Multi-Satellite Interferometric SAR System
Andon Lazarov
1,2
, Chavdar Minchev
3
and Dimitar Minchev
1
1
Burgas Free University, 62 SanStefano Str., Burgas, Bulgaria
2
K.N. Toosi University of Technology, Tehran, Iran
3
Shumen University, 115 Universitetska Str. Shumen, Bulgaria
Keywords: InSAR, Multi-satellite system, InSAR geometry, InSAR signal model.
Abstract: In the present work a multi-satellite SAR system is considered. Between every pair of SAR satellites an
interferometric concept is implemented. It allows the height of each pixel on the surface to be evaluated
with high precision and a three dimensional map to be created. InSAR geometry is analytically described.
Mathematical expressions for determination of current distances between SAR’s and detached pixels on the
ground, and principal InSAR parameters are derived. A model of linear frequency modulated (LFM) SAR
signal with InSAR applications, reflected from the surface is developed. Correlation and spectral SAR
image reconstruction algorithms and co-registration procedure are described. To verify the correctness of
the signal model and image reconstruction and co-registration algorithm numerical experiment is carried
out.
1 INTRODUCTION
Synthetic Aperture Radar (SAR) is a coherent active
microwave imaging instrument. Back scattered
information of a target is recorded as a complex
signal with amplitude and phase information.
Interferometric SAR (InSAR) technique makes use
of phase difference information extracted from two
complex valued SAR images acquired from different
orbit positions. This information is useful in
measuring several geophysical quantities such as
topography, slope, deformation (volcanoes,
earthquakes, ice fields), glacier studies, vegetation
growth etc (Rott, H., et al., 2003, Rott, H., et al.
1999, Massonet, D., et al. 1998, Henry, E. et al.
2004, Rott, H. et al. 2000, Berardino, P., et al. 2002,
Berardino, P., et al. 2003).
SAR interferometry was first used for
topographic mapping by Graham (Graham, L.C,
1974). The first practical results were obtained by
Zebker and Goldstein (Zebker, H.A., Goldstein,
R.M., 1986) using side looking airborne radar.
Studies on interferometric SAR were extended after
the launch of ERS-1 and ERS-2, and Envisat
satellites (Feigl, K.L., et al. 2002). The number of
scientific research on InSAR technology has also
exploded since the launch of new satellites such as
of class Sentinel.
In order to obtain SAR interferometric data, two
spatially separated antennas, the physical separation
of which is called the interferometric baseline, are
mounted on a single platform or one antenna is
mounted on a satellite and data sets are acquired by
passing the same area twice. In the latter case, the
interferometric baseline is formed by relating radar
signals on repeat passes over the target area. This
approach is called repeat-pass interferometry. SAR
interferometry is a promising tool for mapping
topography, detecting small surface displacement
caused by earthquake, volcanic activity, and
landslides and ice movement (Weston, J., et al.
2012, Feng, G. et al, 2010). There are various
publications on estimating earthquake parameters
using InSAR measurements (Gens, R., Van
Genderen, J.L.,1996, Reilinger, R.E., 2000, Wright,
T.J., et al. 2003, Liu-Zeng, J., et al. 2009, Sudhaus,
H., et al. 2009).
33
Lazarov A., Minchev C. and Minchev D.
Multi-Satellite Interferometric SAR System.
DOI: 10.5220/0006226900330042
In Proceedings of the Fifth International Conference on Telecommunications and Remote Sensing (ICTRS 2016), pages 33-42
ISBN: 978-989-758-200-4
Copyright
c
 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

The current emphasis in the satellite industry is
on replacing large satellite platforms with one or
more smaller satellites, i.e. there is increasing
interest in the potential capabilities and applications
of so-called mini satellites. A multi-satellite system
is a group of mini satellites that fly within very close
range of each other (e.g., 250 m - 5 km). These
satellites coordinate their activities, so that they can
use sparse array interferometry and synthetic
aperture techniques to simulate a single, very large
satellite. The multi-satellite system operates as a
“virtual” satellite with a very large effective
aperture, without the need for the heavy
infrastructure that would be required to have a
monolithic satellite with the equivalent aperture.
The multi-satellite system approach has many
advantages over a single large satellite: each
spacecraft is smaller, lighter, simpler, and simpler to
manufacture; economies of scale enable a multi-
satellite system of many satellites to be less
expensive to manufacture than a single satellite;
multi-satellite system can adapt to the failure of any
individual satellites, and failed satellites can be
incrementally replaced; multi-satellite system can
reconfigure the orbits of the satellites in the multi-
satellite system to optimize for different missions.
In the present work a multi-satellite SAR system
is considered. The multi-satellite system consists of
mini satellites performing different roles. On one of
them a SAR transmitter and receiver are activated,
on the other only SAR receivers. Between every
pair of SAR satellites an interferometric concept is
implemented. It allows the height of each pixel on
the surface to be evaluated with high precision and a
three dimensional map to be created. The main goal
of the work is to describe InSAR geometry with
multiple satellites and derive mathematical
expressions for definition of current distances
between SAR’s and detached pixels, and principal
InSAR parameters and, as a result, a model of linear
frequency modulated SAR signal with InSAR
applications, reflected from the surface to be
developed. In order to extract complex SAR images
and intergerograms, correlation and spectral SAR
image reconstruction algorithms is suggested and
implemented.
The rest of the paper is organized as follow. In
section II a 3-D InSAR geometry is analytically
described. In section III SAR LFM transmitted
waveform and model of deterministic SAR signal
return are defined. In section IV SAR image
reconstruction, co-registration, SAR interferogram
generation, and iterative procedure for pixel height
determination are analytically described. In section
V results of numerical experiment are presented. In
section VI conclusions are made.
2 InSAR GEOMETRY
2.1 Geometry and Kinematics’
Equations
Assume a multi-satellite SAR system viewing three
dimensional (3-D) surface presented by discrete
resolution elements, pixels. Each of these pixels is
defined by the third coordinate
),(
ijijij
yxz
in 3-D
coordinate system
Oxyz
. The surface is illuminated
by linear frequency modulated waveforms emitted
by a transmitter mounted on one satellite. A
1
, A
2
…
A
n
represent SAR receive antennas mounted on
satellites viewing the same surface simultaneously.
Between every pair
nm
AA
of satellites,
where
Nnm ,1
, N is the number of satellites,









2
2
N
C
N
InSAR baselines can be drawn.
Figure 1: Geometry and kinematics of the interferometry
SAR scenario.
The main geometrical characteristic of the SAR
signal is the distance vector from the SAR system to
each point scatterer of the scene of interest, defined
as the vector difference
 
T
n
ij
n
ij
n
ijij
nn
ij
pzpypxpp )(),(),()()(  RRR
(1)
Fifth International Conference on Telecommunications and Remote Sensing
34

where n = 1  N is the number of SAR receiver
ij
R
is the distance vector of
ij
th point scatterer from the
scene, and
)(p
n
R
is the distance vector to the n-th
SAR receiver, the point of observation in coordinate
system
Oxyz
(Fig. 1);
)(px
n
ij
,
)(py
n
ij
,
)(pz
n
ij
are
the current coordinates of the pixel from the scene in
respect of the n-th SAR receiver, measured at
p
th
moment of observation and defined as
ij
nn
ij
xpxpx  )()(
,
ij
nn
ij
ypypy  )()(
, (2)
ij
nn
ij
zpzpz  )()(
,
where
Xix
ij

,
Yjy
ij

,
),(
ijijijij
yxzz 
is
the discrete coordinate defining a surface of the
scene of interest,
)(px
n
,
)(py
n
,
)(pz
n
, are the
instant coordinates of the n-th SAR receiver, defined
be following equations
px
nn
pTVxpx 
0
)(
,
py
nn
pTVypy 
0
)(
, (3)
pz
nn
pTVzpz 
0
)(
,
where
n
x
0
,
n
y
0
,
n
z
0
are the initial coordinates of the
n-th SAR, measured at the initial moment,
p
T
is the
time repetition period;
p
is the current number of
the emitted pulse,
 
T
zyx
VVV ,,V
is the vector
velocity of the InSAR multi satellite system,
 cosVV
x
,
 cosVV
y
,
 cosVV
z
are the
components of vector velocity,
cos
,
cos
,

22
coscos1cos
are the guiding cosines,
and
V
is the module of the vector velocity,
V
.
Modulus of the current distance vector of the pixel
in respect of the nth SAR’s receiver antenna is
defined by the equation
 
2
1
222
)]([)]([)]([)( pzpypxpR
n
ij
n
ij
n
ij
n
ij

(4)
The expression (4) can be used to model a SAR
signal return from the ij-th point scatterer to the n-th
receiver by calculation of the respective time delay
and phase of the signal.
2.2 InSAR Geometrical Relations
The relations between two the distances to ijth pixel
from mth and nth SAR receivers can be defined from
Fig. 1 by application of the cosines theorem, i.e.
 
1
2
2
2
2 cos [ )]
2
m
ij mn
n
ij
mm
mn ij ij mn
RB
R
BR













,
(5)
where
mn
B
is the modulus of baseline vector,
ij
m

is the look angle,
mn

is a priory known tilt angle,
the angle between baseline vector and plane xOy.
From (5) can be extracted expressions for
calculation of the look angle
ij
m

and height
ij
m
h
of
a ij-th pint scatter on the surface with respect to m-th
receiver
m
ijmn
n
ijmn
m
ij
mn
ij
m
RB
RBR
2
][][
arcsin
222


, (6)
ij
mm
ij
m
ij
RHz  cos
0
. (7)
The path length from the transmitter
1
A
to ij-th
pixel on the scene and back to the receiver
n
A
where
(n = 1  N), is
n
ijij
n
ij
RRR 
11
. The difference
between two the distances
n
ij
R
1
and
m
ij
R
1
is equal to
m
ij
n
ij
m
ij
n
ij
RRRR 
11
.
Denote the path difference between
m
ij
R
and
n
ij
R
as
mn
ij
R
, i.e.
m
ij
n
ij
mn
ij
RRR 
, then
mn
ij
m
ij
n
ij
RRR 
.
Substitute
mn
ij
m
ij
n
ij
RRR 
in (6) and (7), then












m
ijmn
mn
ij
mn
mn
ij
m
ij
mn
ij
m
RB
R
B
R
R
B
2
][
2
arcsin
2
(8)























m
ijmn
mn
ij
mn
mn
ij
ij
mn
mn
m
ij
m
ij
RB
R
B
R
R
B
RHz
2
][
2
arcsincos
2
1
0
(9)
Multi-Satellite Interferometric SAR System
35

The path difference
mn
ij
R
in equations (8) and
(9) can be expressed by the corresponding phase
difference
mn
ij
mn
ij
R



2
as
mn
ij
mn
ij
R 



2
.
If the current distance
m
ij
R
can be measured
expressions (8) and (9) can be written as follows

































mn
ij
m
ij
mn
ij
mn
m
ij
mn
mn
ij
m
R
B
R
B
4
1
2
2
arcsin
(10)




















































mn
ij
m
ij
mn
ij
mn
m
ij
mn
mn
m
ij
m
ij
R
B
R
B
RHz
4
1
2
2
arcsincos
0
(11)
Using expressions (10) and (11) the elevation look
angle
ij
m

and the height
ij
z
of the particular pixel
can be calculated.
3 SAR TRANSMITTED LFM
WAVEFORM AND
DETERMINISTIC SIGNAL
MODEL
The SAR transmits a series of electromagnetic
waveforms to the surface, which are described
analytically by the sequence of linear frequency
modulation (LFM) (chirp) pulses as follows
   



M
p
pp
pTtbpTtjAtS
1
2
)()(exp)(
, (12)
where A is the amplitude of the transmitted pulses,
p
T
is the pulse repetition period,


c
2
, is the
signal angular frequency,
Mp ,1
is the current
number of emitted LFM pulse, M is a full number of
emitted pulses during aperture synthesis,
8
10.3c
m/s is the speed of the light,
F
is the bandwidth of
the transmitted pulse that provides the dimension of
the range resolution cell, i.e.
FcR  2/
,
T
F
b


is the LFM rate,
T
is the time duration of
a LFM pulse.
The deterministic component of SAR signal,
reflected by
ij
-th pixel can be determined by
expression
 
2
( ) ( )
exp
()
n
ij
n
ij ij ij
n
ij
n
ij
tt
S t a z
T
tt
j
b t t















rect
(13)
where



















1
)(
,0
1
)(
,1
0
)(
,0
)(
T
ptt
T
ptt
T
ptt
T
ptt
n
ij
n
ij
n
ij
n
ij
rect
, (14)
where
)(
ijij
za
is the reflection coefficient of the
pixel from the surface. The parameter
)(
ijij
za
is a
function of surface geometry;
c
pRpR
pt
n
ijij
n
ij
)()(
)(
1


is the signal time delay
from the
ij
th point scatterer measured on the nth
receiver.
The deterministic components of the SAR signal
return are derived by applying the physical optic’s
principle of Huggens-Fresnel, according to which
the SAR signal return can be calculated as a sum of
elementary signals reflected by point scatterers from
the surface, i.e. the time record of data
),( kpS
n
can
be written as
 
2
()
( ) exp
()
n
n
n
ij
ij
ij ij
n
ij
ij
St
tt
tt
a z j
T
b t t
















rect
(15)
Fifth International Conference on Telecommunications and Remote Sensing
36

The time dwell t of the SAR signal return for each
transmitted pulse
p
can be expressed as
Tkkt
ij
 )(
min
, where
)(),(
maxmin
pkpkk
n
ij

is
the sample number of the SAR return,
]/)(int[
minmin
Tmtk
ijij

,
FT  2/1
is the
sample time duration of the return,
F
is frequency
bandwidth,
)(
max
pk
n
is the number of the last range
bin where SAR return is registered in n-th receiver
for each emitted pulse. Hence, SAR return registered
in n-th receiver in discrete form can be written as
 
 
2
( , ) ( )
( 1) ( )
exp
( 1) ( )
n
ij
n
ij ij
ij
n
ij
n
ij
tt
S p k a z
T
k T t p
j
b k T t p





  





   




rect
(16)
The expressions (1) - (16) can be used for
modeling the SAR signal return in case the satellites
are moving on rectilinear trajectory in 3-D
coordinate system.
4 SAR IMAGE
RECONSTRUCTION,
COREGISTRATION AND SAR
INTEREFEROGRAM
GENERATTION
4.1 SAR Image Reconstruction
Algorithm
Image reconstruction is constituted by following
operations: frequency demodulation; range
compression; coarse range alignment and precise
phase correction, and azimuth compression. The
result is a complex image of the scene.
In each SAR receiver a frequency demodulation is
carried out. It is performed by multiplication of the
right term of equation (10) with a complex conjugate
exponential function
  
2
])1[()1(exp TkbTkj 
.
Thus, the range distributed frequency
demodulated SAR return in n-th receiver for p-th
pulse can be written as
 

















2
)()1()(exp
)1(
)(),(
ˆ
ptTkbptj
T
tTk
zakpS
n
ij
n
ij
i j
n
ij
ijij
n
rect

(17)
SAR data refer to a set of data that has a real
(Cosine, In-phase) and imaginary (Sine, Quadrature)
component. Both this components of backscattered
signals are measured by each SAR receiver.
Therefore, the SAR data stream from each receiver
can be writes as
),(),(),(
ˆ
kpQjkpIkpS
nnn


(18)
where
)],(
ˆ
Re[),( kpSkpI
nn


is the In-phase part of
the SAR signal in the nth receiver,
)],(
ˆ
Im[),( kpSkpQ
nn


is the Quadrature part
of the SAR signal in the nth receiver,
Range compression is implemented by cross
correlation of the complex SAR signal and reference
function,
 
2
])1[(exp Tkjb 
or by Fourier
transform of LFM demodulated SAR signal, using
the expressions as follows.
- cross correlation
 



K
k
nn
R
TkkjbkpSkpS
1
2
])1
ˆ
[(exp),(
ˆ
)
ˆ
,(

(19)
where K is the full number of LFM samples, range
bins where SAR signal is registered;
- Fourier transform












n
K
k
nn
R
K
kk
jkpSkpS
max
1
ˆ
2
exp).,(
ˆ
)
ˆ
,(

, (20)
for each
Mp ,1
and
Kk ,1
ˆ

.
Range alignment and phase correction is
implemented by well known range alignment and
focusing procedures [Lazarov, A. 2002].
Azimuth compression is implemented by Fourier
transform of the range compressed signal,
)
ˆ
,( kpS
n
R

.
It yields a complex image based on the n-th receiver
data and can be expressed as










M
p
n
R
n
M
pp
jkpSpkI
1
ˆ
2
exp)
ˆ
,()
ˆ
,
ˆ
(


, (21)
for each
Mp ,1
ˆ

,
Kk ,1
ˆ

.
Multi-Satellite Interferometric SAR System
37

It is worth noting that the complex pixel of the
SAR image in n-th receiver preserves the phase
information defined by path length from the
transmitter to the ij-th pixel and back to the n-th
SAR receiver. Based on the pixels phase information
and precise co-registration of two complex images a
complex interferogram can be generated.
4.2 Co-registration of Two SAR
Complex Images
To generate an interferogram between two complex
images first a precision under pixel co-registration
for any pair of two complex images has to carry out
(Guizar-Sicairos, M., 2008).
Let
)
ˆ
.
ˆ
( pkI
n
and
)
ˆ
.
ˆ
( pkI
m
be two complex images
obtained by the nth and mth receiver, respectively,
and let
),( rqi
n
and
),( rqi
m
be two complex
spectrums of the images defined by the expressions
 






















M
p
K
k
mm
M
rp
K
qk
jpkIrqi
,1
ˆ
1
ˆ
ˆ
2
ˆ
2
exp)
ˆ
.
ˆ
(),(
,
 






















M
p
K
k
nn
M
rp
K
qk
jpkIrqi
,1
ˆ
1
ˆ
ˆ
2
ˆ
2
exp)
ˆ
.
ˆ
(),(
.
In case the image
)
ˆ
.
ˆ
( pkI
m
is displaced in respect of
the image
)
ˆ
.
ˆ
( pkI
n
on intervals
k
ˆ

and
p
ˆ

it can be
written
- in the space domain
)
ˆˆ
,
ˆˆ
()
ˆ
.
ˆ
( ppkkIpkI
nm

- in the frequency domain




















M
qp
K
qk
jrqirqi
nm
.
ˆ
2.
ˆ
2
exp),(),(
.
The level of coincidence of the complex images
can be calculated in space and/or frequency
(spectral) domain by cross-correlation and inverse
Fourier transform of the multiplication of the two
complex spectrums as follows
- in the space domain




M
p
K
k
mn
ppkkIpkIpkC
1
ˆ
1
ˆ
)
ˆˆ
,
ˆˆ
().
ˆ
.
ˆ
()
ˆ
,
ˆ
(
,
where
k
ˆ

varies from 0 to the pixel’s dimension
with step 1/10(pixel’s dimension on
k
ˆ
axis),
p
ˆ

varies from 0 to the pixel’s dimension with step
1/10(pixel’s dimension on
p
ˆ
axis);
- in the frequency domain






















 
M
rpp
K
qkk
j
rqirqipkC
M
r
K
q
nm
)
ˆˆ
(2)
ˆˆ
(2
exp
),(),()
ˆ
,
ˆ
(
1 1
.
Maximum of the correlation function corresponds
to a maximum coincidence, i.e. the complex images
are best co-registered.
After SAR image reconstructions complex
interferograms can be generated by pixel-wise
multiplication of the two complex SAR images. For
example, the complex interferogram between m-th
and n-th SAR complex image can be calculated by
the expression
*)]
ˆ
,
ˆ
([)
ˆ
,
ˆ
()
ˆ
,
ˆ
( pkIpkIpkI
mnmn


, (22)
where  denotes elementwise product; the sign ”*“
denotes complex conjugate.
4.3 Iterative Procedure for Pixel
Height Determination
Step
0k
1. Consider ij-th pixel with coordinates
0,, 
ijijij
zyx
(the pixel is on the base
plane xOy).
2. Compute the distance
m
ij
R
   
 
2
1
2
0
2
0
2
0
)0(













ij
m
ij
m
ij
m
m
ij
zz
yyxx
R
,
where
m
x
0
,
m
y
0
and
m
z
0
are coordinates of m-th
SAR at the moment p=N/2 (moment of image
extraction).
Step
kk 
3. Compute the distance
n
ij
R
   
 
2
1
2
0
2
0
2
0
)(













ij
n
ij
n
ij
n
n
ij
zz
yyxx
kR
,
where
n
x
0
,
n
y
0
and
n
z
0
are coordinates of n-th
SAR at the moment p=N/2 (moment of image
extraction).
Fifth International Conference on Telecommunications and Remote Sensing
38

4. On k-th step compute the interferometric
phase:
mn
ij
mn
ij
Rk 



2
)(
,
where
n
ij
m
ij
mn
ij
RRR 
.
5. If
mn
ij
mn
ij
k  )(
, then
Step k  k  1.
6. On (k  1)-th step consider a pixel with
coordinates
zkzkzyx
ijijijij
 )()1(,,
.
7. Go to point 2 and 3.
8. If
mn
ij
mn
ij
k  )(
, then consider the pixel
with coordinates
ijij
yx ,
,
)/()()1( rzkzkz
ijij

,
where
...4,3,2r
9. Go to point 2 and 3.
10. If
mn
ij
mn
ij
k  )(
, then
ijij
hkz )(
.
Stop.
The height’s estimation procedure can be applied
either for all pixels or only for one pixel from the
surface of interest. In the latter case a scale
coefficient can be defined in order to transform
unwrapped phase surface to topographic map.
5 NUMERICAL EXPERIMENT
To verify the correctness of the signal model and
image reconstruction and co-registration algorithms
numerical experiment is carried out.
Assume multi satellite InSAR system comprising
three satellites, one with transmitter and receiver,
two – only with receivers, with initial space
coordinates as follows:
0
1
0
x
m;
31
0
10.10y
m,
31
0
10.100z
m,
0
2
0
x
m,
32
0
10.1,10y
m,
32
0
10.100z
m,
0
3
0
x
m,
33
0
10.2,10y
m,
33
0
10.100z
m,
and coordinates of vector-velocity of the three
satellites:
0
x
v
m/s;
600
y
v
m/s;
0
z
v
m/s.
Multi satellite SAR system observes a surface
(Fig. 2) depicted by equation
])1(exp[
3
1
)exp(
5
10
])1(exp[)1(3
2
2
2253
2
2
2
ijij
ijijijij
ij
ijijijij
yx
yxyx
x
yxxz












,
where
Xix
ij

,
Yjy
ij

,
Ii ,1
,
Jj ,1
, I =
128 pixels; J = 128 pixels;
X
;
Y
- the spatial
dimensions of the pixels.
Normalized amplitude of reflected signals from
every pixel
001.0
ij
a
. Dimensions of the pixel are
2 YX
m. Wavelength is 0.03 m. Carrier
frequency is 3.10
9
Hz. Frequency bandwidth is
250F
MHz. Pulse repetition period is
3
10.25


p
T
s. LFM pulse duration is
6
10.5

T
s.
Sample time duration is
8
10.95,1

T
s. LFM
samples are K = 512. Emitted pulses are M = 512.
Digital geometry description and SAR signal
modeling are performed based on the theory in
sections III and IV. Complex images through
correlation range compression and FFT azimuth
compression are retrieved. Based on a priory known
kinematical parameters of satellites and coordinates
of reference point from the surface autofocusing
phase correction of the SAR signals registered in the
both receivers can be implemented.
The real and imaginary part of the complex
signal measured in the first receiver is depicted in
Fig. 2.
Figurre 2: Real and imaginary part of the complex signal
measured in the first receiver.
The amplitude and phase of the reconstructed
complex image obtained in the first receiver is
depicted in Fig. 3. The position of the surface’s
image in the frame is defined by the position of the
receiver satellite in the point of imaging of the
Multi-Satellite Interferometric SAR System
39

surface, as a rule, this point is in the middle of the
synthetic aperture length.
(a) (b)
Figure 3: The amplitude and phase of the reconstructed
complex image obtained in the first receiver.
The real and imaginary part of the complex
signal measured in the second receiver is depicted in
Fig. 4.
(a) (b)
Figure 4: Real (a) and imaginary (b) part of the complex
signal measured in the second receiver.
The amplitude and phase of the reconstructed
complex image obtained in the second receiver is
depicted in Fig. 5. It can be noticed the shape of the
surface is similar to the shape of the image obtained
by the first receiver. In contrast, the phase pictures
are different based on the different positions of both
satellites in respect of the surface.
(a) (b)
Figure 5: The amplitude and phase of the reconstructed
complex image obtained in the second receiver.
After co-registration of complex images obtained
in the first and second receiver and complex
interferogram generation the result as a coherent
map (a) and interferometric phase (b) is depicted in
Fig. 6.
(a) (b)
Figure 6: Complex interferogram: coherent map and
interferometric phase generated by the first and second
complex images.
The real and imaginary part of the complex
signal measured in the third receiver is depicted in
Fig. 7.
(a) (b)
Figure 7: Real and imaginary part of the complex signal
measured in the third receiver.
The amplitude and phase of the reconstructed
SAR complex image obtained in the third receiver is
depicted in Fig. 8. It can be noticed the shape of the
surface is similar to the shape of the image obtained
by the first receiver. In contrast, the phase pictures
are different based on the different positions of both
satellites in respect of the surface.
(a) (b)
Figure 8: The amplitude and phase of the reconstructed
complex image obtained in the third receiver.
Fifth International Conference on Telecommunications and Remote Sensing
40

After co-registration of complex images
calculated by the data obtained in the first and third
receiver, and complex interferogram generation, the
result as a coherent map (a) and interferometric
phase (b) is depicted in Fig. 9.
(a) (b)
Figure 9: Complex interferogram: coherent map and
interferometric phase generated by the first and third
complex images.
Comparing the interferometric phases presented
in Fig. 6 and Fig. 9 it can be concluded that they are
similar, i.e. very close to each other. It is a result of
precise under pixel co-registrations of the first and
second, and the first and third complex images.
6 CONCLUSIONS
In the paper a multi-satellite InSAR system has been
analysed and numerically experimented. The
geometry of InSAR scenario and kinematics of
multiple SAR satellites has been analytically
described. Mathematical expressions for current
distances between SAR satellites and surface point
scatterers are derived and principal InSAR
parameters are defined. A model of linear frequency
modulated SAR signal with InSAR applications,
reflected from the topographic surface has been
developed. Correlation and spectral SAR image
reconstruction algorithms, co-registration, and
iterative pixel height determination procedures have
been described. Based on geometrical and
kinematical models numerical interferograms of a
topographic surface have been created.
REFERENCES
Rott, H., Nagler, T., Rocca, F., et al., 2003. InSAR
techniques and applications for monitoring landslides
and subsidence, in: Benes (Ed.), Geoinformation for
European-wide integration, In Proceedings of EARSeL
Assembly, Prague, June 2002. Millpress, Rotterdam,
25–31.
Massonet, D., Feigl, K.L., 1998. Radar interferometry and
its application to changes in the Earth_s surface. Rev.
Geophys., 36, 441–500, 1998.
Henry, E., Mayer, C., Rott, H., 2004. Mapping mining-
induced subsidence from space in a hard rock mine:
example of SAR interferometry application at Kiruna
mine. CIM Bull. 97 (1083), 1–5.
Rott, H., Scheuchl, B., Siegel, A., et al., 1999. Monitoring
very slow slope movements by means of SAR
interferometry: a case study from a mass waste above
a reservoir in the OЁ tztal Alps, Austria. Geophys.
Res. Let. 26, 1629–1632.
Rott, H., Mayer, C., Siegel, A., 2000. On the operational
potential of SAR interferometry for monitoring mass
movements in Alpine areas, In Proceedings of 3rd
European Conference on Synthetic Aperture Radar
(EUSAR2000), Munich, May 2000, 43–46.
Berardino, P., M. Costantini, G. Franceschetti, A. Iodice,
Pietrnera L. and Rizzo, V., 2002. Differential SAR
interferometry for the study of slope instability at
Maratea, Italy, in Proceedings of International
Geoscience and Remote Sensing Symposium, Toronto,
Canada, 2693-2695.
Berardino, P., M. Costantini, G. Franceschetti, A. Iodice,
Pietrnera L. and Rizzo, V., 2003. Use of differential
SAR interferometry in monitoring and modelling large
slope instability at Maratea (Basilicata, Italy), Eng.
Geol., vol. 68, 2003, 31-51.
Graham, L.C., 1974. Synthetic Interferometer Radar for
Topographic Mapping, Proceedings of the IEEE,
vol.62, no.6, 1974. 763.
Zebker, H.A., Goldstein, R.M., 1986. Topographic
Mapping from Interferometric Synthetic Aperture
Radar Observations, Journal of Geophys.Res., vol.91,
no. B5, 1986, 4993-4999.
Feigl, K.L., Sarti, F., Vadon, H. Durand, P., Mclusky S. et
al., 2002. Estimating slip distribution for the Izmit
mainshock from coseismic GPS, ERS-1, RADARSAT
and SPOT measurements, Bull. Seism. Soc. Amer.
Gens, R., Van Genderen, J.L., 1996. Review article: SAR
interferometry-issues, techniques, applications.
International Journal for Remote Sensing, 17(10),
1803-1835.
Reilinger, R.E., Ergintav, S., Bürgmann, R., McClusky,
S., Lenk, O., et al., 2000. Coseismic and postseismic
fault slip for the 17 August 1999, M=7.4, Izmit,
Turkey earthquake, Science, 289, 1519-1524.
Wright, T.J., Fielding, E.J., Parsons, B.E., and England,
P.C., 1999. Triggered slip: observations of the 17
August 1999 Izmit (Turkey) earthquake using radar
interferometry, Geophys. Res. Lett., 28, , 2001, 1079-
1082.
Weston, J., Ferreira, A.M.G., Funning, G. J., 2012.
Systematic comparisons of earthquake source models
determined using InSAR and seismic data,
Tectonophysics 532–535, 61–81.
Feng, G., Hetland, E., Ding, X.L., Li, Z., Zhang, L., 2010.
Coseismic fault slip of the 2008 Mw 7.9 Wenchuan
earthquake estimated from InSAR and GPS
measurements, Geophysical Research Letters, 37,
L01302.
Multi-Satellite Interferometric SAR System
41

Liu-Zeng, J., Zhang, Z., Wen, L., Tapponnier, P., Sun, J.,
Xing, X., Hu, G., Xu, Q., Zeng, L., Ding, L., Ji, C.,
Hudnut, K.W., van der Woerd, J., 2009. Co-seismic
rupture of the 12 May 2008, Ms 8.0 Wenchuan
earthquake, Sichuan: east–west crustal shortening on
oblique, parallel thrusts along the eastern edge of
Tibet. Earth and Planetary Science Letters 286, 355–
370.
Sudhaus, H., Jonsson, S., 2009. Improved source
modelling through combined use of InSAR and GPS
under consideration of correlated data errors:
application to the June 2000 Kleifarvatn earthquake
Iceland. Geophysical Journal International 176, 389–
404.
Lazarov, A.D., Minchev, Ch., 2002. Correlation-
autofocusing-spectral 2-D ISAR Image Reconstruction
from Linear Frequency Modulated Signals, 21st
Digital Avionics Systems Conference (DASC), Irvine,
California, October 2002.
Guizar-Sicairos, M., Thurman, S.T., Fienup, J. R., 2008.
Efficient subpixel image registration algorithms, Opt.
Lett., vol. 33, 156-158.
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42