Optimal Fiducial Marker Placement for Satellite Proximity Operations Using Observability Gramians

2025-01-03

AI Summary

To address insufficient accuracy in relative pose estimation during satellite proximity operations, this paper proposes an observability-driven optimization method for fiducial marker placement. It innovatively incorporates the empirical observability Gramian—derived from dual-quaternion-based relative motion modeling—thereby overcoming limitations of conventional linearized approaches under nonlinear flyby trajectories. Integrating dual-quaternion dynamics with geostationary-orbit flyby simulations, the method performs numerical optimization of marker configurations. Results demonstrate that, for both five- and ten-marker layouts, the optimized placements significantly increase inter-marker spacing and prioritize regions exhibiting high sensitivity to state variations yet short visibility windows. Compared to uniform distributions, the optimized configurations improve relative pose estimation accuracy by up to 37.2%. This work establishes an engineering-practical paradigm for fiducial marker design enabling high-precision autonomous relative navigation.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Algorithm Configuration
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

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.

Problem

• Satellite Proximity Operations
• Signal Marker Optimization
• Intersatellite Measurement Accuracy

Innovation

• Dual Quaternions
• Gram Matrix Method
• Satellite Relative Navigation