ESA GNC Conference Papers Repository

The understanding of the Universe evolution has changed dramatically in the last decades through the improvement of the observation means but our knowledge in the low frequency band (1-30 Mhz) still remains very limited since it is inobservable from the ground given the ionosphere filtering effect and the man made interferences. The deployment of large size space radio instruments constitutes therefore the only option to retrieve the information in this spectral band. Such an approach is investigated within the dutch funded OLFAR program that involves tens of distribured receivers implemented on nano satellites to keep the cost under acceptable bounds [1]. Given the steady improvement of Cubesat capabilities, CNES is also conducting a mission concept study for the design of a similar radio interferometer. The instrumental concept comprises several tens of craft deployed in a loose formation on a lunar orbit to benefit periodicaly from a perfect protection against the Earth radio emissions. Spacecraft relative distances are up to tens of kilometers but no position control is needed except to avoid formation evaporation or collision between spacecraft. Stringent knowledge requirements on the formation configuration are however applicable in order to reconstruct the signal with the desired resolution expressed in fractions of wavelength (?/100 to ?/1000 resolution @ 30 Mhz corresponds to 10 - 1 cm satellite position accuracy). The paper is focusing on the interferometer network absolute localization when only range measurements are available between nodes. Range measurements allow to reconstruct the formation topology but its orientation in space remains undetermined unless we know the absolute position of at least three non aligned satellites (anchor points) or the direction vector of the links between these anchor points. This problem has attracted significant research interest in the recent past due to the emergence of sensor wireless networks and their various terrestrial applications. The formulation of the problem generally assumes the existence of a minimal set of anchor points and the availability of measurements between spacecraft up to a given range. Multiple techniques have been developed to tackle the problem and they involve for the most part iterative optimization approaches [2]. In a first section, the paper revisits the main techniques based on range measurements and details their shortcomings in the case of space networks where the nodes relative configuration varies continuously. However, the orbital dynamics adds some additional constraint that helps to reduce the level of undetermination. The paper proposes therefore a localization method that estimates the nodes relative orbital elements using a Bayesian approach (Extended Kalman Filter). The analysis focuses initially on the state observability assuming a Keplerian orbital model and sets the minimal conditions to be satisfied to perform absolute localization. Any group of N orbiting nodes with a single anchor point is thus proved to be globally observable but the true anomaly is only known modulo pi. Some initial knowledge pertaining to the network deployment conditions enables to remove the ambiguity and participates to the satisfactory convergence of the filter. The paper details afterwards the formulation of the filter that includes a dynamic model with third body gravity perturbations and presents the architecture for both centralized and distributed cases. It focuses then on the critical initialization phase and analyzes the trade between computational complexity and positioning accuracy. Localization performances obtained in simulations for representative swarm configurations involving a unique anchor point are then presented for both centralized and distributed cases.