Equivariant Filter Cascade for Relative Attitude, Target's Angular Velocity, and Gyroscope Bias Estimation

Rendezvous and docking between a chaser spacecraft and an uncooperative target, such as an inoperative satellite, require synchronization between the chaser spacecraft and the target. In these scenarios, the chaser must estimate the relative attitude and angular velocity of the target using onboard sensors, in the presence of gyroscope bias. In this work, we propose a cascade of Equivariant Filters (EqF) to address this problem. The first stage of the cascade estimates the chaser's attitude and the bias, using measurements from a star tracker, while the second stage of the cascade estimates the relative attitude and the target's angular velocity, using observations of two known, non-collinear vectors fixed in the target frame. The stability of the EqF cascade is theoretically analyzed and simulation results demonstrate the filter cascade's performance.

Comments: This work has been submitted to the 2026 European Control Conference