It is known that signal acquisition in Global Navigation Satellite System (GNSS) field provides a rough maximum-likelihood (ML) estimate based on a peak search in a two-dimensional grid. In this paper, the theoretical mathematical expression of the cross-ambiguity function (CAF) is exploited to analyze the grid and improve the accuracy of the frequency estimate. Based on the simple equation derived from this mathematical expression of the CAF, a family of novel algorithms is proposed to refine the Doppler frequency estimate with respect to that provided by a conventional acquisition method. In an ideal scenario where there is no noise and other nuisances, the frequency estimation error can be theoretically reduced to zero. On the other hand, in the presence of noise, the new algorithm almost reaches the Cramer-Rao Lower Bound (CRLB) which is derived as benchmark. For comparison, a least-square (LS) method is proposed. It is shown that the proposed solution achieves the same performance of LS, but requires a dramatically reduced computational burden. An averaging method is proposed to mitigate the influence of noise, especially when signal-to-noise ratio (SNR) is low. Finally, the influence of the grid resolution in the search space is analyzed in both time and frequency domains.