Comparison of different CDGPS solutions for On-The-Fly Integer Ambiguity Resolution in long baseline LEO formations

This paper deals with the real-time onboard accurate relative positioning by Carrier-phase Differential GPS (CDGPS) of LEO formations with baselines of hundreds of kilometers. On long baselines, high accuracy can be achieved only using dual-frequency measurements and exploiting the integer nature of Double Difference (DD) carrier-phase ambiguities. However, large differential ionospheric delays and broadcast ephemeris errors complicate the integer resolution task. The approach presented in this paper relies on separating the integer ambiguities’ resolution from the relative positioning solution. The first task is performed by a closed-loop dynamic-based filter integrating an Extended Kalman Filter with an Integer Least Square (ILS) estimator. Then, the relative position is computed with a conventional kinematic least-square algorithm processing ionospheric-free combination of carrier-phase measurements de-biased of the integer ambiguities. Three different formulations of the dynamic-based filter are compared. The first two formulations use Lear’s model to estimate differential ionospheric delays, the main difference being in the validation step performed on all the ambiguities, in the first case, and only on the wide-lane combination, in the second case. The third scheme is instead based on combining the DD measurements for removing ionospheric delays from the observation model. The performance of the developed solutions is assessed by using flight data from the Gravity Recovery and Climate Experiment mission. Results show that the closed-loop approach based on validating only the wide-lane combinations shows the best performance