Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 305

type of satellite and age of the broadcast data. Range errors due to residual clock
errors are generally the smallest following a control segment upload to a satellite,
and they slowly degrade over time until the next upload (typically daily). At zero
age of data (ZAOD), clock errors for a typical satellite are on the order of 0.8m [5,
6]. Errors 24 hours after an upload are generally within the range of 1-4m. User
equipment that is tracking all visible satellites will observe satellites with ages of
data (AODs) varying from 0 to 24 hours. It is thus appropriate, in the development
of a statistical model for clock errors suitable for position or time error budgets, to
average over AOD. The nominal 1-sigma clock error for the constellation in 2004
averaged over AOD was 1.1m, based on the data presented in [5, 6]. It is expected
that residual clock errors will continue to decrease as newer satellites are launched
with better performing clocks and as improvements are made to the control segment
[7]. Average clock errors are also influenced by the frequency of uploads to each sat-
ellite, as discussed in Chapter 3.
Prior to May 2000, GPS clock errors were dominated by SA. Although SA is
now discontinued, a rudimentary understanding of SA is still of importance because
the presence of the SA dither component influenced the design of many fielded GPS
receivers and augmentations. This intentional dithering of the satellite clock was
observed to impart errors in GPS pseudorange and carrier-phase measurements
with a 1-sigma value of approximately 23m [2]. Errors were observed to be statisti-
cally independent from satellite to satellite with significant correlation over time. SA
errors for one satellite would typically randomly walk from a maximum positive
value to a maximum negative value and back with a period of oscillation of around
2-5 minutes. Several detailed statistical models for simulating observed SA errors
are presented in [2].

7.2.2 Ephemeris Error
Estimates of ephemerides for all satellites are computed and uplinked to the satel-
lites with other navigation data message parameters for rebroadcast to the user. As
in the case of the satellite clock corrections, these corrections are generated using a
curve fit of the control segment's best prediction of each satellite's position at the
time of upload. The residual satellite position error is a vector that is depicted in Fig-
ure 7.2, with typical magnitudes in the range of 1-6m [8]. The effective
pseudorange and carrier-phase errors due to ephemeris prediction errors can be
computed by projecting the satellite position error vector onto the satellite-to-user
LOS vector. Ephemeris errors are generally smallest in the radial (from the satellite
toward the center of the Earth) direction. The components of ephemeris errors in
the along-track (the instantaneous direction of travel of the satellite) and cross-
track (perpendicular to the along-track and radial) directions are much larger.
Along-track and cross-track components are more difficult for the control segment
to observe through its monitors on the surface of the Earth, since these components
do not project significantly onto LOSs toward the Earth. Fortunately, the user does
not experience large measurement errors due to the largest ephemeris error compo-
nents for the same reason. The effective pseudorange or carrier-phase error due to
ephemeris prediction errors is on the order of 0.8m (1 σ ) [6].