Linearized Formation-Flying Dynamics in a Perturbed Orbital Environment

Formation flying is a key technology for the fulfillment of next-generation remote sensing and science missions. Common requirements are an accurate knowledge of the baseline and precise control of the relative configuration. The design of the navigation and control section is therefore of capital importance and can deeply affect the actual feasibility of the mission. Traditional yet very effective tools come from linear systems theory. That is, even if the relative dynamics of the formation is nonlinear (because of the higher order terms of the differential gravity and the differential perturbations), the proximity of the spacecraft enables the implementation of techniques such as linear control regulators and linear Kalman filters. Reliable linear models for formation dynamics are therefore necessary for the implementation of the system plants of these control and navigation approaches. Some of them are very well known: the Hill-Clohessy-Wiltshire model deals with a linearized gravitational field, while others manage to introduce the J2 perturbation or the differential drag. In this work we propose an innovative linear model that includes both J2 and drag perturbation in the Cartesian coordinates orbital frame with little complication. An extended simulation campaign is performed to assess the precision with respect to other linear models in literature, and with respect to a full nonlinear "real" world.