THE RELATIVE CONTRIBUTION OF THE ANNUAL AND DRACONITIC PERIODS IN GPS STATION POSITION SPECTRA Motivation Time Series Analysis Spectra and Results Conclusions Paul Barrett, USNO/EO 2008 IGS Workshop, Miami Beach, 2008 June 2

MOTIVATION Ray, et al. 2008 Power seen at ~1 cpy and its harmonics (possibly to 8th)‏ Attributed to draconitic (or GPS precession; 1.04 cpy) period Not seen in VLBI or SLR data (except annual period)‏ Results from Fourier Analysis Power at multiple harmonics gives a ramp function with sharp jump at fundamental period Implies non-physical signal

DISCRETE FOURIER TRANSFORM (DFT)‏ Schuster (1905) or Lomb-Scargle (1982) periodogram Appropriate for small datasets with even samples and gaps, or Large (>1000 points) datasets with uneven samples and gaps No off-diagonal terms (i.e. cosine*sine term = 0 )‏ Generalized periodogram - Bretthorst (1988)‏ In “Bayesian Spectrum Analysis and Parameter Estimation” Appropriate for unevenly sampled data with gaps 2x2 matrix - including off-diagonal terms Student t-Distribution Unknown errors Marginalize (or integrate-out) standard deviation

SINGLE FREQUENCY SUMMED SPECTRA ITRF 2005 combination data GPS station position residuals 169 stations >400 weekly measurements Sum of individual station spectra Results – two sets of periods Annual period And 1st & 2nd harmonic For each coordinate Draconitic (1.04 cpy) period At 2nd & 3rd harmonics for each coordinate At 5th harmonic for north coord No other signals >7 cpy

DUAL FREQUENCY SUMMED SPECTRA 4x4 matrix w/off-diagonal terms Identifies two frequencies 3.05 cpy & 3.18 cpy

DUAL FREQUENCY SUMMED SPECTRA Identifies one frequency Peak is along diagonal ~6.24 cpy

SINGLE FREQUENCY GLOBAL SPECTRUM All stations combined Only annual frequency significant

VLBI SPECTRAL ANALYSIS Each station separately, then summed Only annual frequency significant All stations combined No significant frequencies

SLR SPECTRAL ANALYSIS Each station separately, then summed Only annual frequency significant All stations combined Annual frequency significant in North position

CONCLUSIONS Individual GPS station position residual spectra show: Annual periods at 1, 2, & 3 cpy Draconitic periods at ~3.12, ~4.16, & ~6.24 cpy No significant periods >7 cpy Global GPS station residuals show only annual periods Draconitic period is coherent on a per station basis, not between stations Implies incorrect modeling of orbits during eclipse Individual and Global SLR station residuals show annual periods Only Individual VLBI station residuals show an annual period