Unaided acquisition of weak GPS signals requires both long coherent integration time and a great amount of noncoherent integration operations. The unknown navigation data bits and bit edges should also be considered. From the point of noncoherent integration of unaided weak GPS signal acquisition method, a new alternative is proposed. Besides the new one, four different noncoherent integration alternatives are introduced. They use different approaches to compute the noncoherent integration at each step in order to reduce calculations and save memory space. Under the same coherent integration time, noncoherent integration operation number and navigation data bit edge number, but different carrier-to-noise ratio, Monte Carlo method is applied to verify the probability of detection and do comparison analysis of the 4 alternatives.