Global Positioning System Reference
In-Depth Information
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angle, orienting both antennas in the same direction can largely eliminate the PO and
PCV. This elimination procedure works only for the same antenna types. For large
baselines or when mixing antenna types, the antenna calibration is necessary and
corrections must be applied. Antenna calibration is also important when estimating
tropospheric parameters, since both the PCV and the tropospheric delay depend on
the elevation angle.
The NGS (Mader, 1999) has developed procedures for relative antenna calibration
using field observations. All test antennas are calibrated with respect to the same
reference antenna, which happens to be an AOAD/M T choke ring antenna. The
basic idea is that if the same reference antenna is always used for all calibrations, the
PO and PCV of the reference antenna cancel when double-differencing observations
of a new baseline and applying the calibrated PO and PCV to both antennas. This
technique is accurate as long as the elevation difference of a satellite, as seen from
both antennas, is negligible in terms of the PCV (which is parameterized as a function
of the elevation angle). Since the PCV amounts to about only 1-2 cm and varies
smoothly with elevation angle, relative phase calibration is applicable to baselines of
several thousand kilometers in length. NGS uses a calibration baseline of 5 m. The
reference antenna and the test antenna are connected to the same type of receiver. Both
receivers use the same rubidium oscillator as an external frequency standard. Because
the test baseline is known, a common frequency standard is used, and because the
tropospheric and ionospheric effects cancel over such a short baseline, the single-
difference discrepancies over time are very flat and can be modeled as
ϕ
p
12
,b
[23
Lin
—
0.0
——
No
*PgE
12
,
0
i
= τ
i
+ α
1
β
+ α
2
β
i
2
+ α
3
β
i
3
+ α
4
β
i
4
ϕ
p
p
i
p
p
p
−
(7.5)
[23
The subscript
i
denotes the epoch, the superscript
p
identifies the satellite having
elevation angle
β
i
, and
τ
i
is the remaining relative time delay (receiver clock error).
The coefficients
τ
i
are estimated by observing all satellites from rising
to setting. The result of the relative calibration of the test antenna is then given by
α
1
to
α
4
and
2
3
4
ϕ
antenna
,
PCV
(
ˆ
β
)
= α
1
β + α
2
β
+ α
3
β
+ α
4
β
+ ξ
(7.6)
The symbol
ξ
denotes a translation such that
ϕ
antenna
,
PCV
(
90°
)
ˆ
=
0. The remaining
clock difference estimate
cancel in double
differencing. Recall that the NGS calibration is relative and therefore (7.6) must
be applied in the double-differencing mode. An example of relative PCV is seen in
τ
is not included in (7.6), Both
τ
and
ξ
Figure 7.3. The vertical axis shows the difference
ϕ
12
,b
−
ϕ
12
,
0
i
−τ
i
for all satellites.
The multipath is clearly visible in this figure; it has a much higher frequency than the
PCV and therefore does not affect the polynomial estimation. Equation (7.6) is used
together with the PO that NGS derives from 24-hour data sets. Again, it is sufficient
to define the PO of the reference antenna because the calibrated POs are used in the
relative mode.
Automated absolute field calibration of GPS antennas in real time is discussed
in Wübbena et al. (2000), Schmitz et al. (2002), and references listed therein. They
use a robotic arm to determine the absolute PO and PCV as a function of elevation
