Digital Signal Processing Reference
In-Depth Information
shift
f
D
in the GPS transmitter frequency
f
T
at the receiver can be expressed as the
projection of the satellite velocities on the ray paths (Kursinski et al.
1997
), such as
k
R
;
f
T
c
V
T
k
T
C
V
R
f
D
D
c
V
T
sin
R
;
f
T
C
V
T
C
V
R
cos
R
C
V
T
D
cos
T
sin
T
(5.17)
where
V
R
and
V
T
are velocity vectors for receiver and transmitter, and
k
R
and
k
T
are unit vectors representing the direction of the ray path at the receiver and
transmitter, and
c
is the velocity of light in vacuum. The superscripts (
r
and )
represent the radial and tangential components of the velocity vectors, and
T
and
R
are the angels between the ray path and the satellite position vectors at the
transmitter and receiver (Fig.
5.4
).
According to Bouguer's rule in Eq. (
5.7
) and the geometry of Fig.
5.4
,wehave:
a
D
n .r
T
/ r
T
sin
T
D
n .r
R
/ r
R
sin
R
D
n .r
t
/ r
t
:
(5.18)
As the transmitter and the receiver are at reasonably high altitudes, we can simply
setting the refractive index equals to unity at both transmitter and receiver, thus we
have
a
D
r
T
sin
T
D
r
R
sin
R
:
(5.19)
The total bending angle ˛ according to the geometry in Fig.
5.4
follows
˛
D
T
C
R
C
;
(5.20)
where,
r
T
,
r
R
, and
r
t
are the distance of the transmitter, receiver and the tangent point
from the center of curvature, and is the open angle between the transmitter and
receiver vectors.
Given the precise measurements of the occultation geometry (transmitter and
receiver position and velocity vectors) and extra Doppler shift, the bending angle can
be derived iteratively from Eqs. (
5.17
,
5.18
,
5.19
, and
5.20
) under the assumption of
local spherically symmetric atmosphere.
5.3.2.2
Radio-Holographic (RH) Method
In the lower troposphere, the multipath problem due to the water vapor gradients
could result in large error in the geometric optics bending retrieval. Also the vertical
resolution of GO retrieval is limited by the size of the Fresnel zone (Kursinski et al.
1997
). In order to tackle the multipath problem and improve the vertical resolution
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