Optimal Fiducial Marker Placement for Satellite Proximity Operations Using Observability Gramians

TL;DR

This paper develops a method to optimally place fiducial markers on a satellite to maximize observability during proximity operations, using dual quaternions and empirical Gramian analysis, with numerical simulations demonstrating improved marker configurations.

Contribution

It introduces a novel approach combining dual quaternion modeling and empirical observability Gramians to determine optimal fiducial marker placement for satellite relative navigation.

Findings

Optimal marker placement maximizes sensitivity to state changes.

Markers placed at locations with greater inter-marker distances improve observability.

The method effectively identifies marker configurations that enhance measurement sensitivity during nonlinear trajectories.

Abstract

This paper investigates optimal fiducial marker placement on the surface of a satellite performing relative proximity operations with an observer satellite. The absolute and relative translation and attitude equations of motion for the satellite pair are modeled using dual quaternions. The observability of the relative dual quaternion system is analyzed using empirical observability Gramian methods. The optimal placement of a fiducial marker set, in which each marker gives simultaneous optical range and attitude measurements, is determined for the pair of satellites. A geostationary flyby between the observing body (chaser) and desired (target) satellites is numerically simulated and the optimal fiducial placement sets of five and ten on the surface of the desired satellite are solved. It is shown that the optimal solution maximizes the distance between fiducial markers and selects marker locations that are most sensitive to measuring changes in the state during the nonlinear trajectory, despite being visible for less time than other candidate marker locations. Definitions and properties of quaternions and dual quaternions, and parallels between the two, are presented alongside the relative motion model.