1. 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

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

3. 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

4. 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

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

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

7. SINGLE FREQUENCY GLOBAL SPECTRUM
All stations combined
Only annual frequency significant

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

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

10. 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