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Title: Effects of linear trends on estimation of noise in GNSS position time-series

A thorough understanding of time-dependent noise in Global Navigation Satellite System (GNSS) position time-series is necessary for computing uncertainties in any signals found in the data. However, estimation of time-correlated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the time-series. In this study, we investigate how linear trends affect the estimation of noise in daily GNSS position time-series. We use synthetic time-series to study the relationship between linear trends and estimates of time-correlated noise for the six most commonly cited noise models. We find that the effects of added linear trends, or conversely de-trending, vary depending on the noise model. The commonly adopted model of random walk (RW), flicker noise (FN) and white noise (WN) is the most severely affected by de-trending, with estimates of low-amplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Non-integer power-law noise estimates are also less affected by de-trending, but are very sensitive to the addition of trend when the spectral index is less than one. We derive an analytical relationship between linear trends and the estimated RW variance for the special case ofmore » pure RW noise. Finally, overall, we find that to ascertain the correct noise model for GNSS position time-series and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.« less
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  1. Stanford Univ., CA (United States). Dept. of Geophysics
Publication Date:
Report Number(s):
Journal ID: ISSN 0956-540X; 637622
Grant/Contract Number:
AC04-94AL85000; 14-EARTH14R-47; 13057
Accepted Manuscript
Journal Name:
Geophysical Journal International
Additional Journal Information:
Journal Volume: 208; Journal Issue: 1; Journal ID: ISSN 0956-540X
Oxford University Press
Research Org:
Stanford Univ., CA (United States)
Sponsoring Org:
USDOE; National Aeronautic and Space Administration (NASA); Southern California Earthquake Center (SCEC) (United States)
Country of Publication:
United States
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Time-series analysis; Transient deformation; noise estimation; GNSS
OSTI Identifier: