Abstract: A method and apparatus for rapidly and accurately determining the position coordinates of a remote, movable receiver relative to a fixed reference receiver. The technique utilizes successive code measurements and carrier phase measurements of both the L.sub.1 and L.sub.2 carrier signals broadcast from four or more orbiting GPS satellites. Code measurements based on a weighted average of the individual L.sub.1 and L.sub.2 code measurements in each satellite/receiver link are adjusted in accordance with the corresponding carrier phase measurement for an L.sub.1 -L.sub.2 carrier difference signal and are further smoothed over time. This yields a rapid determination of the remote receiver's position coordinates, with progressively increasing accuracy. After merely about two to three minutes of processing, a wide laning carrier phase procedure can be implemented to yield a position determination that is accurate to within about one centimeter.