Autonomous State Estimation in Formation Flight

Formation flying missions are extremely demanding in terms of control accuracy, as spacecraft should satisfy strict requirements when following a desired reference trajectory. The fulfillment of the missions' goals usually asks for expensive thrust actions. In order to reduce the otherwise too large DeltaV budget, an optimization of the control strategy is needed, which can be achieved only by providing to the regulator logic the most accurate knowledge of the current kinematic state of the formation. Several different kinds of sensors can be exploited, as satellite based navigation systems (both GPS and augmented (SBAS) GPS), different RF links specific to the mission, and optical techniques. All of these devices are intrinsically limited by noise, even if at a different level, and therefore a filtering action should be pursued in order to obtain the best possible estimate. This paper proposes to compare several possible strategies to improve the state estimation, all of them based on different implementations of a classical tool known as the Kalman filter. Orbital dynamics describing formation flying motion is nonlinear and hard to model in its perturbation effects. Previous works have shown that a first improvement can be achieved if the dynamical plant used for the state and error covariance update is designed so to include perturbation effects, mainly the J2 effect. Because it is possible that linear Kalman filtering might not be the optimal solution, enhanced versions of the filter will be therefore considered. The Extended Kalman Filter is certainly one of the most well known: its use allows for a mitigation of the problem of linearization of the dynamics, even if it introduces open questions about its convergence and its robustness. A complete analysis of the possible causes of malfunctioning is performed. First, the effects of increased error on the available measurements are analyzed and compared with the behaviour of a Linear Filter, showing good agreement. Then, robustness with respect to increasing formation dimensions and poor initial guess accuracy is investigated; the Extended Kalman Filter offers good stability properties in the formation flying case: the only strict requirement for proper filter behavior is that the measurements' update rate be quite frequent. A reference should be always made to the limited resources available on board, which dictate, together with performance requirements, the selection of the optimal approach. Simulations are carried on with an accurate modeling of the orbital environment and a sample of typical formation flying reference orbit and relative desired behaviour.