Digital Signal Processing Reference
In-Depth Information
For a target that has translational and rotational motion and, for
simplicity, assuming the target's azimuth angle
a
is zero, then the range of
a point-scatterer at (
x
,
y
,
z
= 0) in the target coordinate system can be
rewritten as
R
P
(
t
)=
R
(
t
)
+
x
cos
u
(
t
)
-
y
sin
u
(
t
) and the returned signal
in (5.11) can be rewritten as
s
R
(
t
) = exp{
-
j
4
p
f
0
R
(
t
)/
c
}
¥
-¥
¥
-¥
¥
-¥
r
(
x
,
y
,
z
)
(5.12)
exp
H
-
j
2
p
[
xf
x
(
t
)
-
yf
y
(
t
)]
J
dxdydz
for
2
R
P
(
t
)/
c
£
t
£
T
PRI
+
2
R
P
(
t
)/
c
where the components of the spatial frequency are determined by
f
x
(
t
)=
2
f
0
cos
u
(
t
)
(5.13)
c
and
f
y
(
t
)=
2
f
0
sin
u
(
t
)
(5.14)
c
From (5.12) we know that if the target's initial range
R
0
is known
exactly and the velocity
V
R
and acceleration
a
R
of the target's motion are
known exactly over the entire coherent processing interval, then the extrane-
ous phase term of the motion exp{
-
j
4
p
f
0
R
(
t
)/
c
} can be exactly removed
by multiplying exp{
j
4
p
f
0
R
(
t
)/
c
} on both sides of (5.12). Therefore, the
reflectivity density function
r
(
x
,
y
,
z
) of the target can be obtained simply
by taking the inverse Fourier transform of the phase-compensated baseband
signal
s
R
(
t
) exp{
j
4
p
f
0
R
(
t
)/
c
}.
The process of estimating the target's motion and removing the extrane-
ous phase term is called range tracking. This is a fundamental step in
the standard motion compensation procedure, also called coarse motion
compensation. Then, the inverse Fourier transform may be used to recon-
struct the reflective density function of the target.
In order to use the Fourier transform properly, certain conditions must
be satisfied. During the entire coherent imaging processing time, the scatterers
must remain in their range cells, and their Doppler frequency shifts must
Search WWH ::
Custom Search