Increasing the dwell time in two-dimensional frequency-time hypothesis testing is, in practical terms, one of the most effective ways for Assisted Global Navigation Satellite Systems (A-GNSS) and GNSS receivers to achieve higher sensitivity. In an asynchronous cellular network, however, a mobile terminal may have a non-negligible unknown clock drift rate error originating from the received cellular downlink signal. In such a case, increasing the dwell time may not necessarily result in the expected sensitivity improvement. In addition, a mobile terminal in a rich multipath environment may experience jitters in the code phase of the resolved first arrival path due to short-delay multipaths, which also degrades the sensitivity. In this paper, new decision variables using a lone or a pair of adjacent.. 1 cells for code phase hypothesis testing and clock drift rate hypothesis testing are proposed to cope with the unknown code phase drift rate error and the effect of code phase jitter in a parallel acquisition system. The statistics of the proposed decision variables are analyzed in a Rayleigh fading channel, and the performances of the proposed decision variables are compared with that of the conventional decision variable.