Effects of linear trends on estimation of noise in GNSS position timeseries
Abstract
A thorough understanding of timedependent noise in Global Navigation Satellite System (GNSS) position timeseries is necessary for computing uncertainties in any signals found in the data. However, estimation of timecorrelated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the timeseries. In this study, we investigate how linear trends affect the estimation of noise in daily GNSS position timeseries. We use synthetic timeseries to study the relationship between linear trends and estimates of timecorrelated noise for the six most commonly cited noise models. We find that the effects of added linear trends, or conversely detrending, 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 detrending, with estimates of lowamplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Noninteger powerlaw noise estimates are also less affected by detrending, 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 »
 Authors:

 Stanford Univ., CA (United States). Dept. of Geophysics
 Publication Date:
 Research Org.:
 Stanford Univ., CA (United States)
 Sponsoring Org.:
 USDOE; National Aeronautic and Space Administration (NASA); Southern California Earthquake Center (SCEC) (United States)
 OSTI Identifier:
 1340237
 Report Number(s):
 SAND20163023J
Journal ID: ISSN 0956540X; 637622
 Grant/Contract Number:
 AC0494AL85000; 14EARTH14R47; 13057
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Geophysical Journal International
 Additional Journal Information:
 Journal Volume: 208; Journal Issue: 1; Journal ID: ISSN 0956540X
 Publisher:
 Oxford University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Timeseries analysis; Transient deformation; noise estimation; GNSS
Citation Formats
Dmitrieva, K., Segall, P., and Bradley, A. M. Effects of linear trends on estimation of noise in GNSS position timeseries. United States: N. p., 2016.
Web. doi:10.1093/gji/ggw391.
Dmitrieva, K., Segall, P., & Bradley, A. M. Effects of linear trends on estimation of noise in GNSS position timeseries. United States. doi:10.1093/gji/ggw391.
Dmitrieva, K., Segall, P., and Bradley, A. M. Thu .
"Effects of linear trends on estimation of noise in GNSS position timeseries". United States. doi:10.1093/gji/ggw391. https://www.osti.gov/servlets/purl/1340237.
@article{osti_1340237,
title = {Effects of linear trends on estimation of noise in GNSS position timeseries},
author = {Dmitrieva, K. and Segall, P. and Bradley, A. M.},
abstractNote = {A thorough understanding of timedependent noise in Global Navigation Satellite System (GNSS) position timeseries is necessary for computing uncertainties in any signals found in the data. However, estimation of timecorrelated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the timeseries. In this study, we investigate how linear trends affect the estimation of noise in daily GNSS position timeseries. We use synthetic timeseries to study the relationship between linear trends and estimates of timecorrelated noise for the six most commonly cited noise models. We find that the effects of added linear trends, or conversely detrending, 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 detrending, with estimates of lowamplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Noninteger powerlaw noise estimates are also less affected by detrending, 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 of pure RW noise. Finally, overall, we find that to ascertain the correct noise model for GNSS position timeseries and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.},
doi = {10.1093/gji/ggw391},
journal = {Geophysical Journal International},
number = 1,
volume = 208,
place = {United States},
year = {2016},
month = {10}
}