Global Positioning System Reference
In-Depth Information
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D
A
h
C
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B
(a) Satellite and aircraft.
(b) Geometry to determine aircraft altitude.
FIGURE 12.25
Direct and reflected signals from a satellite to an aircraft.
down is used to determine the altitude of an aircraft. This altimeter is passive,
and no transmitter is required.
The arrangement is to mount a two-channel receiver on the aircraft: channels
1 and 2. Channel 1 has an antenna facing upward. This antenna is right-hand
polarized to receive signals directly from the satellites. Channel 2 has a left-
hand polarized antenna facing downward to receive the reflected signals from
ground. The schematic of each channel is the same as shown in Figure 6.5a.
The local oscillators and the digitizing clocks in both channels are phase locked.
The two channels are physically close. The same local oscillator and digitizing
clock are used for both channels. Figure 12.25a shows the relation of the satellite
and the aircraft. Figure 12.25b shows the geometric relationship and is used to
determine the altitude of the aircraft. Because the satellite is much higher than
the aircraft, the direct rays reaching the aircraft and the reflection point on the
ground are parallel.
The height of the aircraft can be found as follows: The difference distance
d
between the direct and reflected paths is measured and expressed as
d
≡
AB
+
BC
=
AB(
1
+
cos 2
θ)
or
(
12
.
20
)
d
1
+
cos 2
θ
AB
=
where
AB
and
BC
are distances and
θ
is the reflection angle, shown in
Figure 12.25b. The altitude of the aircraft
h
(or
DB
) can be found as
d
cos
θ
1
+
cos 2
θ
=
d
cos
θ
1
+
2cos
2
θ
−
1
=
d
2cos
θ
h
≡
DB
=
AB
cos
θ
=
(
12
.
21
)
If the distance
d
and the angle
θ
are known, the altitude of the aircraft can
be found.
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