A global positioning system includes a base GNSS receiver that determines position and carrier phase measurements for GNSS satellites in view and a rover GNSS receiver, which is a single frequency receiver that captures GNSS satellite signals transmitted in the single frequency band during a capture window from a plurality of GNSS satellites, the plurality being large enough to provide a carrier phase data set from which a solution to associated integer carrier phase ambiguities is over determined. The system determining from the captured signals, a search space associated with the satellites in view, the code phase delays and associated position uncertainty. The system resolving the integer carrier cycle ambiguities using double difference carrier phase measurements associated with signal power values that are over a predetermined threshold value. The system resolving the carrier cycle ambiguities over the capture window to a single solution set and determining the position of the rover GNSS receiver to an accuracy within centimeters using the resolved carrier phase measurements.