Global Positioning System Reference
In-Depth Information
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There are other approaches available for absolute antenna calibration. For exam-
ple, Schupler and Clark (2001) mount the antenna on a platform that allows it to
be rotated in elevation and azimuth and then place the whole device in an anechoic
chamber. The interior of the chamber is lined with radiofrequency absorbent material
that reduces signal reflections or “echoes” to a minimum. A signal source antenna
generates the signals. Since the source antenna can transmit at different frequencies,
these anechoic chamber techniques are suitable for studying the frequency depen-
dency of PO and PCV for L1, L2, and other frequencies.
The PO can be dealt with like an eccentricity offset at the station in order to
reference it to the surveying monument. Since the up component
u
PO
is the largest
one it might be sufficient to correct the carrier phase by
ϕ
PO
= λ
−
1
u
PO
sin
∆
θ
(7.7)
[23
where
λ
denotes the wavelength and
θ
is the elevation angle.
7.
2.4 Multipath
Lin
—
1.0
——
Lon
PgE
Once the satellite signals reach the earth's surface, ideally they enter the antenna
directly. However, objects in the receiver's vicinity may reflect some signals before
they enter the antenna, causing unwanted signatures in pseudorange and carrier phase
observations. Although the direct and reflected signals have a common emission time
at the satellite, the reflected signals are always delayed relative to the line-of-sight sig-
nals because they travel longer paths. The amplitude (voltage) of the reflected signal
is always reduced because of attenuation. The attenuation depends on the properties
of the reflector material, the incident angle of the reflection, and the polarization. In
general, reflections with very low incident angle have little attenuation. In addition,
the impact of multipath on the GPS observables depends on the sensitivity of the an-
tenna in terms of sensing signals from different directions, and the receiver's internal
processing to mitigate multipath effects. Multipath is still one of the dominating, if
not the dominant, sources of error in GPS positioning.
Signals can be reflected at the satellite (satellite multipath) or in the surroundings
of the receiver (receiver multipath). Satellite multipath is likely to cancel in the single-
difference observables for short baselines. Reflective objects for receivers on the
ground can be the earth's surface itself (ground and water), buildings, trees, hills,
etc. Rooftops are known to be bad multipath environments because there are often
many vents and other reflective objects within the antenna's field of view.
The impact of multipath on the carrier phases can be demonstrated using a planar
vertical reflection surface at distance
d
from the antenna (Georgiadou and Kleusberg,
1988; Bishop et al., 1985). The geometry is shown in Figure 7.5. We write the direct
line-of-sight carrier phase observable for receiver
k
and satellite
p
as
[23
S
D
=
A
cos
ϕ
(7.8)
In Equation (7.8) we do not use the subscript
k
and superscript
p
in order to simplify
the notation. The symbols
A
and
ϕ
denote the amplitude (signal voltage) and the
phase, respectively. The reflected signal is written as
