### 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 »

- Publication Date:

- Report Number(s):
- SAND2016-3023J

Journal ID: ISSN 0956-540X; 637622

- Grant/Contract Number:
- AC04-94AL85000; 14-EARTH14R-47; 13057

- Type:
- Accepted Manuscript

- Journal Name:
- Geophysical Journal International

- Additional Journal Information:
- Journal Volume: 208; Journal Issue: 1; Journal ID: ISSN 0956-540X

- Publisher:
- 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

- Language:
- English

- Subject:
- 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Time-series analysis; Transient deformation; noise estimation; GNSS

- OSTI Identifier:
- 1340237

```
Dmitrieva, K., Segall, P., and Bradley, A. M..
```*Effects of linear trends on estimation of noise in GNSS position time-series*. United States: N. p.,
Web. doi:10.1093/gji/ggw391.

```
Dmitrieva, K., Segall, P., & Bradley, A. M..
```*Effects of linear trends on estimation of noise in GNSS position time-series*. United States. doi:10.1093/gji/ggw391.

```
Dmitrieva, K., Segall, P., and Bradley, A. M.. 2016.
"Effects of linear trends on estimation of noise in GNSS position time-series". 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 time-series},

author = {Dmitrieva, K. and Segall, P. and Bradley, A. M.},

abstractNote = {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 of 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.},

doi = {10.1093/gji/ggw391},

journal = {Geophysical Journal International},

number = 1,

volume = 208,

place = {United States},

year = {2016},

month = {10}

}