Time-Dependent Noise in GPS Position Time Series By a Network Noise Estimator

Some current estimates of GPS velocity uncertainties for continuous stations with more than a decade of data can be very low, < 0.1 mm per year. Yet, velocities with respect to rigid plates can be an order of magnitude larger, even in nominally stable plate interiors. This could be caused by underestimating low frequency, time-dependent noise, such as random walk. Traditional estimators, based on individual time series, are insensitive to low amplitude random walk, yet such noise significantly increases GPS velocity uncertainties.

We develop a new approach to estimating noise in GPS time series, focusing on areas where the signal in the data is well characterized. We analyze data from the seismically inactive parts of central US. The data is decomposed into signal, plate rotation and Glacial Isostatic Adjustment (GIA), and various noise components. Our method processes multiple stations simultaneously with a Kalman Filter, and estimates average noise components for the network by maximum likelihood. Currently, we model white noise, flicker noise and random walk. Synthetic tests show that this approach correctly estimates the velocity uncertainty by determining a good estimate of random walk variance, even when it is too small to be correctly estimated by traditional approaches.

We present preliminary results from a network of 15 GPS stations in the central USA. The data is in a North America fixed reference frame, we subtract seasonal components and GIA displacements used in the SNARF model. Hence, all data in this reference frame is treated as noise. We estimate random walk of 0.82 mm/yr^0.5, flicker noise of 3.96 mm/yr^0.25 and white noise of 1.05 mm. From these noise parameters the estimated velocity uncertainty is 0.29 mm/yr for 10 years of daily data. This uncertainty is significantly greater than estimated by the traditional methods, at 0.12 mm/yr. The estimated uncertainty is still less than the median residual velocity in the North America fixed reference frame, which could indicate that the true uncertainties are even larger.

Additionally we estimated noise parameters and velocity uncertainties for the vertical component and for the data with common-mode signal removed. We are planning to extend this work by processing larger networks.