Abstract: This paper puts forward the concept of the Generalized Phase Spectrum (GPS) Time Delay Estimation (TDE) and calculates the variance of GPS TDE, the relation between GPS TDE and The Generalized Cross-Correlation (GCC) TDE is derived. The method of Amplitude Square (AS) weighting for TDE, one of suboptimum GPS TDE, is proposed. A multipath signal model is considered. The results of theoretical calculation and computer simulation experiment show that in multipath environments the performance of AS weighting TDE is superior to that of the Phase Data (PD) TDE proposed by Piersol. Comparing with the technical realization of GCC TDE GPS TDE can efficiently utilize single chip FFT processor to simplify the signal processing equipment, mitigate computation load and raise estimate speed for TDE.