Trajectory Design for Improving Observability of Angles-Only Relative Navigation between Two Satellites

Abstract

This study focuses on designing a relative rendezvous trajectory for angles-only navigation between two satellites. The main purpose of this paper is to design a rendezvous trajectory which provides better observability for the whole mission period. The second purpose is to improve fuel consumption efficiency. For the trade-off between the observability maneuver and fuel consumption, it is important to minimize the fuel consumption while ensuring sufficient observability since a small-size satellite has a tight mass budget. To design such a trajectory, this study proposes implementing the observability constraint at each optimization node. Then the cost function is aimed at minimizing fuel consumption. A numerical optimization technique is implemented to solve the optimization problem. Simulation for the estimator is performed to verify the designed trajectory. To get physical insight into the relationship between relative trajectory and observability, an observability analysis is also presented using a geometrical relationship between two satellites and the Fisher information matrix as a measure of observability.