Digital Signal Processing Reference
In-Depth Information
2.4.2
Multipath Variations
Two types of polarized signals from GNSS satellites or the surfaces can be acquired
by ground GNSS receiver, Right-Hand Circular Polarization (RHCP) and Left-Hand
Circular Polarization (LHCP) (Fig.
2.4
). In multipath propagation, one or multiple
reflections and diffraction of the transmitted signal may occur. For different surfaces,
e.g., ocean, land, snow, ice and vegetation as well as oil, the reflection processes are
different. In the case of reflection of the incident field, the reflection coefficients will
indicate how much the reflected field will be attenuated and how the polarization
state of the incident field will be deformed.
Multipath signal depends on four parameters, the GNSS wavelength (œ), ratio of
the reflected wave amplitude relative to the direct wave ('), GNSS satellite elevation
angle (") and the GNSS antenna height (H) (See Fig.
2.4
), which can be written as
(Elosegui et al.
1995
; Ray and Cannon
1999
)
ıˆ
D
tan
1
˛ sin
4
H
sin "
!
1
C
˛ cos
4
H
sin "
D
ıˆ .; ˛; "; H/
(2.26)
where •ˆ is the reflected wave phase shifted value related to the total (the reflected
wave plus direct one). Here two conditions as the following are discussed.
2.4.2.1
Multipath Variations with Elevation Angle
D
4
H
,theEq.(
2.26
) can be written as
ıˆ
D
tan
1
˛ sin .M sin "/
1
C
˛ cos .M sin "/
When M
D
ıˆ .˛; M; "/
(2.27)
When the GNSS antenna height (H) does not change,
M
would not vary during
the time, so the changes in multipath during the time (velocity of multipath signal
(V•ˆ)) related to the changes in the satellite elevation angle (") (velocity of satellite
elevation angle (V")) can be defined as:
dıˆ
.
dt
d"
.
dt
d
d"
˛ sin .M sin "/
1
C
˛ cos .M sin "/
V
ıˆ
V
"
dıˆ
d"
D
D
D
(2.28)
2
˛ sin .M sin "/
1
C
˛ cos .M sin "/
1
C
and thus after simplicity of Eq. (
2.28
), it can be written as:
V
ıˆ
V
"
dıˆ
d"
D
M˛
˛ cos "
C
cos " cos .M sin "/
D
(2.29)
.1
C
˛ cos .M sin "//
2
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