A double dwell, maximum likelihood, serial sliding acquisition system (10) employs two thresholds which are a function of maximum likelihood thresholds, and not predetermined optimal thresholds. The two thresholds have values that are signal dependent, and are obtained in real time from a correlation of a received PN signal and a locally generated PN sequence during the acquisition process. The acquisition system continuously monitors the reliability of the detected signal. As a result, the decision making process is continuously performed so as to terminate the acquisition process whenever the detected signal is determined to be reliable. The acquisition system employs a principle that an optimal threshold level, in the power domain, is 6 dB lower than that of the maximum likelihood signal. The acquisition system obtains the maximum signal power from a maximum likelihood detector portion to adaptively update a threshold estimate, and then uses the adaptive threshold estimate for monitoring the reliability of the detected signal. After the reliable signal is detected the search process continues for an additional interval of time which is a function of a false alarm probability. The limited interval for which the search process continues is preferably a fraction or multiple of the second, longer dwell time. This additional searching interval is referred to as a post-detection search interval. During the post-detection search interval, the acquisition system monitors the received signal samples and, when no additional signal is detected, the acquisition process is terminated.