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Network-based estimation of time-dependent noise in GPS position time series

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Abstract

Some estimates of GPS velocity uncertainties are very low, \(<\)0.1 mm/year with 10 years of data. Yet, residual velocities relative to rigid plate models in nominally stable plate interiors can be an order of magnitude larger. This discrepancy could be caused by underestimating low-frequency time-dependent noise in position time series, such as random walk. We show that traditional estimators, based on individual time series, are insensitive to low-amplitude random walk, yet such noise significantly increases GPS velocity uncertainties. Here, we develop a method for determining representative noise parameters in GPS position time series, by analyzing an entire network simultaneously, which we refer to as the network noise estimator (NNE). We analyze data from the aseismic central-eastern USA, 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. To test NNE on actual data, we analyze a heterogeneous 15 station GPS network from the central-eastern USA, assuming the noise is a sum of random walk, flicker and white noise. For the horizontal time series, NNE finds higher average random walk than the standard individual station-based method, leading to velocity uncertainties a factor of 2 higher than traditional methods.

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Acknowledgments

We thank James Davis (Columbia University) for providing the SNARF GIA model. We acknowledge Sang-Ho Yun for writing the notch filter code. We appreciate fruitful discussions and computational help from Andrew Bradley. We thank the reviewer Matt King, editor Simon Williams, and two anonymous reviewers for extremely helpful suggestions. This work was supported by NASA Headquarters under the NASA Earth and Space Science Fellowship Program—Grant 14-EARTH14R-47 and by the USGS Grant G13AP00020.

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  1. Stanford University, Stanford, CA, 94305, USA

    Ksenia Dmitrieva & Paul Segall

  2. University of Wisconsin, Madison, WI, 53706, USA

    Charles DeMets

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  1. Ksenia Dmitrieva
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  2. Paul Segall
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Correspondence to Ksenia Dmitrieva.

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Dmitrieva, K., Segall, P. & DeMets, C. Network-based estimation of time-dependent noise in GPS position time series. J Geod 89, 591–606 (2015). https://doi.org/10.1007/s00190-015-0801-9

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