Real-time decimeter accuracy GPS positioning can be achieved using carrier phase measurements. This requires fast and reliable on-the-fly integer ambiguity resolution. However, in GPS challenged areas (e.g. Urban canyons, tunnels, thick canopy etc.) the GPS receiver may not be able to track a sufficient number of satellites to resolve the integer ambiguities within one epoch. In this paper, we would like to find the optimal solution by combining the measurements from several epochs. In this paper, we present the theoretical derivation for a fast and efficient method for GPS integer ambiguity resolution with multiple GPS epoch measurements. Simulation results show the effectiveness of the proposed approach.