Global Positioning System Reference
In-Depth Information
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Figure 7.5
Geometry for reflection on a vertical planar plane.
[23
S
R
= α
A
cos
(ϕ
+ θ
) ,
0
≤ α ≤
1
(7.9)
Lin
—
0.5
——
Nor
PgE
A
/A
, where
A
is the amplitude
of the reflected signal. The total multipath phase shift is
The amplitude reduction factor (attenuation) is
α =
θ =
∆τ + φ
f
(7.10)
where
f
is the frequency,
is the fractional shift. The
multipath delay shown in Figure 7.5 is the sum of the distances
AB
and
BC
, which
equals 2
d
cos
∆τ
is the time delay, and
φ
[23
β
. Converting this distance into cycles and then to radians gives
4
π
d
θ =
cos
β + φ
(7.11)
λ
where
is the carrier wavelength. The composite signal at the antenna is the sum of
th
e direct and reflected signal,
λ
S
=
S
D
+
S
R
=
R
cos
(ϕ
+ ψ
)
(7.12)
It
can be verified that resultant carrier phase voltage
R(A,
α
,
θ
)
and the carrier phase
m
ultipath delay
ψ
(
α
,
θ
)
are
A
1
2
1
/
2
R(A,
α
,
θ
)
=
+
2
α
cos
θ + α
(7.13)
tan
−
1
α
sin
θ
ψ
(
α
,
θ
)
=
(7.14)
1
+ α
cos
θ
Regarding notation, we used the symbols
d
k,
1
and
d
k,
2
in Chapter 5 to denote the total
multipath, i.e., the multipath effect of all reflections on L1 and L2, respectively. If we
consider the case of constant reflectivity, i.e.,
α
is constant, the maximum path delay
