This paper investigates a combined Doppler and pseudorange (DPR) solution using two or three satellites for a stand-alone, dual-frequency, stationary receiver. The three solutions presented in this paper use novel Doppler track equations, seemingly simplified yet fully capable of obtaining high-accuracy Doppler solutions. Unlike previously developed DPR solutions, none of these solutions require a reference or differential correction station, and the solution update rate is 10 to 100 s to achieve horizontal positioning with better than 10 m accuracy (RMS). For the two-satellite solution, both vertical and oscillator aiding are analyzed and compared. The three-satellite solution does not require aiding. Error sensitivity analyses are performed to characterize the performance of the solutions. Both a computer simulation and GPS measurement data are used to demonstrate the feasibility of all three solutions. Horizontal Root Mean Square (RMS) errors below 10 m were achieved for solutions with good satellite geometry. Based on a 12-hr GPS data set from a rooftop antenna, the two-satellite DPR solutions experienced good geometry more than 85% of the time, while the three-satellite DPR solutions experienced good geometry 100% of the time.