
This website examines the performance of the GPS satellite orbits determined by each Analysis Center (AC) participating in the IGS Reprocessing Campaign #1. A companion site looks at the associated polar motion time series. Orbits for the 1025 days through week 1459 (end of 2007) have been used to obtain consistent, comparable, and modern results from all ACs. This span covers epochs from MJD 53439.5 through 54463.5, which corresponds to the period 10 Mar 2005 (week 1313_5) through 29 Dec 2007 (week 1459_6). In the cases where more than the usual 96 15minute epochs are reported in the AC SP3 files, only those between 00:00 and 23:45 are used here.
As there is no absolute knowledge of the true GPS orbits, we use a measure of satellite position repeatability to characterize each AC product set. Each daily AC satellite ephemeris for each pair of consecutive days has been treated as pseudoobservations in a fit to the extended CODE orbit model (three position and three velocity parameters plus nine nuisance solar radiation parameters), then extrapolated to the midpoint epoch between the days, and the geocentric satellite position differences computed to give time series of orbit repeatabilities for each satellite and AC. Occasional data gaps have been filled by linear interpolation, then FFT power spectra computed, and the spectra stacked over the full GPS constellation for each AC and lightly smoothed in frequency (using a sliding boxcar over each three adjacent frequencies). Results are shown in the plots below.
In an earlier application of this method to operational IGS combined GPS orbits, Griffiths and Ray (2009) found the error introduced by the fitting and extrapolation process to range between 0 and 8 mm (mean = 3 mm) per geocentric component with 3D differences of 3 to 10 mm (mean = 6 mm). So, the effect of the orbit fittingextrapolation process nearly always adds insignificant noise to these dayboundary orbit comparisons. That conclusion is also evident in the obvious diversity of results among AC orbits found here.
Most continuous geophysical processes and most physical noise processes
possess power spectra that decrease as the frequency raised to some
characteristic negative power ("spectral index"). The spectra are usually
"reddish" in the sense of having more power at the lower frequencies
(i.e., longer periods). For reference, a power law with spectral index
of 1 is drawn on each plot (not a fit). This corresponds to the
behavior of a flicker phase noise process. White noise has a flat
power spectrum independent of frequency and probably explains the
asymptotic highfrequency flattening apparent in most AC spectra.
Several interesting spectral lines are also indicated in each plot
below.
CODE — ps file 
EMR — ps file 
ESA — ps file 
GFZ — ps file 
JPL — ps file 
MIT — ps file 
NGS — ps file 
PDR — ps file 
SIO — ps file 
ULR — ps file 
Our analysis reveals highly varied AC orbit behaviors. But most AC spectra generally follow a flicker phase powerlaw trend (slope 1) from the longest down to about monthly periods. This characteristic of the IGS orbits probably has much to do with the longappreciated temporal correlations in GPS station position time series (e.g., Williams et al., J. Geophys. Res., 109(B03412), doi: 10.1029/2003JB002741, 2004). Several spectra show superposed broadly distributed semiannual power, which is probably related mostly to satellite eclipse seasons, while diffuse fortnightly bands are also common to most ACs. The latter could possibly be linked to a range of tidal modeling or perhaps nutation errors. In addition, we have marked several harmonics of the GPS draconitic year (1.040 cpy), of which the even multiples appear to be present with varying amplitudes in most spectra. For a summary of the AC spectral features, see the table at bottom below.
Recall that the point of comparison between the successive daily orbital arcs is at the fixed epoch 23:52:30 (GPS time), 7.5 minutes after the end of one SP3 file and 7.5 minutes before the next. As the orbit differences advance in 1day steps, this comparison point moves around the GPS ellipse about 1 degree per day. A full circuit is completed in the 351.4 d of the GPS draconitic year due to the slow precession of the orbit plane because of the Earth's oblateness. During this time, two eclipse seasons are encountered for each GPS orbit plane. It is the beating of these two cycles that probably explains the appearance of the even 1.040 cpy harmonics in nearly all the spectra.
Highfrequency white noise floors can be detected in most AC orbit spectra, with a minimum asymptotic sigma of about 10.5 mm for JPL. ESA and MIT have slightly higher highfrequency scatters of about 14 mm while the remaining ACs are somewhat higher still. However, the orbit discontinuity scatters for JPL are probably not fully comparable to most other ACs because JPL uses overlapping 30hr processing arcs (3 hr of extra data at each end of the day). This practice introduces correlations between the orbits of successive days and attenuates the orbit discontinuities by an unknown amount. A similar but greater attenuating effect is expected for CODE and PDR since they report the midday values for each sliding 3day processing arc (with constrained velocity breaks introduced every 12 hr). The observed orbit discontinuities for CODE are as expected. But unexpectedly, the highfrequency character of the PDR orbit discontinuities is more erratic than for nearly all other ACs, rather than being smoother. The remaining ACs (except GFZ, see below) use strictly 24 hr of data for each daily orbit. (Note, though, that even with daily independent orbit arcs, some level of correlation between days is expected due to the weekly stacking of the station coordinates used by the IGS.)
The orbit discontinuity spectrum for GFZ is unique. Tidal features are not seen, but in addition to the even harmonics of 1.040 cpy, there are harmonics of a weekly frequency (0.1429 cpy) up to at least the third multiple. The weekly harmonics each seem to be split into dense spectral combs by some unknown modulation. To check whether this behavior could be an artifact of the fitandextrapolate method we have used here to compute the dayboundary discontinuities, two tests have been performed. In the first (left plot below), the GFZ orbits have been fit using the same extended CODE model and the result of the fit at 00:00 is compared to the originally reported values (no extrapolation involved). The plot shows the associated power spectrum for those differences. In the second test (right plot below), the same fit is made but omitting values for the 23:45 epoch, then the fit is extrapolated and compared to the originally reported value at 23:45. The associated power spectrum for those differences is shown.
While similar features are seen in the test spectra as in the
previous GFZ discontinuity plot, the power is much lower. So we do
not believe that the GFZ result is an artifact. Instead it seems
likelier that the GFZ orbits contain signal components that are not
well fitted by the extended CODE model, which show up also in the tests.
But the presumed nononceperrevolution GFZ signals also contribute
even more to the orbit discontinuities. This is especially difficult
to understand for GFZ because their reported repro1 SP3 files span periods
longer than 24 hours suggesting that some implicit smoothing has
been enforced in their data processing (if the extra epochs are not
merely extrapolations but use observational data).
orbit fit error spectrum — ps file 
orbit fit & extrapolation error spectrum — ps file 
A possible explanation for the weekly harmonics in the GFZ orbit discontinuities can be found by inspecting the spectrum of the dayboundary discontinuities for their reported UT1S/LODS values. See this companion site for details and explanations; the UT1S/LODS discontinuity spectra for GFZ and PDR are reproduced below. UT1S/LODS dayboundary discontinuities are much more difficult to interpret than corresponding polar motion discontinuities. Because the polar motion offsets and rates are both estimated freely and in a fully selfconsistent way, their discontinuities afford insights into the data modeling and processing. The same is not true for UT1/LOD because UT1 is not observable by satellite methods due to direct correlation with the orbit node parameters that must also be estimated simultaneously. Some constraint must be applied to fix UT1 at some epoch and variations in UT1 (equivalent to LOD) determined at other epochs relative to the fixed epoch. Nevertheless, the UT1S/LODS discontinuities can provide some insight into the UT1 fixation process used by the ACs.
GFZ — ps file 
PDR — ps file 
GFZ and PDR (and perhaps other ACs) both have interesting dense UT1S/LODS spectral features around the weekly period and its second and third harmonics, which is not surprising for a weekly fixation of UT1. For GFZ, however, these features match the similar structures seen above in their reprocessed dayboundary orbit discontinuities. In principle, one might imagine that a causal relationship could operate in either direction. However, it seems more likely that weekly UT1 fixation has somehow affected the GFZ and PDR orbit nodes and induced corresponding errors in their orbits. (GTZ has not submitted reprocessed orbits.) The even starker weekly UT1S/LODS discontinuity resonances in the PDR spectrum are less clearly expressed in their orbit spectra than for GFZ, possibly because the PDR UT1S/LODS discontinuity power levels are considerably lower than for GFZ. So rather than inducing clear features in the PDR orbit spectra, the UT1 fixation effect appears only as an excess of highfrequency orbit scatter.
The table below summarizes the features that can be observed in the spectra of the AC orbit discontinuity plots above.
Features in Spectra of AC Dayboundary Orbit Discontinuities  
AC  annual  semiannual  tidal/other bands  1.040 cpy harmonics  Remarks 
COD    Y  14 d band  4^{th}  3 * 24 hr arc 
EMR    Y  14 d band  4^{th}, 6^{th}, 8^{th}, 10^{th}  24 hr arc 
ESA    ?  14 d band  4^{th}?  24 hr arc 
GFZ    Y?  7 d comb, 3.5 d comb, 2.33 d comb  4^{th}, 6^{th}, 10^{th}  3 * 24 hr arc 
JPL    Y  14d band  4^{th}, 6^{th}  3 + 24 + 3 hr arc 
MIT    ?  14 d band, 7 d band?  4^{th}  24 hr arc 
NGS  ?    14 d band  4^{th}, 6^{th}, 8^{th}  24 hr arc 
PDR  ?  ?  too noisy  4^{th}?, uncertain  3 * 24 hr arc 
SIO    Y  14 d band, 7 d band?  4^{th}, 8^{th}?  24 hr arc 
ULR    ?  14 d band, 4 d band?  3^{rd}  24 hr arc 
Send comments to Jake Griffiths  (updated 13 May 2009) 