Systems and methods are disclosed herein to use sieving to reduce the number of hypotheses and the length of time for acquisition of GPS satellite signals. In sieving, hypothesis testing is performed after a short non-coherent integration duration on a first set of hypotheses. At the end of the non-coherent integration time, multiple candidate hypotheses having high likelihood of signal detection are identified. Further non-coherent integration of each candidate hypothesis is performed by using a tracking loop to remove Doppler frequency and code phase variations on the signal. In parallel, additional hypotheses testing is performed on a second set of hypotheses. At the end of the next non-coherent integration time, the best candidate hypotheses among the candidate hypotheses sieved from the first set of hypotheses running in the tracking loops and the candidate hypotheses from the second set of hypotheses are identified. This new set of candidate hypotheses replaces the previous candidate hypotheses and is tracked by the tracking loops. This process of short non-coherent integrations followed by track is repeated until a candidate hypothesis has a non-coherent integration that exceeds a detection threshold.