Noise in multivariate GPS position time-series

A methodology is developed to analyze a multivariate linear model, which occurs in many geodetic and geophysical applications. Proper analysis of multivariate GPS coordinate time-series is considered to be an application. General, special, and more practical stochastic models are adopted to assess the noise characteristics of multivariate time-series. The least-squares variance component estimation (LS-VCE) is applied to estimate full covariance matrices among different series. For the special model, it is shown that the multivariate time-series can be estimated separately, and that the (cross) correlation between series propagates directly into the correlation between the corresponding parameters in the functional model. The time-series of five permanent GPS stations are used to show how the correlation between series propagates into the site velocities. The results subsequently conclude that the general model is close to the more practical model, for which an iterative algorithm is presented. The results also indicate that the correlation between series of different coordinate components per station is not significant. However, the spatial correlation between different stations for individual components is significant (a correlation of 0.9 over short baselines) both for white and for colored noise components.

[1]  N. Crocetto,et al.  Simplified formulae for the BIQUE estimation of variance components in disjunctive observation groups , 2000 .

[2]  N. Perfetti,et al.  Detection of station coordinate discontinuities within the Italian GPS Fiducial Network , 2006 .

[3]  A H Dodson,et al.  Using continuous GPS and absolute gravity to separate vertical land movements and changes in sea-level at tide-gauges in the UK , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[4]  Norbert Mielenz,et al.  Schätzung von Varianzkomponenten mit Gruppenmittelwerten am Beispiel von Legehennen, gehalten in Gruppenkäfigen , 2003 .

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

[6]  Yehuda Bock,et al.  High‐rate real‐time GPS network at Parkfield: Utility for detecting fault slip and seismic displacements , 2004 .

[7]  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 .

[8]  John Langbein,et al.  Noise in GPS displacement measurements from Southern California and Southern Nevada , 2008 .

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

[10]  AliReza Amiri-Simkooei,et al.  Least-squares variance component estimation: theory and GPS applications , 2007 .

[11]  Zuheir Altamimi,et al.  ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications , 2002 .

[12]  P. Teunissen,et al.  Least-squares variance component estimation , 2008 .

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

[14]  P. Teunissen,et al.  Assessment of noise in GPS coordinate time series : Methodology and results , 2007 .

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

[16]  J. Zumberge,et al.  Precise point positioning for the efficient and robust analysis of GPS data from large networks , 1997 .

[17]  Peter Bona,et al.  Precision, Cross Correlation, and Time Correlation of GPS Phase and Code Observations , 2000, GPS Solutions.

[18]  Peiliang Xu,et al.  Estimability analysis of variance and covariance components , 2007 .

[19]  John Langbein,et al.  Noise in two‐color electronic distance meter measurements revisited , 2004 .

[20]  Georgia Fotopoulos,et al.  Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data , 2005 .

[21]  Hans-Peter Plag,et al.  A continuous GPS coordinate time series analysis strategy for high-accuracy vertical land movements , 2008 .

[22]  Marinos Kavouras,et al.  Assessment of observations using minimum norm quadratic unbiased estimation (minque) , 1990 .

[23]  Mike P. Stewart,et al.  Aliased tidal signatures in continuous GPS height time series , 2003 .

[24]  Yehuda Bock,et al.  Seismic wave observations with the Global Positioning System , 2001 .

[25]  Carine Bruyninx,et al.  EPN coordinate time series monitoring for reference frame maintenance , 2004 .

[26]  C. R. Rao,et al.  Estimation of variance and covariance components--MINQUE theory , 1971 .

[27]  J. Beavan.  Noise properties of continuous GPS data from concrete pillar geodetic monuments in New Zealand and comparison with data from U.S. deep drilled braced monuments , 2005 .

[28]  Markus Rothacher,et al.  The International GPS Service (IGS): An interdisciplinary service in support of Earth sciences , 1999 .

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

[30]  Chris Rizos,et al.  A SIMPLIFIED MINQUE PROCEDURE FOR THE ESTIMATION OF VARIANCE-COVARIANCE COMPONENTS OF GPS OBSERVABLES , 2002 .

[31]  Yehuda Bock,et al.  Southern California permanent GPS geodetic array: Error analysis of daily position estimates and site velocities , 1997 .

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

[33]  C. Tiberius,et al.  ESTIMATION OF THE STOCHASTIC MODEL FOR GPS CODE AND PHASE OBSERVABLES , 2000 .

[34]  J. Kusche,et al.  Noise variance estimation and optimal weight determination for GOCE gravity recovery , 2003 .

[35]  J. Kusche,et al.  A Monte-Carlo technique for weight estimation in satellite geodesy , 2003 .

[36]  William H. Press,et al.  Numerical recipes , 1990 .

[37]  Wolfgang Bischoff,et al.  A Procedure for Estimating the Variance Function of Linear Models and for Checking the Appropriateness of Estimated Variances: A Case Study of GPS Carrier-phase Observations , 2006 .

[38]  Ou Ziqiang,et al.  Estimation of variance and covariance components , 1989 .

[39]  C. R. Henderson.  ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS , 1953 .

[40]  Burkhard Schaffrin,et al.  Best invariant covariance component estimators and its application to the generalize multivariate adjustment of heterogeneous deformation observations , 1981 .

[41]  A. Amiri-Simkooei,et al.  Assessing receiver noise using GPS short baseline time series , 2006 .

[42]  Karl-Rudolf Koch,et al.  Parameter estimation and hypothesis testing in linear models , 1988 .

[43]  Peiliang Xu,et al.  Variance Component Estimation in Linear Inverse Ill-posed Models , 2006 .

[44]  Christian Tiberius,et al.  VARIANCE COMPONENT ESTIMATION AND PRECISE GPS POSITIONING: CASE STUDY , 2003 .

[45]  Jinling Wang,et al.  Stochastic Modeling for Static GPS Baseline Data Processing , 1998 .

[46]  F. Wyatt.  Displacement of surface monuments: Horizontal motion , 1982 .

[47]  Kenneth W. Hudnut,et al.  Southern California Permanent GPS Geodetic Array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes , 1997 .

[48]  J. Ray,et al.  Anomalous harmonics in the spectra of GPS position estimates , 2008 .

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

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

[51]  Mike P. Stewart,et al.  GPS height time series: Short‐period origins of spurious long‐period signals , 2007 .

[52]  C.C.J.M. Tiberius,et al.  Weighting GPS Dual Frequency Observations: Bearing the Cross of Cross-Correlation , 1998, GPS Solutions.

[53]  Steffen Schön,et al.  A proposal for modelling physical correlations of GPS phase observations , 2008 .

[54]  W. Caspary.  Concepts of network and deformation analysis , 1987 .

[55]  Derek D. Lichti,et al.  Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares , 2005 .

[56]  Peter Teunissen,et al.  Variance Component Estimation by the Method of Least-Squares , 2008 .

[57]  Wolfgang Bischoff,et al.  A procedure for testing the assumption of homoscedasticity in least squares residuals: a case study of GPS carrier-phase observations , 2005 .

[58]  É. Calais,et al.  Continuous GPS measurements across the Western Alps, 1996–1998 , 1999 .

[59]  Steffen Schön,et al.  Atmospheric turbulence theory applied to GPS carrier-phase data , 2008 .

[60]  Karl-Rudolf Koch,et al.  Maximum likelihood estimate of variance components , 1986 .