Global Positioning System Reference
In-Depth Information
T
k,
0
=
ZHD
k
m
h
(ϑ
p
)
ZWD
k
m
wv
(ϑ
p
)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
+
(7.62)
can be computed from the zenith hydrostatic delay (ZHD) and the zenith wet delay
(ZWD) models (6.17) and (6.18) and meteorological data. The mapping functions
m
h
and
m
wv
follow from (6.22). The estimated zenith total delay then becomes
T
k,
0
m(ϑ
p
)
+
T
k
=
dT
k
(7.63)
Zumberge et al. (1998a) introduced PPP at centimeter level with GPS. One of their
go
als was to use postprocessed data from a permanently operating global network of
sta
tions to compute highly accurate positions for individual receivers that are not part
of
the permanent network. They also viewed PPP as a data compression strategy when
th
ey addressed the relationship between achievable position accuracy for individual
sta
tions as a function of the number of permanently observing network stations.
Zu
mberge et al. (1998b) reported centimeter-level accuracy for static receivers and
su
bdecimeter-level accuracy for kinematic receivers, even at a time when selective
av
ailability was still active. They modeled the receiver clock as white noise and the
tro
pospheric delay as random walk in the Kalman filter.
JPL provides a free Internet processing service for PPP (Zumberge, 1998). Witcha-
ya
ngkoon and Segantine (1999) used this service to test the technique for various data
se
ts varying from 1 hour to 24 hours. They reported generally 1 dm repeatability for
1-
hour data sets and 1-2 cm repeatability for data sets greater than 4 hours. Of course
th
e performance characteristics change for the better as the PPP model improves over
ti
me. The JPL service can be used to substitute baseline processing by submitting both
data files of the baseline stations separately. Figure 7.13 further confirms the high
accuracy of the PPP approach. In this particular test the solid earth tides corrections
were not applied. Instead, the station coordinates were estimated every epoch together
with the other parameters after the Kalman filter had initially stabilized. The top part
of the figure shows the estimated variation in coordinates, estimated every 30 seconds
using JPL's high clock rate ephemeris, whereas the bottom part shows the solid earth
tides, computed from software downloaded from the IERS website. The outliers in
the estimated up component are caused by the addition of a rising satellite.
Absolute positioning with only single-frequency observations is expected to be
less accurate, especially in the height. An obvious reason for the degradation in
accuracy is the effect of unmodeled ionospheric delays (Lachapelle et al., 1996).
Øvstedal (2002) used the global ionospheric model provided by the IGS in connection
with single-frequency observations and demonstrated a horizontal epoch-to-epoch
accuracy of better than 1 m and a vertical accuracy of about 1 m.
As pointed out by Kouba (2001), the success of PPP depends on applying a
consistent set of corrections. For example, whereas it is clear that the satellite an-
tenna offsets must be carefully taken into consideration since there is no differenc-
ing of observations between stations that would effectively cancel the impact of
these offsets, knowledge of the satellite clock errors is extremely important for PPP
positioning to be accurate. However, the estimates of satellite antenna offsets and
[25
Lin
—
1.9
——
No
PgE
[25
