Digital Signal Processing Reference
In-Depth Information
It can be seen that the function of multipath signal based on satellite elevation
angle significantly depends on the H value since M is a function of H. When GNSS
satellite elevation angle is equal to zero or /2, it can as deduced as
dıˆ
d"
D
M˛
˛
C
1
.1
C
˛/
2
M˛
1
C
˛
"
D
0
!
D
(2.30)
2
!
dıˆ
d"
D
0
"
D
(2.31)
2.4.2.2
Multipath Variations with Antenna Height
The multipath signal variability with respect to the GNSS antenna height can be
written as:
dıˆ
.
dt
dH
.
dt
d
dH
˛ sin.NH /
1
C
˛ cos.NH /
V
ıˆ
V
H
D
dıˆ
dH
D
D
(2.32)
2
˛ sin.NH /
1
C
˛ cos.NH /
1
C
where N is defined as a function of satellite elevation angle (") as the following:
4
N
D
sin "
(2.33)
Similarly the following simplicity relation between multipath signal's velocity
and
H
can be expressed as:
V
ıˆ
V
H
D
dıˆ
dH
.cos.NH /
C
˛/
.˛
C
cos.NH //
2
D
N˛
(2.34)
C
sin
2
.NH /
Therefore, in a similar way, if the GNSS antenna height becomes zero as
H
D
0, so
dıˆ
dH
˛
1
C
˛
D
N
(2.35)
The satellite elevation angle is important to affect the multipath signals variability
when the GNSS antenna heights are changing parallel. Moreover, to understand
when or where the multipath signals variability is going to be zero with respect to
the changes in GNSS antenna height, it can be seen
8
<
"
D
sin
1
8H
dıˆ
dH
D
0
!
N˛ .cos.NH /
C
˛/
D
0
!
(2.36)
"
D
sin
1
3
16H
:
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