4.3 Object Velocity Measurement Methods
73
In both cases, a majority part of tasks of velocity measuring are solved through
use of Doppler effect. Doppler effect—a frequency change of observed signal in
comparison to radiated one at reciprocal displacement of a source of radiation and
receiver—has been taken as a basis for measuring of relative speed of target movement, and also is a basis for methods of target discrimination and resolution in range
of its radial movement velocity.
Examine in first turn a case when a radiated signal is a monochromatic, and a
target moves away (approaches) relatively to a radar with constant speed. In this
case, a range to a target is a function of time which can be performed as follows:
D(t) = D 0 + V r t,
(4.23)
where V r =
dD(t)
dt
—radial velocity of target motion.
Since a distance D(t) is linear in time, then a frequency of received signal f rcv
can be represented as:
f rcv =
1
2π
dϕ rcv (t)
dt
=
1
2π
d
dt
ω 0
t −
2D(t)
c
+ ϕ 0
= f 0
1 −
2
c
dD(t)
dt
= f 0
1 −
2V r
c
= f 0 −
2V r
λ
.
(4.24)
As we can see from (4.24), a frequency of received signal f rcv differs from
frequency f 0 of radiated signal at value F d = −
2V r
λ
, called a Doppler frequency
shift (Doppler frequency). It is necessary to mention that at target distant D
(t) > 0;
hence a Doppler frequency shift F d is negative, and, consequently, a frequency of
received signal is smaller than radiation frequency. At target approaching to radar—
vice versa: A frequency of received signal is bigger than a frequency of radiated
signal, i.e., D
(t) < 0.
In this way, by comparing a frequency of received signal f rcv with frequency of
radiated one f 0 , we can determined a Doppler shift F d
f rcv = f 0 ± F d ,
and, consequently, a radial velocity of target movement as:
V r =
2
λ
F d .
(4.25)
The radar systems are usually use signals which have different modulation (amplitude or angular). At reflection of such signals by moving targets a distortion of
spectrum shape and time signal structure result, as each component in spectrum is
changed in accordance with (4.24), i.e., as:
73
In both cases, a majority part of tasks of velocity measuring are solved through
use of Doppler effect. Doppler effect—a frequency change of observed signal in
comparison to radiated one at reciprocal displacement of a source of radiation and
receiver—has been taken as a basis for measuring of relative speed of target movement, and also is a basis for methods of target discrimination and resolution in range
of its radial movement velocity.
Examine in first turn a case when a radiated signal is a monochromatic, and a
target moves away (approaches) relatively to a radar with constant speed. In this
case, a range to a target is a function of time which can be performed as follows:
D(t) = D 0 + V r t,
(4.23)
where V r =
dD(t)
dt
—radial velocity of target motion.
Since a distance D(t) is linear in time, then a frequency of received signal f rcv
can be represented as:
f rcv =
1
2π
dϕ rcv (t)
dt
=
1
2π
d
dt
ω 0
t −
2D(t)
c
+ ϕ 0
= f 0
1 −
2
c
dD(t)
dt
= f 0
1 −
2V r
c
= f 0 −
2V r
λ
.
(4.24)
As we can see from (4.24), a frequency of received signal f rcv differs from
frequency f 0 of radiated signal at value F d = −
2V r
λ
, called a Doppler frequency
shift (Doppler frequency). It is necessary to mention that at target distant D
(t) > 0;
hence a Doppler frequency shift F d is negative, and, consequently, a frequency of
received signal is smaller than radiation frequency. At target approaching to radar—
vice versa: A frequency of received signal is bigger than a frequency of radiated
signal, i.e., D
(t) < 0.
In this way, by comparing a frequency of received signal f rcv with frequency of
radiated one f 0 , we can determined a Doppler shift F d
f rcv = f 0 ± F d ,
and, consequently, a radial velocity of target movement as:
V r =
2
λ
F d .
(4.25)
The radar systems are usually use signals which have different modulation (amplitude or angular). At reflection of such signals by moving targets a distortion of
spectrum shape and time signal structure result, as each component in spectrum is
changed in accordance with (4.24), i.e., as: