The use of ambient seismic noise has been intensively investigated to perform passive tomography at various scales. Besides passive tomography, passive monitoring is another application of seismic noise correlation as was shown by the recent observation of postseismic velocity changes around the San Andreas Fault in Parkfield, California. One of the drawbacks of using ambient noise correlation for passive monitoring is the need to average the correlations over a long time period in order to obtain a sufficient signal-to-noise ratio (SNR) for the phase fluctuations to be measured accurately. For the application to passive monitoring, one wants the possibility of following short-term velocity variations (one day or less) using noise correlation functions calculated on short time windows. Another difficulty may then appear when the spatial distribution of noise sources also evolves with time. The aim of this paper is to introduce an adaptive filter to the Parkfield dataset in order to improve the SNR output of the ambient noise correlation functions. When applied to passive monitoring, the temporal resolution can be increased from 30 days up to 1 day. With this improved temporal resolution, the velocity drop observed at Parkfield is shown to be cosesimic with the September 24, 2004 M_w=6.0 event. The relationship between the measured velocity fluctuations and the time-evolution of the spatial distribution of the noise wavefield is also investigated. Finally, the error bar in the amplitudes of the velocity variations are compared with a theoretical expectation.