Ambiguity function methods are based on the magnitude of the sum of unit vectors (phasors) defined by differences between observed and calculated global positioning system (GPS) phase data, thereby eliminating integer ambiguity parameters. In a novel approach using only cosines of the carrier phases, least squares techniques are implemented to facilitate convergence from approximate positions to a true position. With dual-frequency phase measurements, a simultaneous estimation of residual ionospheric path delays is proven feasible. Accuracy analyses show centimeter-level root mean square errors for both static and kinematic satellite positionings. Although the approach is not affected by cycle slips, its Limitation on position approximation deserves more attention. Together with L1/L2 phase measurements from wide-area tracking or monitoring stations, a potential application for single-frequency GPS users is briefly described.