This letter considers the decentralized detection of a noncooperative moving target by employing a wireless sensor network. Suppose that, if present, the target moves along a direction with a constant velocity, and it emits an unknown signal experiencing distance-dependent attenuation that is periodically sampled by sensors. The sensor observations are quantized into one-bit data individually and then sequentially transmitted to a fusion center, which is in charge of making a global decision. We first derive the generalized Rao test statistic as a more computationally efficient alternative when compared to the typical generalized likelihood ratio test statistic. Then, we propose a truncated one-sided sequential (TOS) test rule by imposing a finite maximum stopping time (namely the deadline) on typical one-sided sequential tests. With a deadline slightly larger than the sample size of a benchmarked fixed-sample-size (FSS) test, the proposed TOS test rule provides the same detection performance and significantly accelerates the target-detection process on average, which is corroborated by simulation results.