Robust filter setting in GPS-based relative positioning of small-satellite LEO formations

Formations of small satellites are becoming more and more important to many space applications, since they offer the possibility of distributing the payload functionality among the different elements of the formation, so to improve scientific return, providing at the same time a number of advantages in terms of overall system reliability, flexibility and modularity. However, precise autonomous determination of the relative positions of the formation members is required for formation acquisition and maintenance, and scientific objective achievement. For Low-Earth-Orbit formations, this task can be performed exploiting GPS-based relative positioning techniques. The technique exploited in this paper is designed for on board usage. It processes double differenced pseudo-range and carrier phase observables on two frequencies within a hybrid filtering scheme to get satisfactory precision and high robustness. However, relative positioning by GPS is affected by the capability of correctly estimating differential ionospheric delays, and, then, by the status of ionosphere activity. Hence, the filter includes an ionospheric model capable of reproducing ionosphere horizontal gradients with a minimum number of parameters, which can be estimated on the fly. In addition, a robust tuning approach is developed in the paper to get stable filter performance over long period of times. Specifically, the proposed approach combines an empirical tuning technique with a randomized algorithm to get the best filter tuning. Filter performance and tuning approach effectiveness are successfully verified using freely available GPS flight data of Gravity Recovery and Climate Experiment mission.