Anomalous harmonics in the spectra of GPS position estimates

Prior studies of the power spectra of GPS
position time series have found pervasive seasonal signals
against a power-law background of flicker noise
plus white noise. Dong et al. (2002) estimated that less
than half the observed GPS seasonal power can be
explained by redistributions of geophysical fluid mass
loads. Much of the residual variation is probably caused
by unidentified GPS technique errors and analysis artifacts.
Among possible mechanisms, Penna and Stewart
(2003) have shown how unmodeled analysis errors at
tidal frequencies (near 12- and 24-hour periods) can be
aliased to longer periods very efficiently. Signals near
fortnightly, semiannual, and annual periods are expected
to be most seriously affected. We have examined spectra
for the 167 sites of the International GNSS (Global
Navigation Satellite Systems) Service (IGS) network
having more than 200 weekly measurements during
1996.0–2006.0. The non-linear residuals of the weekly
IGS solutions that were included in ITRF2005, the latest
version of the International Terrestrial Reference Frame(ITRF), have been used. To improve the detection of
common-mode signals, the normalized spectra of all sites
have been stacked, then boxcar smoothed for each local
north (N), east (E), and height (H) component. The
stacked, smoothed spectra are very similar for all three
components. Peaks are evident at harmonics of about 1
cycle per year (cpy) up to at least 6 cpy, but the peaks
are not all at strictly 1.0 cpy intervals. Based on the 6th
harmonic of the N spectrum, which is among the
sharpest and largest, and assuming a linear overtone
model, then a common fundamental of 1.040 ± 0.008
cpy can explain all peaks well, together with the expected
annual and semiannual signals. A flicker noise
power-law continuum describes the background spectrum
down to periods of a few months, after which the
residuals become whiter. Similar sub-seasonal tones are
not apparent in the residuals of available satellite laser
ranging (SLR) and very long baseline interferometry
(VLBI) sites, which are both an order of magnitude less
numerous and dominated by white noise. There is weak
evidence for a few isolated peaks near 1 cpy harmonics
in the spectra of geophysical loadings, but these are
much noisier than for GPS positions. Alternative explanations
related to the GPS technique are suggested by
the close coincidence of the period of the 1.040 cpy
frequency, about 351.2 days, to the ‘‘GPS year’’; i.e., the
interval required for the constellation to repeat its inertial
orientation with respect to the sun. This could indicate
that the harmonics are a type of systematic error related
to the satellite orbits. Mechanisms could involve orbit
modeling defects or aliasing of site-dependent positioning
biases modulated by the varying satellite geometry.