A Symmetry-based Observer for Relative Navigation of Orbital Modules

Kurzfassung

On-orbit servicing requires reliable relative-state estimates between a servicer spacecraft and a client spacecraft. In close-proximity rendezvous and motion control, relative velocity feedback is needed in addition to relative pose, but it is often not directly measured by onboard exteroceptive sensors. Vision or LiDAR systems can provide relative-pose measurements; however, estimating velocity by numerical differentiation of noisy, low-rate pose data can lead to unreliable estimates, especially under limited sampling or measurement dropouts. This thesis develops a relative-navigation estimator for a free-floating servicer–client system, motivated by the symmetry and momentum structure of the underlying mechanical model. The relative pose is represented on SE(3), while the velocity dynamics are expressed in passive-decomposed variables. In this formulation, the locked velocity captures the motion associated with the conserved momentum, while the shape velocity represents the relative motion. Together, they provide reduced velocity coordinates adapted to the symmetry and momentum structure of the free-floating model. Building on this model, a symmetry-based extended Kalman filter (SEKF) is designed. The pose states are treated geometrically using invariant error coordinates on SE(3), and the relative-pose kinematic block is linearized according to the invariant-error construction used in IEKF theory. However, the complete augmented pose–velocity model contains configuration-dependent couplings through the passive-decomposed dynamics and reconstructed twists. The full system is therefore not claimed to satisfy the group-affine assumptions that yield exact IEKF log-linear propagation. The resulting filter is symmetry-based in a precise but limited sense: its pose treatment and passive-decomposed process model reflect the geometric and momentum structure of the system, while the non-group-affine coupled terms are handled by conventional EKF linearization. The estimator is assessed in simulation under measurement noise, sampling effects, and dropouts, and is then applied to processed experimental relative-pose data from an on-ground test facility. The results show that the proposed SEKF tracks the relative pose and estimates the reduced velocity states without relying on direct numerical differentiation of pose measurements, while using a dynamics model consistent with the momentum structure motivating the formulation.