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26 October 2010
The uncertainties in a GPS analysis, however, cannot be treated with white noise
statistics because errors with temporal correlations dominate both the phase observations
and estimates of station coordinates (the quasi-observations input to GLOBK). In the
phase residuals (from cview or the sky plots produced by sh_gamit), the visible noise—
from multipathing and tropospheric fluctuations—is typically correlated over spans of
15-30 minutes. This implies that only samples taken at these intervals are independent,
and, to a first approximation, we would get realistic uncertainties by multiplying the
formal errors by the square root of the ratio of this interval to the sampling interval
used—e.g., for the 2 minute sampling commonly used in solve, we would increase the
uncertainties by a factor of 3-5. There also errors with longer correlation times that do
not show up in the residuals but are absorbed into the parameter adjustments. Assessing
the magnitude of these errors requires us to use noise visible in the residuals (phase or
coordinates) to infer the character of the noise at lower frequencies. There are a number
of excellent studies of the character of GPS errors discussed in the presentation
‘Error_Analysis.ppt’ from our most recent workshops on the Documentation page of the
GAMIT/GLOBK web site (e.g., Mao et al. [1999], Dixon et al. [2000], and Williams
[2003]). Once you have adopted a particular weighting of the data, it is often possible to
use external knowledge of the expected behavior of the coordinates or velocities to
validate the uncertainties; see McClusky et al. [2000], Davis et al. [2003], and McCaffrey
et al. [2006].
In GAMIT/GLOBK there are several ways you can control the uncertainties you obtain
for coordinates and velocities, and it is important for you to keep clearly in mind how
each of these operates. The uncertainties generated by solve and passed to GLOBK in the
h-file are determined by the a priori error assigned to the phase observations and by the
sampling interval—solve does not rescale by the square root of χ
2
/df (“postfit nrms” in
the q-file). In the initial (“preliminary”) solution, we normally assign an uncertainty of
10 mm to each one-way L1 phase. By Equation (1), the assigned uncertainty in an LC
phase becomes 32 mm. The mean rms of one-way LC residuals is typically ~6-9 mm, so
the nrms computed by solve is 0.2-0.3. In the second (“final”) solution, we normally
reweight the observations using a constant and elevation-dependent term computed in
data editing by program autcln from the actual (one-way LC) phase residuals. In order to
keep the overall weighting approximately the same as with the 10 mm constant error, the
values computed by autcln (ATLEV table in file autcln.post.sum) are multiplied by an
arbitrary factor of 1.7 (in script sh_sigelv) before being input to solve (via the N-file). We
chose to use inflated values of the a priori phase error and not rescale by the nrms in
order to generate coordinate uncertainties that (in the presence of correlated noise) are
approximately realistic with 2-minute sampling. An equally valid approach would be to
rescale by the nrms (i.e. make χ
2
/df =1.0) and compensate later for the unrealistically low
coordinate uncertainties. With whatever weighting you use in solve, you can increase the
coordinate uncertainties used by GLOBK by rescaling all covariances on the h-file or by
adding white noise or random-walk noise to the variances of individual stations. We
discuss in Section 4.3 why the latter approach is usually preferred.