=Paper=
{{Paper
|id=Vol-2076/paper-06
|storemode=property
|title=Modeling the Clutter Reflection Suppression Algorithm In Synthetic-Aperture Radar
|pdfUrl=https://ceur-ws.org/Vol-2076/paper-06.pdf
|volume=Vol-2076
|authors=Leonid G. Dorosinskiy,Andrew A. Kurganski
}}
==Modeling the Clutter Reflection Suppression Algorithm In Synthetic-Aperture Radar==
https://ceur-ws.org/Vol-2076/paper-06.pdf
Modeling the Clutter Reflection Suppression
Algorithm in Synthetic-Aperture Radar
Leonid G. Dorosinskiy1 and Andrew A. Kurganski1
Ural Federal University, pr. Mira, 19, Yekaterinburg, 620002, Russian Federation
k-and92@mail.ru
Abstract. Modeling the clutter reflection suppression algorithm in syn-
thetic-aperture radar is considered in the article. The proposed algorithm
allows one to increase the signal detection efficiency with closely located
sources of clutter due to the use of a priori data of static objects of the
infrastructure.
Keywords: Optimal detection algorithm, SAR, clutter suppression
1 Introduction
The forming problem of the optimal algorithm for signal detection in the
radar with synthesized aperture (SAR) under the presence of the clutter reflec-
tions from the local objects and the design of the efficiency estimation method
of such detection are the main problems in the development air and satellite
observational platforms for remote earth and water surfaces sensing system.
2 Algorithm development
Devoted to the problems of signal processing within the SAR papers [1–3]
pay great attention to research of the detection algorithms under clutter impact
caused by the reflection from the underlying surface and noises. A SAR antenna
pattern in some practical situations (along with the valid signal reflected from
the multiple-unit target) has powerful clutter signals produced by the reflec-
tions from the clutter objects. Therefore, in these cases the processing algorithm
should be formed accounting both the distribution target character and the clut-
ter presence. Determination of the main principles of algorithm construction and
the analysis methods present the content of this paper. Suppose the side-looking
radar moves along the linear path. The range resolution cell has the target and
clutter signals formed by the separate reflectors, which are distant at dti (i = 1, n)
and dci (i = 1, N ) from the coordinate origin with the ∆t step, and n and N are
the numbers of the target and clutter reflectors respectively (Fig. 1). Under the
discrete time processing, the vector of the observed data is presented in the
following form:
Y = βT AT + βC AC + NN (1)
50
X(dt1,1 ), X(dt2,1 ), . . . , X(dtn,1 )
X(dt1,2 ), X(dt2,2 ), . . . , X(dtn,2 )
βT = (2)
...
X(dt1,M ), X(dt2,M ), . . . , X(dtn,M )
where w 4π t w
X(dtn,k ) =w exp(−j dn rk ) w (3)
w w
λR0
is the phase signal distribution reflected from i-target element on the points of
synthesized aperture with the coordinates rk , k = 1, M (λ is the wavelength);
AT and AC are (n × 1) and (N × 1) vectors of complex target and clutter am-
2
plitudes which are normal random variables with zero mean and dispersions σTi
2
and σCi respectively; matrix βC is determined similarly to (2) and (3), NN is the
complex amplitude vector of gaussian noise.
Fig. 1. Task geometry
Recording the observed data in the form (1), the quadric form of sufficient statis-
tics for the detection of the target signal is
α = Y ∗T ΘY, (4)
−1 −1
where Θ = RC − RTC is the processing weight function,
∗T −1
RTC = βT QT βT + RC , (5)
∗T
RC = βC QC βC + RN , (6)
are the correlation matrices of vector (1) with and without the target signal
respectively
2 2
QT = diag(σT 1
, . . . , σT n
), (7)
51
2 2
QC = diag(σC 1
, . . . , σC N
), (8)
2
RN = σN E (9)
where * is a complex conjugation, T is a transpose sign, E is the identity matrix
2
with the noise dispersion σN = 1. Using Woodbury formula for the determination
of the optimal weight function the equation of the sufficient statistics derives as
α = ZP Z ∗T , (10)
where
∗T −1
P = (E + QT βT RC βT )−1 QT , (11)
−1 −1 −1 ∗T −1 ∗T −1
RC = RN − RN βC (E + QC βC RN βC )−1 QC βC RN , (12)
N
X
−1 ∗
Z = Y T RC βT = Y T X ∗ (dti ) − χli Y T X ∗ (dcl ), (13)
l=1
n
X
χli = ρlt X T (dct )X ∗ (dci ) (14)
t=1
where ρlt is the matrix (11) element.
The schematic structure with the optimal algorithm (10) is shown on Fig. 2.
The main functional operation in (13) is
M
X 4π t
Y T X ∗ (di ) = exp(−j d rk ) (15)
λR0 i
k=1
that presents the chirp demodulation and the discrete Fourier transform (DFT)
estimated for the spatial frequencies 2di /λR0 that corresponding to all elements
of target (clutters).
3 Algorithm analysis
The relative gain of the optimal processing in comparison with the traditional
one in SAR does not allow one to estimate the absolute values of the detection
characteristics with multiple-unit sources of signals and clutters. On the other
hand, the exact calculation of these characteristics is connected with the sig-
nificant calculation difficulties caused in the determination and integration of
distributed statistics (10). Therefore, the efficiency estimation of the considered
algorithm uses the method based on the Chernoff bound [3], according to which
the detection and false alarm probabilities are counted the formulas
PD = −exp[γ(ν(s) + (1 − s)(ν̇(s) + 0.5(1 − s)2 )ν̈(s))]
p
×erfc[(1 − s) γ ν̈(s)], (16)
52
Fig. 2. Optimal algorithm flowchart
PF = exp[γ(ν(s) + sν̇(s) + 0.5s2 ν̈(s))]
p
×erfc[s γ ν̈(s)], (17)
where
Z∞ Z∞ 2
Y
ν(s) = ln ... P [P (Y /C)]1−s dY, (18)
T +C
−∞ −∞
and ν̇(s) and ν̈(s) are the first and second derivatives of (18), s = 0 . . . 1 is the
dummy argument, γ is the number of independent tests (for SAR γ is the nlook,
e.g. the number of used frequencies with multi frequency probing or the number
of non-coherent summed synthesized images for partly coherent SAR working
mode), P (Y /(T + C)), P (Y /C) are the probability densities of the observed
vector under presence or absence of the target signal.
According to the case presented in the paper, formula (18) has the following
form:
ν(s) = −0.5 × ln(det(RT ) × s + det(RC ) × (1 − s)
+0.5s × ln(RT ) + 0.5(1 − s) ln(det(RC )). (19)
Using formulas (16)–(19), the performance and detection characteristics are
calculated. The perfomance curves shown in Fig. 3—5 are calculated for the
2 2 2
case when there is only one target and one clutter, σT = σC = σN = 1, and the
number of observation periods is M = 1300.
In the graphs, the performance curves are also shown for the no-clutter case
and for processing that does not use the algorithm presented in the article.
53
Figure 3 shows curves for different values of target-clutter space and ∆d at
γ = 1. The graph shows that processing using the algorithm described in the
article improves the detection characteristics even at γ = 1. With increasing
target-clutter space, starting from 10 m, the performance curve approaches to
the case when the clutter is completely absent.
Fig. 3. Perfomance curves for 1 target and 1 clutter
Fig. 4 shows the curves for different values of γ at ∆d = 20 m. Figure 5 is
the zoomed part of Fig. 4. With increasing γ, detection characteristics have a
significant gain in comparison with processing without clutter compensation.
Detection characteristics of a multi-element target (n = 5) against a back-
2 2
ground of multiple-element clutter (N = 5) for σN = 1, σC = {0.1; 1; 0.1; 0.7; 0.5},
M = 100, γ = 2 for different target-clutter location cases (Fig. 6) are shown in
Fig. 7.
From the presented curves it follows that with a greater spatial separation
of the target and clutters the algorithm significantly increases the detection
probability of the target.
54
Fig. 4. Perfomance curves for 1 target and 1 clutter
Fig. 5. Perfomance curves for 1 target and 1 clutter (zoomed)
55
Fig. 6. Detection perfomance for 5 targets and 5 clutters
56
Fig. 7. Target-clutter location cases
57
4 Conclusion
Clutter reflection suppression algorithm in SAR presented in the article sig-
nificantly improves the detection efficiency of the signals reflected from targets,
which are locatered closely with clutter objects, even in cases where the clutters
overlap targets.
References
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No. 11 (2015)
2. Baumgartner, S. V.: Fast GMTI algorithm for traffic monitoring based on a priori
knowledge. IEEE transactions on geoscience and remote sensing. Vol. 50, No. 11
(2012)
3. Dorosinskiy, L. G.: The research of the distributed objects radar image recognition
algorithms. Applied and fundamental studies. Proceedings of the 2st International
academic vonference. Vol. 1, 211–214 (2013)