The Binary Offset Carrier (BOC) and Alternate BOC (AltBOC) waveforms, introduced for Galileo signaling, are designed to enable high time delay estimation accuracy. However, their autocorrelation functions have multiple narrow peaks, thus leading to potential acquisition bias, in particular in presence of multipaths. In order to detect the first path, a high sampling rate is considered. Unfortunately, this introduces noise correlation. In this paper, we compare a technique developed for multipath channel estimation based on Monte Carlo Markov Chain (MCMC) simulation with the standard acquisition approach, in multipath environments, considering both accuracy and computational load issues.