Investigation of the noise properties at low frequencies in long GNSS time series

  • X. He
  • M. S. BosEmail author
  • J. P. Montillet
  • R. M. S. Fernandes
Original Article


The accuracy by which velocities can be estimated from GNSS time series is mainly determined by the low-frequency noise, below 0.2–0.1 cpy, which are normally described by a power-law model. As GNSS observations have now been recorded for over two decades, new information about the noise at these low frequencies has become available and we investigate whether alternative noise models should be considered using the log-likelihood, Akaike and Bayesian information criteria. Using 110 globally distributed IGS stations with at least 12 years of observations, we find that for 80–90% of them the preferred noise models are still the power law or flicker noise with white noise. For around 6% of the stations, we found the presence of random-walk noise, which increases the linear trend uncertainty when taken into account in the stochastic noise model of the time series by about a factor of 1.5 to 8.4, in agreement with previous studies. Next, the Generalised Gauss–Markov with white noise model describes the stochastic properties better for 4% and 5% of the stations for the East and North component, respectively, and 13% for the vertical component. For these stations, the uncertainty associated with the tectonic rate is about 2 times smaller compared to the case when the standard power-law plus white noise model is used.


GNSS Time series analysis Error analysis Information criteria 



We would like to acknowledge Dr. Jürgen Kusche (Editor-in-Chief) and the anonymous reviewers for their valuable comments and suggestions. Machiel Bos was sponsored by national Portuguese funds through FCT in the scope of the Project IDL-FCT-UID/GEO/50019/2019 and Grant Number SFRH/BPD/89923/2012. The Portuguese team used computational resources provided by C4G—Collaboratory for Geosciences (PINFRA/22151/2016), supported by FCT (Portugal). Note that the latest version of the software Hector used to produce the results in this work is available at ( Xiaoxing was sponsored by National key R&D Program of China (2018YFC1503600), Nation science foundation for distinguished young scholars of China (41525014), National Natural Science Foundation of China (41704030, 41804007, 41604013, 41674005, 41501502, 41761089), Jiangxi Province Key Lab for Digital Land (DLLJ201801 & 03), Natural Science Foundation of Jiangxi Province (20181BAB203027) and Chongqing Bureau of Quality and technology Supervision (CQZJKY2018004).

Supplementary material

190_2019_1244_MOESM1_ESM.docx (45 kb)
Supplementary material 1 (DOCX 45 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil Engineering and ArchitectureEast China Jiaotong UniversityNan ChangChina
  2. 2.GNSS Research CenterWuhan UniversityWuhanChina
  3. 3.Instituto D. LuizUniversidade da Beira InteriorCovilhãPortugal
  4. 4.Space and Earth Geodetic Analysis LaboratoryUniversidade da Beira InteriorCovilhãPortugal
  5. 5.Institute of Earth Surface DynamicsUniversity of LausanneLausanneSwitzerland

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