GNSS-TS-NRS: An Open-Source MATLAB-Based GNSS Time Series Noise Reduction Software

The global navigation satellite system (GNSS) has seen tremendous advances in measurement precision and accuracy, and it allows researchers to perform geodynamics and geophysics studies through the analysis of GNSS time series. Moreover, GNSS time series not only contain geophysical signals, but also unmodeled errors and other nuisance parameters, which affect the performance in the estimation of site coordinates and related parameters. As the number of globally distributed GNSS reference stations increases, GNSS time series analysis software should be developed with more flexible format support, better human–machine interaction, and with powerful noise reduction analysis. To meet this requirement, a new software named GNSS time series noise reduction software (GNSS-TS-NRS) was written in MATLAB and was developed. GNSS-TS-NRS allows users to perform noise reduction analysis and spatial filtering on common mode errors and to visualize GNSS position time series. The functions’ related theoretical background of GNSS-TS-NRS were introduced. Firstly, we showed the theoretical background algorithms of the noise reduction analysis (empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD)). We also developed three improved algorithms based on EMD for noise reduction, and the results of the test example showed our proposed methods with better effect. Secondly, the spatial filtering model supported five algorithms on a separate common model error: The stacking filter method, weighted stacking filter method, correlation weighted superposition filtering method, distance weighted filtering method, and principal component analysis, as well as with batch processing. Finally, the developed software also enabled other functions, including outlier detection, correlation coefficient calculation, spectrum analysis, and distribution estimation. The main goal of the manuscript is to share the software with the scientific community to introduce new users to the GNSS time series noise reduction and application.

[1]  J. L. Nolan,et al.  Numerical calculation of stable densities and distribution functions: Heavy tails and highly volatil , 1997 .

[2]  Laurence C. Breaker,et al.  Estimating Rates of Acceleration Based on the 157-Year Record of Sea Level from San Francisco, California, U.S.A. , 2012 .

[3]  Yingchun Shen,et al.  TSAnalyzer, a GNSS time series analysis software , 2017, GPS Solutions.

[4]  Yunfeng Tian,et al.  iGPS: IDL tool package for GPS position time series analysis , 2011, GPS Solutions.

[5]  Matt A. King,et al.  Accuracy assessment of ocean tide models around Antarctica , 2005 .

[6]  Jeanne Sauber,et al.  Crustal deformation associated with glacial fluctuations in the eastern Chugach Mountains, Alaska , 2000 .

[7]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  Alvaro Santamaría-Gómez.  SARI: interactive GNSS position time series analysis software , 2019, GPS Solutions.

[9]  Tieding Lu,et al.  Accuracy enhancement of GPS time series using principal component analysis and block spatial filtering , 2015 .

[10]  S. Williams.  The effect of coloured noise on the uncertainties of rates estimated from geodetic time series , 2003 .

[11]  Jingnan Liu,et al.  Comparative Analysis of the Effect of the Loading Series from GFZ and EOST on Long-Term GPS Height Time Series , 2020, Remote. Sens..

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

[13]  K. Rattan,et al.  Introductory Mathematics for Engineering Applications , 2011 .

[14]  Jean-Philippe Montillet,et al.  Estimation of offsets in GPS time-series and application to the detection of earthquake deformation in the far-field , 2015 .

[15]  Jean-Philippe Montillet,et al.  One-step solution to local tie vector determination at co-located GNSS/VLBI sites , 2018, Studia Geophysica et Geodaetica.

[16]  Nikolaos Doulamis,et al.  GNSSGET and GNSSPLOT Platforms - Matlab GUIs for Retrieving GNSS Products and Visualizing GNSS Solutions , 2018, VISIGRAPP.

[17]  R. Nikolaidis.  Observation of geodetic and seismic deformation with the Global Positioning System , 2002 .

[18]  Yehuda Bock,et al.  Physical applications of GPS geodesy: a review , 2016, Reports on progress in physics. Physical Society.

[19]  Mate Boban,et al.  User Manual, Version 1.2 , 2015 .

[20]  Guillaume Ramillien,et al.  Glacial isostatic adjustment and nonstationary signals observed by GRACE , 2009 .

[21]  Peter J. Clarke,et al.  Ocean tide loading displacements in western Europe: 2. GPS‐observed anelastic dispersion in the asthenosphere , 2015 .

[22]  Boudewijn Ambrosius,et al.  Defining the plate boundaries in the Azores region , 2006 .

[23]  Xianghong Hua,et al.  Review of current GPS methodologies for producing accurate time series and their error sources , 2017 .

[24]  K. Moffett,et al.  Remote Sens , 2015 .

[25]  Kegen Yu,et al.  Application of Lévy processes in modelling (geodetic) time series with mixed spectra , 2019, Nonlinear Processes in Geophysics.

[26]  Thomas A. Herring,et al.  MATLAB Tools for viewing GPS velocities and time series , 2003 .

[27]  Boudewijn Ambrosius,et al.  Angular velocities of Nubia and Somalia from continuous GPS data: implications on present-day relative kinematics , 2004 .

[28]  Paolo Dabove,et al.  GNSS Positioning Using Mobile Devices with the Android Operating System , 2020, ISPRS Int. J. Geo Inf..

[29]  J. Montillet,et al.  Geodetic Time Series Analysis in Earth Sciences , 2020 .

[30]  Bofeng Li,et al.  Spatiotemporal filtering of regional GNSS network’s position time series with missing data using principle component analysis , 2013, Journal of Geodesy.

[31]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[32]  Manuel R. Arahal,et al.  A Matlab Educational GUI for Analysis of GNSS Coverage and Precision , 2015 .

[33]  Kegen Yu,et al.  Application of Lévy Processes in Modelling (Geodetic) Time Series With Mixed Spectra , 2020 .

[34]  Xavier Collilieux,et al.  Global sea-level rise and its relation to the terrestrial reference frame , 2009 .

[35]  Yehuda Bock,et al.  Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake , 1997 .

[36]  A. Vitti.  Sigseg: a tool for the detection of position and velocity discontinuities in geodetic time-series , 2012, GPS Solutions.

[37]  Umberto Tammaro,et al.  Strain Pattern and Kinematics of the Canary Islands from GNSS Time Series Analysis , 2020, Remote. Sens..

[38]  John Langbein,et al.  Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors , 2017, Journal of Geodesy.

[39]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[40]  Harald Schuh,et al.  The Role of GNSS Vertical Velocities to Correct Estimates of Sea Level Rise from Tide Gauge Measurements in Greece , 2017 .

[41]  Yehuda Bock,et al.  Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis , 2006 .

[42]  Xavier Collilieux,et al.  Nontidal ocean loading: amplitudes and potential effects in GPS height time series , 2012, Journal of Geodesy.

[43]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[44]  Simon D. P. Williams,et al.  Offsets in Global Positioning System time series , 2003 .

[45]  Janusz Bogusz,et al.  On the Handling of Outliers in the GNSS Time Series by Means of the Noise and Probability Analysis , 2015 .