Extracting white noise statistics in GPS coordinate time series

Jean Philippe Montillet*, Paul Tregoning, Simon McClusky, Kegen Yu

*Corresponding author for this work

Research output: Contribution to journalArticle

21 Citations (Scopus)


The noise in GPS coordinate time series is known to follow a power-law noise model with different components (white noise, flicker noise, and random walk). This work proposes an algorithm to estimate the white noise statistics, through the decomposition of the GPS coordinate time series into a sequence of sub time series using the empirical mode decomposition algorithm. The proposed algorithm estimates the Hurst parameter for each sub time series and then selects the sub time series related to the white noise based on the Hurst parameter criterion. Both simulated GPS coordinate time series and real data are employed to test this new method; the results are compared to those of the standard (CATS software) maximum-likelihood (ML) estimator approach. The results demonstrate that this proposed algorithm has very low computational complexity and can be more than 100 times faster than the CATS ML method, at the cost of a moderate increase of the uncertainty (∼ 5%) of the white noise amplitude. Reliable white noise statistics are useful for a range of applications including improving the filtering of GPS time series, checking the validity of estimated coseismic offsets, and estimating unbiased uncertainties of site velocities. The low complexity and computational efficiency of the algorithm can greatly speed up the processing of geodetic time series.

Original languageEnglish
Article number6329405
Pages (from-to)563-567
Number of pages5
JournalIEEE Geoscience and Remote Sensing Letters
Issue number3
Publication statusPublished - 2013
Externally publishedYes


  • Empirical mode decomposition (EMD)
  • fractional Brownian motion (fBm)
  • GPS coordinates
  • Hurst parameter
  • power-law noise
  • white noise amplitude

Fingerprint Dive into the research topics of 'Extracting white noise statistics in GPS coordinate time series'. Together they form a unique fingerprint.

Cite this