Edinburgh Research Explorer Model-Based Evaluation of Signal-to-Clutter Ratio for Landmine Detection Using Ground-Penetrating Radar Citation for published version: Giannakis, I, Giannopoulos, A & Yarovoy, A 2016, 'Model-Based Evaluation of Signal-to-Clutter Ratio for Landmine Detection Using Ground-Penetrating Radar' IEEE Transactions on Geoscience and Remote Sensing, vol 54, no. 6, pp. 3564 - 3573. DOI: 10.1109/TGRS.2016.2520298 Digital Object Identifier (DOI): 10.1109/TGRS.2016.2520298 Link: Link to publication record in Edinburgh Research Explorer Document Version: Early version, also known as pre-print Published In: IEEE Transactions on Geoscience and Remote Sensing General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 16. Jul. 2018
48
Embed
Model-Based Evaluation of Signal to Clutter Ratio for Landmine … · Ratio for Landmine Detection Using Ground Penetrating Radar Iraklis Giannakis, Antonios Giannopoulos, and Alexander
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Edinburgh Research Explorer
Model-Based Evaluation of Signal-to-Clutter Ratio for LandmineDetection Using Ground-Penetrating Radar
Citation for published version:Giannakis, I, Giannopoulos, A & Yarovoy, A 2016, 'Model-Based Evaluation of Signal-to-Clutter Ratio forLandmine Detection Using Ground-Penetrating Radar' IEEE Transactions on Geoscience and RemoteSensing, vol 54, no. 6, pp. 3564 - 3573. DOI: 10.1109/TGRS.2016.2520298
Digital Object Identifier (DOI):10.1109/TGRS.2016.2520298
Link:Link to publication record in Edinburgh Research Explorer
Document Version:Early version, also known as pre-print
Published In:IEEE Transactions on Geoscience and Remote Sensing
General rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.
Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact [email protected] providing details, and we will remove access to the work immediately andinvestigate your claim.
Iraklis Giannakis, Antonios Giannopoulos, and Alexander Yarovoy ∗†‡
November 16, 2015
Abstract
A regression model is developed in order to estimate in real time
the signal to clutter ratio (SCR) for landmine detection using ground
penetrating radar (GPR). Artificial neural networks (ANN) are em-
ployed in order to express SCR with respect to the soil’s properties, the
depth of the target and the central frequency of the pulse. The SCR is
∗Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, per-mission to use this material for any other purposes must be obtained from the IEEE bysending a request to [email protected].†Iraklis Giannakis and Alexander Yarovoy are with the Delft University of Technology,
department of Microelectronics, group of Microwave Sensing, Signals and Systems MS3,TU Delft, Faculty EEMCS (building 36), Mekelweg 4, 2628 CD Delft, Netherlands. (e-mail: [email protected], [email protected]).‡Antonios Giannopoulos is with the Institute of Infrastructure and Environment,
School of Engineering, The University of Edinburgh, Edinburgh EH9 3JL, U.K. (e-mail:[email protected]).
1
2
synthetically evaluated for a wide range of diverse and controlled sce-
narios using the finite difference time-domain (FDTD) method. Frac-
tals are used to describe the geometry of the soil’s heterogeneities as
well as the roughness of the surface. The dispersive dielectric proper-
ties of the soil are expressed with respect to traditionally used soil’s
parameters, namely, sand fraction, clay fraction, water fraction, bulk
density and particle’s density. Through this approach, a coherent and
uniformly distributed training set is created. The overall performance
of the resulting non-linear function is evaluated using scenarios which
are not included in the training process. The calculated and the pre-
dicted SCR are in good agreement indicating the validity and the
generalisation capabilities of the suggested framework.
Index Terms – ANN, clutter, FDTD, fractals, GPR, landmines,
regression, SCR.
I Introduction
The term “Anti-Personnel (AP) landmine” includes a wide range
of different explosive devices designed to maim or kill pedestrians
[1], [2]. AP landmines are typically shallow-buried (no more than
10 cm) [1], [2] and can be found in a wide range of environments
(urban environments, deserts, jungles and so on) [3]. Humanitarian
demining tries to detect and disable AP and anti-vehicle landmines
while balancing between efficiency and safety. Numerous approaches
3
from a diverse set of scientific fields have been proposed in an effort to as-
sist humanitarian demining, from metal detector (MD) [4], [5] and electrical
Figure 1: Scattering field from PMA-1 with and without dipolar losses. TheAP landmine is buried in a homogeneous saturated sand with S = 1, C = 0,ρb = 1.5 gr/cm3, ρs = 2.66 gr/cm3 and fw = 0.3. The depth of the landmineis 10 cm. The surface of the soil is flat and the central frequency of the pulseis equal to 2 GHz. The dipolar losses incorporated into the Debye pole cansubstantially decrease both the amplitude and the central frequency of thescattering field.
37
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2
1 100
0.2
0.4
0.6
0.8
1
Frequency (GHz)
Norm
alise
d Am
plitu
de
5.6 5.8 6 6.2 6.4 6.6 6.8 7−1
−0.5
0
0.5
Time (ns)
Norm
alise
d E z
Conductive term + Debye poleConductive term
Fig. 1. Scattering field from PMA-1 with and without dipolar losses. TheAP landmine is buried in a homogeneous saturated sand with S = 1, C = 0,⇢b = 1.5 gr/cm3, ⇢s = 2.66 gr/cm3 and fw = 0.3. The depth of thelandmine is 10 cm. The surface of the soil is flat and the central frequencyof the pulse is equal to 2 GHz. The dipolar losses that are incorporated intothe Debye pole can substantially decrease both the amplitude and the centralfrequency of the scattering field (when high frequencies are used).
and highly related to the environment, the post-processing andthe antenna unit [22], [23]. In the present study we suggesta back-propagation ANN framework [24] which unravels theunderlying relationship of SCR (subject to a generic groundremoval processing scheme) to the soil’s properties, the rough-ness of the surface, the depth of the landmine and the centralfrequency of the pulse. Due to computational constrains, 2Dgeometries are considered in the present study. If adequatecomputational resources are available, the proposed frameworkcan be trivially expanded to 3D geometries providing a real-time platform for comparing the performance of differentantenna units to a wide range of diverse scenarios.
Synthetic data, evaluated using the FDTD method [25], [26],are employed in the present paper for both training andtesting purposes. Soil’s heterogeneities and soil’s topographyare simulated using fractal correlated noise. The latter, it hasbeen proven that can sufficiently represent both the spatialcorrelation of the soil’s properties [27], [28] as well as thesoil’s topography [29], [30]. Regarding the dielectric propertiesof the soil, a semi-empirical model [31], [32] is used whichexpresses soil’s (dispersive) dielectric properties with respectto its sand fraction, clay fraction, water volumetric fraction,particle’s density and bulk density [31], [32]. The target ofinterest is represented by the AP landmine PMA-1. Lastly,a Gaussian-modulated sinusoidal pulse (typical of the one’semployed in GPR) is implemented to FDTD as an impressedcurrent source.
A large number of randomly chosen scenarios are employedduring the training process in an effort to accurately resolvethe complexity of the feature space. Subject to the train-ing set, the weights of the ANN are tuned using a scaledcomplex-conjugate optimization method [36]. Subsequently,the performance of the resulting ANN is evaluated in scenarios
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cmcm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cmcm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
60
70
80
90
100
2 4 6 8 10 12 14 16 18 20
✏sStatic relative permittivity
Fig. 2. A representative sample of the models used to train the suggestedregression framework.
which are not included in the training process. The predicted(using ANN) and the calculated (using FDTD) SCR arein good agreement indicating that the suggested regressionframework can sufficiently model (in real-time) the nature andthe behaviour of SCR.
II. SCR EVALUATION USING FDTDA. Dielectric properties of soil
Soil is a complex medium which is primarily consistedof sand, clay, water and air. The size of the soil’s particles,as well as the volume of the pores are orders of magnitudesmaller than the typical wavelengths employed in GPR. Dueto that, the bulk dielectric properties of the soil can beaccurately expressed with respect to the dielectric propertiesof its elements [33], [34].
In the present study we use the semi-empirical modelinitially suggested by [31] for the frequency range of 1.4-18GHz. The main advantage of the semi-empirical model is thatit evaluates the frequency-dependent electrical permittivity ofthe soil based on its most dominant elements (sand, clay, waterand air). The semi-empirical model was initially proposed forhigh frequency applications [27]. Later on, a modification wasproposed by [32], [35] in order to expand the semi-empiricalmodel to lower frequencies (0.3-1.3 GHz). In the present studythe adaptation proposed by [32], [35] is employed since itsrange of validity is closer to the frequency range used for APlandmine detection.
The semi-empirical model [31], [32], [35] is described bythe equations (1)-(9), where ✏ = ✏0 + j✏00, j is the imaginaryunit
�j =
p�1�, fw is the water volumetric fraction, ⇢s
is the particle’s density (g/cm3), ⇢b is the bulk density ofthe soil (g/cm3), ✏s is the relative permittivity of the sandparticles, a = 0.65 is an experimentally derived constant, Sis the sand mass fraction and C is the clay mass fraction
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cmcm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
cm
cm
10 20 30
10
20
30
Figure 2: A representative sample of the models used to train the suggestedregression framework.
38
0.1 1 100
0.01
0.02
0.03
0.04
0.05
Frequency (GHz)
Ampl
itude
0 0.5 1 1.5 2 2.5 3−0.5
0
0.5
1
Time (ns)
Impr
esse
d Pu
lse
0.9 GHz1.4 GHz1.9 GHz2.4 GHz3 GHz
Figure 3: Gaussian-modulated sinusoidal pulses using different central fre-quencies (11). The fractional bandwidth is constant and equals to bw = 0.9.
39
−60 −40 −20 0 20 40 60 800
0.005
0.01
0.015
0.02
0.025
0.03
0.035
SCR (dB)
Prob
abilit
yPDF
Figure 4: The resulting PDF of SCR using the procedure described in sectionII.5. Red colour illustrates the values that lie within two standard deviationseither side of the mean (-5.9 dB).
40
S
m
M
�w
�T
T
fc
SCR
BiasesSigmoid AFLinear AFWeights
D
Figure 5: A feedforward ANN is used in an effort to model SCR. The pro-posed scheme is consisted of two hidden layers with ten and five neurones,respectively.
41
0 50 100 150 200−40
−30
−20
−10
0
10
20
30
Data unit
SCR
(dB)
One stantard deviationSCR using ANNSCR using FDTD
Figure 6: The calculated (using FDTD) and the predicted (using the sug-gested regression framework) SCR. The blue area represents the range (onestandard deviation) of the calculated SCR. The present scenarios are ran-domly chosen and they are not included into the training set. For illustrationpurposes the data are plotted with incremental order.
42
−8 −6 −4 −2 0 2 4 6 8 100
0.05
0.1
0.15
0.2
0.25
Error (dB)
Prob
abilit
y PDF
Figure 7: PDF of the error between the calculated (using FDTD) and theestimated (using ANN) SCR. Red colour illustrates the error that lies withintwo standard deviations either side of the mean.
43
0 10 20 30 40 50 60 70 80 90 1004
6
8
10
12
14
16
18
20
Mea
n sq
uare
d er
ror (
dB)
Percentage % of data used for training
Figure 8: Averaged (over twenty different ANN trained using different initialconditions) mean squared error between the calculated (using FDTD) andthe predicted (using ANN) SCR using different percentages of the originaldatabase for training and validation purposes. In each case, 10 % of thetraining set are employed for validation purposes. The error bounds denoteone standard deviation of the squared error using different initial weights andbiases prior to the training process.
44
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
15
20
25
30
35
40
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
10
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
6
8
10
12
14
16
18
20
22
24
26
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
15
20
25
30
35
40
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
10
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
6
8
10
12
14
16
18
20
22
24
26
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60SC
R (d
B)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Figure 9: The input parameters are m = 0.1, M = 0.101, C = 0.5, βT = 3,βw = 1, fc = 0.9 − 3 GHz and D = 0 − 60 mm. Three different surface’smaximum absolute deviation are considered, A) T = 0 mm, B) T = 2 mmand C) T = 20 mm. Black circles depicts the optimal central frequency withrespect to landmine’s depth.
45
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
15
20
25
30
35
40
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
10
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
6
8
10
12
14
16
18
20
22
24
26
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
15
20
25
30
35
40
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
10
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
6
8
10
12
14
16
18
20
22
24
26
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
25
30
35
40
45
50
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SC
R (d
B)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60SC
R (d
B)
25
30
35
40
45
50
Dept
h (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
12
14
16
18
20
22
24
26
28
30
Dep
th (m
m)
Frequency (GHz)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
SCR
(dB)
−10
−8
−6
−4
−2
0
2
4
6
8
10
A.
B.
C.
Figure 10: The input parameters are m = 0.05, M = 0.2, C = 0.5, βT = 3,T = 0, fc = 0.9− 3 GHz and D = 0− 60 mm. Three different water fractiondistributions are examined, A) βw = 0, B) βw = 0.8 and C) βw = 1.4.Black circles depicts the optimal central frequency with respect to landmine’sdepth.
46
2 2.5 3 3.5 4 4.510
12
14
16
18
20
22
`T
SCR
(dB)
T=4 mmT=6 mmT=8 mmT=10 mm
Figure 11: The input parameters are m = 0.10, M = 0.101, C = 0.5, βw = 1.fc = 1.5 GHz, D = 35 mm, T = 4− 10 and βT = 2− 4.5.
47
X axis (cm)
Dep
th (c
m)
`T=2
20 40 60 80
0102030
X axis (cm)
Dep
th (c
m)
`T=3
20 40 60 80
0102030
X axis (cm)
Dep
th (c
m)
`T=4
20 40 60 80
0102030
X axis (cm)
Tim
e (n
s)
Average removal
20 40 60 80
0246
X axis (cm)
Tim
e (n
s)
Average removal
20 40 60 80
0246
X axis (cm) T
ime
(ns)
Average removal
20 40 60 80
0246
X axis (cm)
Tim
e (n
s)
SVD
20 40 60 80
0246
X axis (cm)
Tim
e (n
s)
SVD
20 40 60 80
0246
X axis (cm)
Tim
e (n
s)SVD
20 40 60 80
0246
Figure 12: The input parameters are m = 0.2, M = 0.2, C = 0.5, fc = 2GHz, D = 40 mm, T = 30 mm and βT = [2, 3, 4]. Average removal and SVD(λi, i < 3) are employed in an effort to remove the direct wave and the groundreflection. Notice that increasing βT slightly decreases the performance ofground removal techniques as predicted in Fig. 11.