Abstract: A method for accurately determining the position of a roving receiver positioned on or above the Earth's surface, relative to the position of a reference receiver whose position is known with sufficient accuracy, using measurements of signal phase transmitted at one or more carrier frequencies and received from each of four or more satellites in a Satellite Positioning System (SPS). Phase double differences are formed, using the reference and roving receivers and any two satellites drawn from four or more satellites, using phase information obtained from either or both of the two carrier signal frequencies. Phase correction information, in the form of estimates of integer wavelength ambiguities, is then obtained from two sets of ambiguity estimates computed with the roving receiver antenna in each of two specified positions, with the reference receiver antenna lying between and being collinear with the two roving receiver-antenna positions.