Methods and apparatus are presented for determining a position of an antenna of a GNSS rover from observations of GNSS signals collected at the antenna over multiple epochs and from correction data for at least one of the epochs. A first-epoch rover position relative to a base location is determined for a first epoch using a single-differencing process based on one of (i) fixed carrier-phase ambiguities and (ii) a weighted average of carrier-phase ambiguity candidates which is converged to a predetermined threshold. A second-epoch rover position relative to a base location is determined for a second epoch using a single-differencing process. A second-epoch update of the first-epoch rover position relative to the base location is determined for the second epoch using a single-differenced delta phase process and the first-epoch rover position is combined with the second-epoch update to obtain a second-epoch delta phase rover position relative to a moving base location of the second epoch. The second-epoch delta phase rover position is selected as reliable if the second-epoch rover position is not based on one of (i) fixed carrier-phase ambiguities and (ii) a weighted average of carrier-phase ambiguity candidates which is converged to a predetermined threshold.