A time-varying environment may not allow performing a long-time time-delay measurement between sensors when localizing a signal source. Finite measurement time causes the estimate of the Generalized Cross Correlation (GCC) not only biased but also incurred a high estimation variance, which intends to increase the estimation anomalies. This paper analyses the performance of the GCC based time-delay estimators with finite measurement time. Also, a simple method based on detection theory is proposed to determine the minimal measurement time requirement using the Gaussian model.