Novel closed-loop approaches for precise relative navigation of widely separated GPS receivers in LEO

This paper deals with the relative navigation of a formation of two spacecrafts separated by hundreds of kilometers based on processing dual-frequency differential carrier-phase GPS measurements. Specific requirements of the considered application are high relative positioning accuracy and real-time on board implementation. These can be conflicting requirements. Indeed, if on one hand high accuracy can be achieved by exploiting the integer nature of double-difference carrier-phase ambiguities, on the other hand the presence of large ephemeris errors and differential ionospheric delays makes the integer ambiguities determination challenging. Closed-loop schemes, which update the relative position estimates of a dynamic filter with feedback from integer ambiguities fixing algorithms, are customarily employed in these cases. This paper further elaborates such approaches, proposing novel closed loop techniques aimed at overcoming some of the limitations of traditional algorithms. They extend techniques developed for spaceborne long baseline relative positioning by making use of an on-the-fly ambiguity resolution technique especially developed for the applications of interest. Such techniques blend together ionospheric delay compensation techniques, nonlinear models of relative spacecraft dynamics, and partial integer validation techniques. The approaches are validated using flight data from the Gravity Recovery and Climate Experiment (GRACE) mission. Performance is compared to that of the traditional closed-loop scheme analyzing the capability of each scheme to maximize the percentage of correctly fixed integer ambiguities as well as the relative positioning accuracy. Results show that the proposed approach substantially improves performance of the traditional approaches. More specifically, centimeter-level root-mean square relative positioning is feasible for spacecraft separations of more than 260 km, and an integer ambiguity fixing performance as high as 98% is achieved in a 1-day long dataset. Results also show that approaches exploiting ionospheric delay models are more robust and precise of approaches relying on ionospheric-delay removal techniques.