GPS position measurements are widely used for studying various geophysical phenomena  including plate movement, strain accumulation, volcanic deformation, post-glacial rebound, subsidence,  and sea-level change.  Understanding the accuracy of GPS data is therefore paramount.  Traditional methods for estimating noise in GPS time series do not appear to be consistent with residual velocities in the central US where plate motion and post-glacial rebound should be the dominant signals.  We are developing methods  for determining representative  noise parameters in GPS position time series, by analyzing an entire  network simultaneously, that we refer to as the Network Noise Estimator (NNE).  We analyze data from the aseismic central-eastern US, assuming that residual motions relative to North-America, corrected for glacial isostatic adjustment (GIA), represent noise. The position time series are decomposed into signal (plate rotation and GIA), and noise components. NNE simultaneously processes multiple stations  with a Kalman filter, and solves for average noise components for the network by maximum likelihood estimation. Synthetic tests show that NNE correctly estimates even low level random walk, thus providing better estimates of velocity uncertainties than conventional, single station methods.  Figure shows horizontal velocities in a North American fixed reference frame as well as the mean power spectrum which is modeled as a sum of random walk, flicker noise, and white noise.