Extracting White Noise Statistics in GPS Coordinate Time Series

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.

[1]  G. Blewitt,et al.  Global deformation from the great 2004 Sumatra-Andaman Earthquake observed by GPS: Implications for rupture process and global reference frame , 2006 .

[2]  Simon D. P. Williams,et al.  CATS: GPS coordinate time series analysis software , 2008 .

[3]  John Langbein,et al.  Correlated errors in geodetic time series: Implications for time‐dependent deformation , 1997 .

[4]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[5]  Manfred Schroeder,et al.  Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise , 1992 .

[6]  Kegen Yu,et al.  Leaky LMS Algorithm and Fractional Brownian Motion Model for GNSS Receiver Position Estimation , 2011, 2011 IEEE Vehicular Technology Conference (VTC Fall).

[7]  Yehuda Bock,et al.  Error analysis of continuous GPS position time series , 2004 .

[8]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[9]  Paul Tregoning,et al.  Atmospheric effects and spurious signals in GPS analyses , 2009 .

[10]  T. Herring,et al.  Introduction to GAMIT/GLOBK , 2006 .

[11]  Matt A. King,et al.  A first look at the effects of ionospheric signal bending on a globally processed GPS network , 2010 .

[12]  T. Dixon,et al.  Noise in GPS coordinate time series , 1999 .

[13]  Jose Alvarez-Ramirez,et al.  1/fα fractal noise generation from Grünwald–Letnikov formula , 2009 .

[14]  L. Oxley,et al.  Estimators for Long Range Dependence: An Empirical Study , 2009, 0901.0762.

[15]  CinC challenge 2002 undertaken by non-stationary and fractal techniques , 2002, Computers in Cardiology.

[16]  H. Schuh,et al.  Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium‐Range Weather Forecasts operational analysis data , 2006 .

[17]  Simon D. P. Williams,et al.  Fast error analysis of continuous GPS observations , 2008 .

[18]  Gabriel Rilling,et al.  Empirical mode decomposition as a filter bank , 2004, IEEE Signal Processing Letters.

[19]  W. Willinger,et al.  ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY , 1995 .