The Global Positioning System (GPS) is an all-weather, worldwide, continuous coverage, satellite based navigation system. GPS satellites transmit signals that allow one to determine, with great accuracy, the location of GPS receivers. In GPS a typical technique for dynamic position estimation is differential positioning where two receivers are used, one receiver is stationary and its exact position is known, the other is roving and its position is to be estimated. In this talk we describe the physical situation and derive the mathematical model. We then present a recursive least squares approach for position estimation based on the difference of the measurements at the stationary and roving receivers. We take full account of the structure of the problem to make our algorithm efficient and use orthogonal transformations to ensure numerical reliability of the algorithm. Simulation results will be presented to demonstrate the performance of the algorithm. A comparison with the van Graas and Lee positioning algorithm will be given.