Relative clock estimation method between two LEO satellites with a double-difference solution constraint

A method of estimating the relative clocks between two spaceborne global positioning system (GPS) receivers based on the single-difference (SD) observations is investigated in this paper. Especially, the advantages of introducing a double-difference (DD) solution constraint, including the orbits and ambiguities, are discussed with the simulated data and the real data of Gravity Recovery And Climate Experiment (GRACE) satellites. The theoretical accuracy analysis shows that the accuracy of the relative clocks is improved and the edge effects are eliminated with a DD solution constraint. The simulations indicate a potential accuracy improvement of at least 30% of the relative clocks with the constraint. Furthermore, one month׳s real data is processed and the overlapping data arcs are used to validate the accuracy of the relative clock solutions. The average overlapping root mean square (RMS) of the relative clock solutions is approximate 99 ps and 31 ps without and with the DD solution constraint, respectively. Moreover, the jumps of the day boundaries are weakened evidently by adding the DD solution constraint. This paper demonstrates that the accuracy and stability of the estimated relative clocks between two low earth orbit (LEO) satellites from SD observations are improved obviously with the DD solution constraint.