Navigation Issues in Different Baseline Formation Flying Missions

A basic requirement for a satellite's formation is the precise knowledge of the spacecraft's relative configuration. The design of the navigation subsystem is significantly affected by this peculiar issue: in fact, the accuracy required for the fulfillment of the formation tasks is much greater than the one usually required for a single satellite. A standalone Global Positioning System (GPS) can be insufficient at the scope. The architecture of the formation itself suggests the design of differential GPS techniques. The close proximity of the spacecraft in fact make it possible to exchange information about the common visible GPS satellites in order to cancel the correlated error sources. Different approaches are available and, specifically, differential carrier-phase double difference GPS allows for remarkable accuracy at millimeter level. However, the actual applicability of this technique in real time applications presents a serious problem concerning the resolution of the ambiguity on the number of integer wavelengths from the spacecraft to the GPS satellites. Codebased differential GPS, easier to exploit, allows for lower precision, since some of the errors on the pseudorange measurements are uncorrelated, mainly regarding the user segment (receiver and multipath noise). However, other terms in the pseudorange error budget can be easily considered spatially correlated: ephemeris error, satellite clock stability and atmospheric propagation can be wiped out if differential techniques are used. In the proposed paper, the performance of differential GPS is analyzed for a wide range of formation missions. Two extended Kalman filters, based on the relative dynamics of the formation, are proposed to improve the accuracy of the estimates of the relative state. The first one evaluates the measurements of the relative coordinates from the delta-pseudoranges, while in the second one the delta-pseudoranges themselves are used as measurements. Therefore, the latter includes a more complicated measurement equation and requires the inclusion of the differential clock offset among the state variables to be estimated. However, simulations for different mission scenarios show that this is the only way to obtain fairly good and consistent accuracy of the relative position estimate in generic configurations.