theoretical convergence guarantees; and fuse event-camera and conventional camera observations to mitigate performance degradation caused by low measurement rates. Results: Rigorous observability analysis, Monte Carlo simulations, and real-platform experiments—including fiducial markers and event-camera data—demonstrate that the proposed method achieves superior statistical robustness and estimation accuracy compared to state-of-the-art nonlinear filters.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Low Level & Physics-based Vision
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Estimating relative attitude and target angular velocity accurately
• Designing Equivariant Filter for noisy non-collinear vector observations
• Validating filter performance with simulations and experimental data

Innovation

• Equivariant Filter for attitude estimation
• Symmetry group lift for system analysis
• Event cameras for experimental validation