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The earthquake early warning (EEW) system is difficult to provide consistent magnitude estimate in the early stage of an earthquake occurrence because only few stations are triggered and few seismic signals are recorded. One of the feasible methods to measure the size of earthquakes is to extract amplitude parameters using the initial portion of the recorded waveforms after P-wave arrival. However, for a large-magnitude earthquake (M w > 7.0), the time to complete the whole ruptures resulted from the corresponding fault may be very long. The magnitude estimations may not be correctly predicted by the initial portion of the seismograms. To estimate the magnitude of a large earthquake in real-time, the amplitude parameters should be updated with ongoing waveforms instead of adopting amplitude contents in a predefined fixed-length time window, since it may underestimate magnitude for large-magnitude events. In this paper, we propose a fast, robust and less-saturated approach to estimate earthquake magnitudes. The EEW system will initially give a lower-bound of the magnitude in a time window with a few seconds and then update magnitude with less saturation by extending the time window. Here we compared two kinds of time windows for measuring amplitudes. One is P-wave time window (PTW) after P-wave arrival; the other is whole-wave time window after P-wave arrival (WTW), which may include both P and S wave. One to ten second time windows for both PTW and WTW are considered to measure the peak ground displacement from the vertical component of the waveforms. Linear regression analysis are run at each time step (1- to 10-s time interval) to find the empirical relationships among peak ground displacement, hypocentral distances, and magnitudes using the earthquake records from 1993 to 2012 in Taiwan with magnitude greater than 5.5 and focal depth less than 30 km. The result shows that considering WTW to estimate magnitudes has smaller standard deviation than PTW. The magnitude estimations using 1-s time widow have larger uncertainties. Progressively adopting peak displacement amplitudes (P d ) from 2- to 10-s WTW is suggested for EEW systems. [ABSTRACT FROM AUTHOR]