US 2008/0174475 A1 · SIGNAL PROCESSING FOR ACCELERATING MOVING TARGETS

Abstract

A method for performing signal processing for accelerating moving targets, in one implementation, encompasses a method for performing coherent integration of pulses within a CPI for SMTI radar. In an embodiment, the method comprises the steps of determining the Fast Fourier Transform (FFT) for each pulse, and multiplying the FFT by a pulse compression reference function. The method then proceeds by shifting phase of the pulse-compressed FFT by applying a first factor derived from a ground reference point and a second factor derived from a velocity-acceleration hypothesis to provide phase-shifted data, shifting the envelope of the phase-shifted data by applying one factor derived from range history and a second factor derived from a velocity-acceleration hypothesis to provide aligned data, and determining the Inverse FFT for the aligned data to provide a set of target data of the form H(p,i1,i2,i3), where p is CPI number, i1 is range index, i2 is velocity index, and i3 is coarse acceleration index, the latter three indices each referenced to the starting time of the first CPI. In a further embodiment, the invention encompasses first performing coherent integration for each CPI within a dwell of CPIs, then performing non-coherent integration in an efficient way, taking full advantage of the alignment to the starting time of the first CPI.

Claims25

Dependent claims

A method for processing pulses within a CPI for SMTI radar, the method comprising the steps of:

(a) determining Fast Fourier Transform (FFT) for each pulse;
(b) multiplying the FFT by a pulse compression reference function;
(c) shifting phase of the pulse-compressed FFT by applying a first factor derived from a ground reference point and a second factor derived from a velocity-acceleration hypothesis to provide phase-shifted data;
(d) shifting envelope of the phase-shifted data by applying one factor derived from range history and a second factor derived from a velocity-acceleration hypothesis to provide aligned data;
and
(e) determining Inverse FFT for the aligned data to provide a set of target data of the form H(p,i1,i2,i3), where p is CPI number, i1 is range index, i2 is velocity index, and i3 is coarse acceleration index.

3 more elements

A method for processing pulses within a CPI for SMTI radar, wherein the SMTI radar has a characteristic transmitted chirp waveform, the method comprising the steps of:

(a) determining Fast Fourier Transform (FFT) for each pulse;
(b) multiplying the FFT by a pulse compression reference function to provide a pulse-compressed FFT by:
determining a transfer function of the transmitted chirp waveform;
determining a conjugate of the transfer function;
and
multiplying the FFT by the conjugate of the transfer function of the transmitted chirp waveform;
(c) selecting a set of velocity hypotheses given by
V
0

(
i
2
)
=
(
i
2
-
N
2
-
1
2
)

Δ


V
,
i
2
=
0
,
…

,
N
2
-
1
and selecting a set of acceleration hypotheses given by
A

(
i
3
)
=
(
i
3
-
N
3
-
1
2
)

Δ


A
,
i
3
=
0
,
…

,
N
3
-
1
;
(d) multiplying the pulse-compressed FFT by
exp

{
j

4

π
λ

[
R
G

(
t
p
+
n


Δ


t
)
-
R
G

(
t
p
)
-
N
2
-
1
2

Δ


V
·
n


Δ


t
]
}
.

exp

{
j

2

π
s

k
^
M

[
R
G

(
t
p
+
n


Δ


t
)
-
R
G

(
0
)
-
N
2
-
1
2

Δ


V

(
t
p
+
n


Δ


t
)
]
}
where:
M represents number of samples;
and
k
^
=
{
k
,
k
=
0
,
…

,
M
/
2
-
1
k
-
M
,
k
=
M
/
2
,
…


M
-
1
}
;
(e) determining
fact

(
n
,
k
)
=
2

π

[
1
λ

n


Δ


t
·
(
2


t
p
+
n


Δ


t
)
+
k
^
2


sM

(
t
p
+
n


Δ


t
)
2
]
for n=0, . . . ,N−1, and k=0, . . . ,M−1;
(f) determining
W

(
k
)
=
exp

[
j


2

πΔ


V


Δ


t

(
2
λ
+
k
^
sM
)
]
for k=0, . . . ,M−1, and
FFT{W(k)−n2/2};
(g) for i3=0, . . . ,N3−1, performing the following operations:
(1) multiply the result of step (d) by
exp[jA(i3)fact(n,k)]
for n=0, . . . ,N−1, and k=0, . . . ,M−1, yielding a result of the form F(k,n,i3);
(2) perform a transformation from the pulse index n to the velocity hypothesis index i2 by a Chirp-Z Transform computation comprising:
G(k,i2,i3)=Σn=0N−1F(k,n,i3)W(k)i2n
for k=0, . . . ,M−1, and i2=0,. . . ,N2−1;
(3) multiply G(k,i2,i3) by
exp

(
j


2

πΔ


Vt
p

k
^
sM

i
2
)
for k=0, . . . ,M−1, and i2=0, . . . ,N2−1;
and
(4) perform an IFFT with respect to k to yield an output of the form H(p,i1,i2,i3), where p is CPI number, i1 is range index, i2 is velocity index, and i3 is coarse acceleration index.

369 more elements

A method for processing radar data over a dwell of CPIs for SMTI radar, the method comprising the steps of:

(a) performing coherent integration for each CPI within the dwell to provide an output of the form H(p,i1,i2,i3), where p is CPI number, i1 is range index, i2 is velocity index, and i3 is coarse acceleration index;
(b) establishing an increment value ΔA′ between acceleration hypotheses such that
Δ


A
′
≤
β

λ
T
C

T
D
where:
β denotes a fraction of a velocity resolution cell that an actual velocity is allowed to migrate through due to acceleration mismatch;
TD denotes dwell time;
and
TC denotes length of a CPI;
(c) introducing an increased number of acceleration hypotheses corresponding to
A
′

(
i
3
′
)
=
(
i
3
′
-
N
3
′
-
1
2
)

Δ


A
′
,
i
3
′
=
0
,
…

,
N
3
′
-
1
where:
i3′ denotes an index associated with the increased number of acceleration hypotheses;
and
N3′ denotes total number of increased acceleration hypotheses;
(d) choosing an acceleration index according to the relation
i
~
3
=
N
3
-
1
2
+
round

[
(
i
3
′
-
N
3
′
-
1
2
)

Δ


A
′
Δ


A
]
;
(e) choosing a velocity hypothesis index according to the relation
i
~
2
=
i
2
+
round

{
[
A
′

(
i
3
′
)
-
A

(
i
~
3
)
]

t
p
Δ


V
}
;
(f) summing power over all CPIs in the dwell to complete the NCI process through the relation
Σp=0P−1|H(p,i1,ĩ2,ĩ3)|2;
where:
P is the total number of CPIs in the dwell.

145 more elements

An SMTI radar system for processing radar data over a dwell of CPIs comprising:

means for performing coherent integration for each CPI within the dwell to provide an output of the form H(p,i1,i2,i3), where p is CPI number, i1 is range index, i2 is velocity index, and i3 is coarse acceleration index;
means for establishing an increment value ΔA′ between acceleration hypotheses such that
Δ


A
′
≤
β


λ
T
C

T
D
where:
β denotes a fraction of a velocity resolution cell that an actual velocity is allowed to migrate through due to acceleration mismatch;
TD denotes dwell time;
and
TC denotes length of a CPI;
means for introducing an increased number of acceleration hypotheses corresponding to
A
′

(
i
3
′
)
=
(
i
3
′
-
N
3
′
-
1
2
)

Δ


A
′
,
i
3
′
=
0
,
…

,
N
3
′
-
1
where:
i3′ denotes an index associated with the increased number of acceleration hypotheses;
and
N3′ denotes total number of increased acceleration hypotheses;
means for choosing an acceleration index according to the relation
i
~
3
=
N
3
-
1
2
+
round

[
(
i
3
′
-
N
3
′
-
1
2
)

Δ


A
′
Δ


A
]
;
means for choosing a velocity hypothesis index according to the relation
i
~
2
=
i
2
+
round

{
[
A
′

(
i
3
′
)
-
A

(
i
~
3
)
]

t
p
Δ


V
}
;
means for summing power over all CPIs in the dwell to complete the NCI process through the relation
Σp=0P−1|H(p,i1,ĩ2,ĩ3)|2;
where:
P is the total number of CPIs in the dwell.

146 more elements

A method for processing radar return pulse data over a dwell of CPIs for SMTI radar, the method comprising the steps of:

(a) determining Fast Fourier Transform (FFT) for each pulse;
(b) multiplying the FFT by a pulse compression reference function to provide a pulse-compressed FFT by:
determining a transfer function of the transmitted chirp waveform;
determining a conjugate of the transfer function;
and
multiplying the FFT by the conjugate of the transfer function of the transmitted chirp waveform;
(c) selecting a set of velocity hypotheses given by
V
0

(
i
2
)
=
(
i
2
-
N
2
-
1
2
)

Δ


V
,

i
2
=
0
,
…

,
N
2
-
1
and selecting a set of acceleration hypotheses given by
A

(
i
3
)
=
(
i
3
-
N
3
-
1
2
)

Δ


A
,

i
3
=
0
,
…

,
N
3
-
1
;
(d) multiplying the pulse-compressed FFT by
exp

{
j


4

π
λ

[
R
G

(
t
p
+
n


Δ


t
)
-
R
G

(
t
p
)
-
N
2
-
1
2

Δ


V
·
n


Δ


t
]
}
·
exp

{
j


2

π
s

k
^
M

[
R
G

(
t
p
+
n


Δ


t
)
-
R
G

(
0
)
-
N
2
-
1
2

Δ


V

(
t
p
+
n


Δ


t
)
]
}
where:
M represents number of samples;
and
k
^
=
{
k
,
k
=
0
,
…

,
M
/
2
-
1
k
-
M
,
k
=
M
/
2
,
…


M
-
1
}
;
(e) determining
fact

(
n
,
k
)
=
2

π

[
1
λ

n


Δ


t
·
(
2

t
p
+
n


Δ


t
)
+
k
^
2

sM

(
t
p
+
n


Δ


t
)
2
]
for n=0, . . . ,N−1, and k=0, . . . ,M−1;
(f) determining
W

(
k
)
=
exp

[
j2πΔ


V


Δ


t

(
2
λ
+
k
^
sM
)
]
for k=0, . . . ,M−1, and
FFT{W(k)−n2/2};
(g) for i3=0, . . . ,N3−1, performing the following operations:
(1) multiply the result of step (d) by
exp[jA(i3)fact(n,k)]
for n=0, . . . ,N−1, and k=0, . . . ,M−1, yielding a result of the form F(k,n,i3);
(2) perform a transformation from the pulse index n to the velocity hypothesis index i2 by a Chirp-Z Transform computation comprising:
G(k,i2,i3)=Σn=0N−1F(k,n,i3)W(k)i2n
for k=0, . . . ,M−1, and i2=0, . . . ,N2−1;
(3) multiply G(k,i2,i3) by
exp

(
j2πΔ


Vt
p

k
^
sM

i
2
)
for k=0, . . . ,M−1, and i2=0, . . . ,N2−1;
and
(4) perform an IFFT with respect to k to yield an output of the form H(p,i1,i2,i3), where p is CPI number, i1 is range index, i2 is velocity index, and i3 is coarse acceleration index;
(h) establishing an increment value ΔA′ between acceleration hypotheses such that
Δ


A
′
≤
β


λ
T
C

T
D
where:
β denotes a fraction of a velocity resolution cell that an actual velocity is allowed to migrate through due to acceleration mismatch;
TD denotes dwell time;
and
TC denotes length of a CPI;
(i) introducing an increased number of acceleration hypotheses corresponding to
A
′

(
i
3
′
)
=
(
i
3
′
-
N
3
′
-
1
2
)

Δ


A
′
,

i
3
′
=
0
,
…

,
N
3
′
-
1
where:
i3′ denotes an index associated with the increased number of acceleration hypotheses;
and
N3′ denotes total number of increased acceleration hypotheses;
(j) choosing an acceleration index according to the relation
i
~
3
=
N
3
-
1
2
+
round

[
(
i
3
′
-
N
3
′
-
1
2
)

Δ


A
′
Δ


A
]
;
(e) choosing a velocity hypothesis index according to the relation
i
~
2
=
i
2
+
round

{
[
A
′

(
i
3
′
)
-
A

(
i
~
3
)
]

t
p
Δ


V
}
;
(k) summing power over all CPIs in the dwell to complete the NCI process through the relation
Σp=0P−1|H(p,i1,ĩ2,ĩ3)|2;
where:
P is the total number of CPIs in the dwell.

509 more elements

Dependencies are inferred from the claim text.

Signal processing for accelerating moving targets

Life of this patent

Signal processing for accelerating moving targets

Life of this patent

Abstract

Claims25