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Direct global position system precision code acquisition is desirable for providing stronger anti-jamming and anti-spoofing capabilities than the handover from a coarse acquisition code. Because of the high chip rate and long period of the precision code (P-code), direct acquisition is challenging. By averaging incoming and local signals respectively, to reduce the number of code phases to be searched, previously proposed direct and overlap average methods provide an efficient way to rapid acquisition. To further analyse the performance of average methods the previously proposed direct and overlap average methods are generalised, the corresponding mathematical modelling is established, the correlation properties of the averaged P-code are studied and the detection and mean acquisition time performances are investigated. By increasing the weighting of the local signal, which has a code phase shift in samples of half of the average length, improved overlap average methods are proposed. Compared with the previously proposed direct and overlap average methods, the improved overlap average methods have better detection performance and can further improve acquisition performance, that is, shorten the mean acquisition time. Numerical results demonstrate the enhancement.