A network of 13 continuous GPS stations near Parkfield, California has been converted from 30 second to 1 second sampling with positions of the stations estimated in real-time relative to a master station. Most stations are near the trace of the San Andreas fault, which exhibits creep. The noise spectra of the instantaneous 1 Hz positions show flicker noise at high frequencies and change to frequency independence at low frequencies; the change in character occurs between 6 to 8 hours. Our analysis indicates that 1-second sampled GPS can estimate horizontal displacements of order 6 mm at the 99% confidence level from a few seconds to a few hours. High frequency GPS can augment existing measurements in capturing large creep events and postseismic slip that would exceed the range of existing creepmeters, and can detect large seismic displacements.