Global Positioning System Reference
In-Depth Information
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
and the vector
i
k
that completes the right-handed coordinate system (also
located in the sun-satellite-earth plane). For example, the offsets adopted for Block
II/IIA satellites are
x
=
=
j
×
1
.
023]
T
[0
.
279
0
meters. It can readily be verified that
[
ijk
]
x
x
sa
=
x
sc
+
(7.4)
where
x
sa
is the position of the satellite antenna and
x
sc
denotes the position of the
satellite's center of mass.
The satellite phase center offsets must be determined for each satellite type. When
estimating the offsets from observations while the satellite is in orbit, the effect of
the offsets might be absorbed, at least in part, by other parameters. An example is the
offset in direction
k
and the receiver clock error. Mader and Czopek (2001) report on
an effort to calibrate the phase center of the satellite antenna for a Block IIA antenna
using ground measurements.
[23
7.
2.3 Receiver Antenna Phase Center Offset and Variation
Lin
—
0.0
——
Nor
PgE
The immediate reference point in positioning with GPS is the phase center of the
receiver antenna. Since the phase center cannot be accessed directly with tape we
need to know the relationship between the phase center and an external antenna
reference point (ARP) in order to relate the GPS-determined positions to a surveying
monument. Unfortunately, the phase center is not well defined. Its location varies
with the elevation angle of the arriving signal, i.e., the direction of the satellite. For
some antennas it also depends, although slightly, on the azimuth. The relationship
between the ARP and the phase center, which is the object of antenna calibration, is
usually parameterized in term of phase offset (PO) and phase center variation (PCV).
The largest offset is in height, which can be as much as 10 cm. The PO and the PCV
also depend on the frequency.
Imagine a perfect antenna that has an ARP and a phase center offset that is well
known. Imagine further that you connect a “phase meter” to the antenna and that you
move a transmitter along the surface of a sphere that is centered on the phase center.
In this ideal case, since the distance from the transmitter to the phase center never
changes, the output phase will always read a constant amount. In actuality, there is no
perfect antenna, and that situation can never be realized. Instead, one effectively moves
a source along a sphere centered on a point that one selects as an average phase center.
Now instead of recording a constant phase, one detects phase variations, primarily as
a function of elevation. Since the distance from source to antenna is constant, these
phase variations must be removed so that constant geometric distance is represented
by constant phase measurements. Had we picked another phase center, we would get
another set of phase variations. That is why the PO and PCVs must be used together
and why different POs and PCVs sets will lead one back to the same ARP.
For a long observation series one might hope that the average location of the PCV
is well defined and that the position refers to the average phase center. For RTK
applications there is certainly no such averaging possible. For short baselines where
the antennas at the ends of the line see a satellite at approximately the same elevation
[23
