SAR Processing Algorithm with Built-In Geometric Correction
Synthetic aperture radar (SAR) systems onboard small aircrafts suffer from trajectory deviations and
 instabilities of antenna orientation. These kinds of motion errors lead to significant geometric distortions
 in SAR images. In order to correct the distortions, we propose a time-do...
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Радіоастрономічний інститут НАН України
2011
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| Cite this: | SAR Processing Algorithm with Built-In Geometric Correction / O.O. Bezvesilniy, I.M. Gorovyi, S.V. Sosnytskiy, V.V. Vynogradov, D.M. Vavriv // Радиофизика и радиоастрономия. — 2011. — Т. 16, № 1. — С. 98-108. — Бібліогр.: 14 назв. — англ. |
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| author | Bezvesilniy, O.O. Gorovyi, I.M. Sosnytskiy, S.V. Vavriv, D.M. Vynogradov, V.V. |
| author_facet | Bezvesilniy, O.O. Gorovyi, I.M. Sosnytskiy, S.V. Vavriv, D.M. Vynogradov, V.V. |
| citation_txt | SAR Processing Algorithm with Built-In Geometric Correction / O.O. Bezvesilniy, I.M. Gorovyi, S.V. Sosnytskiy, V.V. Vynogradov, D.M. Vavriv // Радиофизика и радиоастрономия. — 2011. — Т. 16, № 1. — С. 98-108. — Бібліогр.: 14 назв. — англ. |
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| description | Synthetic aperture radar (SAR) systems onboard small aircrafts suffer from trajectory deviations and
instabilities of antenna orientation. These kinds of motion errors lead to significant geometric distortions
in SAR images. In order to correct the distortions, we propose a time-domain multi-look stripmap SAR
processing algorithm with built-in geometric correction. In the algorithm, the azimuth reference functions
and range migration curves are designed to produce SAR images directly on a correct rectangular grid
on the ground plane. The proposed technique has been successfully tested by using a Ku-band airborne
SAR system installed onboard light-weight aircraft.
Радиолокационные системы с синтезированной апертурой (РСА), установленные на небольших самолетах, подвержены влиянию отклонений траектории и нестабильности ориентацииантенны. Такие ошибки движения приводят
к значительным геометрическим искажениям на радиолокационных изображениях (РЛИ). Чтобы исправить эти искажения, мы предлагаем алгоритм многовзглядовой обработки со встроенной геометрической коррекцией,
работающий во временной области и предназначенный для РСА бокового обзора. В этом алгоритме азимутальные опорные функции и кривые миграции строятся таким образом, чтобы получать РЛИ сразу на прямоугольной сетке в плоскости земли. Предложенный метод был успешно испытан с использованием самолетного РСА сантиметрового диапазона длин волн, установленного на легком самолете.
Радіолокаційні системи з синтезованою апертурою (РСА), встановлені на невеликих
літаках, зазнають впливу відхилень траєкторії і нестабільності орієнтації антени. Такі помилки руху призводять до значних геометричних спотворень на радіолокаційних зображеннях (РЛЗ). Аби виправити ці спотворення, ми пропонуємо алгоритм багатопоглядової обробки з вбудованою геометричною корекцією, який
працює у часовому просторі та призначений для РСА бічного огляду. У цьому алгоритмі азимутальні опорні функції та криві міграції формуються таким чином, щоб отримувати РЛЗ одразу на прямокутній сітці в площині землі. Запропонований метод було успішно випробувано з використанням РСА сантиметрового діапазону довжин хвиль, встановленому на легкому літаку.
|
| first_indexed | 2025-12-07T18:57:08Z |
| format | Article |
| fulltext |
Радиофизика и радиоастрономия, 2011, т. 16, №1, с. 98-108
ISSN 1027-9636 © O. O. Bezvesilniy, I. M. Gorovyi, S. V. Sosnytskiy, V. V. Vynogradov, and D. M. Vavriv, 2011
SAR Processing Algorithm with Built-In Geometric Correction
O. O. Bezvesilniy, I. M. Gorovyi, S. V. Sosnytskiy, V. V. Vynogradov, and D. M. Vavriv
Institute of Radio Astronomy, National Academy of Sciences of Ukraine
4, Chervonopraporna St., Kharkiv, 61002, Ukraine
E-mail: vavriv@rian.kharkov.ua
Received October 11, 2010
Synthetic aperture radar (SAR) systems onboard small aircrafts suffer from trajectory deviations and
instabilities of antenna orientation. These kinds of motion errors lead to significant geometric distortions
in SAR images. In order to correct the distortions, we propose a time-domain multi-look stripmap SAR
processing algorithm with built-in geometric correction. In the algorithm, the azimuth reference functions
and range migration curves are designed to produce SAR images directly on a correct rectangular grid
on the ground plane. The proposed technique has been successfully tested by using a Ku-band airborne
SAR system installed onboard light-weight aircraft.
Keywords: synthetic aperture radar, airborne SAR, geometric distortions, multi-look processing,
motion error compensation
1. Introduction
The formation of high-quality multi-look SAR
images with airborne SAR systems installed on-
board small aircrafts is a difficult problem be-
cause of significant motion and orientation errors
of such light-weight platforms. Deviations of the
aircraft trajectory and instabilities of the antenna
orientation lead to geometric and radiometric er-
rors in SAR images [1-3].
Geometric distortions in SAR images can be
corrected by interpolation of images to a rectan-
gular grid on the ground plane taking into account
the measured aircraft trajectory and orientation
of the synthetic aperture beams (SAR beams).
However, this approach could be inefficient in the
case of significant geometric distortions.
The commonly-used clutter-lock technique [4],
which is based on the estimation of the Doppler
centroid from radar data, helps prevent radiomet-
ric errors very effectively in the case of unknown
and slowly-varying antenna orientation. Howe-
ver, the clutter-lock should not be used in the case
of fast and significant instabilities of the antenna
orientation since it leads to strong geometric er-
rors in SAR images.
Instabilities of aircraft orientation can be com-
pensated by the antenna stabilization. However,
it is a complicated and expensive solution. Appli-
cation of a wide-beam antenna firmly mounted
on the aircraft is another way to guarantee the
uniform illumination of the ground scene in the
central part of the antenna footprint despite of
the instabilities of the platform orientation.
In this paper, we describe a time-domain multi-
look stripmap SAR processing algorithm with
built-in correction of geometric distortions. In the
algorithm, the azimuth reference functions and
range migration curves are specially designed to
produce SAR images directly on a correct rectan-
gular grid on the ground plane.
The proposed approach does not use the clut-
ter-lock technique – the synthetic aperture beams
do not follow the orientation of the real antenna
beam. Therefore, the algorithm works well without
an additional radiometric correction only for a wide-
beam antenna and for central SAR looks, which
synthetic beams are directed close to the center of
the real antenna beam. In order to produce a multi-
look SAR image composed of all possible SAR
looks, we have proposed an effective radiometric
correction technique based on multi-look proces-
sing with extended number of looks [5].
SAR Processing Algorithm with Built-In Geometric Correction
99Радиофизика и радиоастрономия, 2011, т. 16, №1
The proposed method of the built-in geometric
correction has been successfully tested by using
a Ku-band airborne SAR system [6], installed
onboard a light-weight aircraft. First experimental
results and brief theoretical description of the
method were presented at conferences [7], [8].
This paper describes the method in details.
2. Formation of Synthetic Aperture
in Time Domain
The geometry of a stripmap SAR mode is
shown in Fig. 1. The local coordinate system (xyz)
is chosen so that the origin O goes along the pro-
jection of the aircraft trajectory onto the ground
plane (xy). The x-axis is always directed along
the current horizontal component of the aircraft
velocity vector, viz.
( ,0, ).x zV V=V (1)
The z-axis is directed upward and goes through
the antenna phase center. H is the current aircraft
flight altitude above the ground.
The orientation of the real antenna is described
by the antenna pitch angle α and the antenna
yaw angle .β The line AB is the intersection of the
elevation plane of the real antenna pattern and the
ground plane. This line is called the Doppler cen-
troid line. The coordinates of the point ( , )R Rx y
on this line at the slant range R are given by
( )22tan cos sin cos ,Rx H R H= α β+ β − α (2)
( )22tan sin cos cos .Ry H R H= − α β+ β − α
(3)
The slant range vector
( , , )x y H= −R (4)
is directed from the antenna phase center to the
point ( , )x y on the ground plane at which the
synthetic beam should be aimed. In Fig. 1, the
synthetic beam is pointed at the center of the real
antenna beam, that is at the point ( , )R Rx y on the
Doppler centroid line (2), (3).
In order to form the synthetic aperture, the
received radar pulses should be summed up co-
herently during the time of synthesis ST taking
into account the propagation phase ( )ϕ τ =
4 ( ) ,R− π τ λ where ( )R τ is the slant range to
the target, τ is the time within the interval of
synthesis, 2 2,S ST T− ≤ τ ≤ λ is the radar
wavelength. The formation of the synthetic aper-
ture ( )I t (t is the flight time along the trajectory)
can be considered as a matched filtering of the
received signal ( )s t with the azimuth reference
function ( ) :h τ
22
2
1( ) ( ) ( )d ,
S
S
T
S T
I t s t h
T −
= + τ τ τ∫ (5)
4( ) ( )exp ( ) .h w i Rπ⎡ ⎤τ = τ τ⎢ ⎥λ⎣ ⎦
(6)
The weighting window ( )w τ is applied to im-
prove the side-lobe level of the synthetic aperture
pattern.
If the slant range ( )R τ to the target changes
during the time of synthesis ST more than the size
of the range resolution cell, then the target signal
“migrates” through several range cells. This ef-
fect, known as the range migration, should be
taken into account during the aperture synthesis.
The one-dimensional backscattered signal ( ),s t
which is convolved with the reference functionFig. 1. Geometry of a stripmap SAR mode
O. O. Bezvesilniy, I. M. Gorovyi, S. V. Sosnytskiy, V. V. Vynogradov, and D. M. Vavriv
100 Радиофизика и радиоастрономия, 2011, т. 16, №1
in Eq. (5), should be obtained from the two-di-
mensional “azimuth – slant range” matrix of the
range-compressed radar data by the interpolation
along the migration curve:
2
( ) .
2 2 2DC DRR R F Fλ λ ττ ≈ − τ − (7)
The Doppler centroid DCF and the Doppler
rate DRF are given by
2 ( ) ,DCF
R
⋅=
λ
R V (8)
2 2
2 2
2 ( ) ( )1 .DR
VF
R RR V
⎡ ⎤⎛ ⎞⋅ ⋅= − − −⎢ ⎥⎜ ⎟λ ⎢ ⎥⎝ ⎠⎣ ⎦
R V R A (9)
Here A is the aircraft acceleration vector. No-
tice here that the aircraft flight altitude, velocity
and acceleration, as well as the antenna beam
orientation angles are assumed to be constant
during the time of synthesis, but may change slowly
during longer times.
The azimuth resolution is given by
.x x
X w w
D DR S
V VK K
F F T
ρ = =
Δ
(10)
The coefficient wK describes the broadening of
the main lobe of the synthetic aperture pattern
caused by windowing. The interval of synthesis in
time domain ST corresponds to the frequency
bandwidth DFΔ is the azimuth Doppler frequency
domain.
It is worth describing here briefly the SAR
processing procedure in time domain. The received
range-compressed radar data is stored in a mem-
ory buffer. The buffer size in range corresponds
to the swath width, the buffer size in azimuth is
determined by the time of synthesis .ST The basic
step of the SAR processing procedure for a given
range R includes the following calculations:
1) calculation of the Doppler centroid (8), the
Doppler rate (9), and the time of synthesis from
Eq. (10),
2) interpolation along the migration curve (7),
3) multiplication by the reference function with
windowing (6),
4) and, finally, coherent summation (5).
As a result, we obtain one pixel of the SAR
image representing the ground point at which the
synthetic beam was aimed. This basic step is re-
peated for all ranges within the swath producing
a single line of the SAR image in range direction.
In order to form the next line of the SAR image,
the data in the buffer is shifted in azimuth and
supplemented with new radar data, and the com-
putations are repeated. The new data consists
of SARK radar pulses so that the azimuth sampling
interval of the SAR image is
,x
SAR SAR
Vx K
PRF
Δ = (11)
where PRF is the radar pulse repetition frequency.
The described time-domain SAR processing
is a streaming processing which forms SAR ima-
ges line-by-line. It is different from the frame-
based SAR processing algorithms [9] which use
the fast Fourier transform (FFT) and work in fre-
quency domain, forming a SAR image frame im-
mediately. Prior to the usage of any of FFT-based
algorithms, one should apply motion compensa-
tion to the received radar data [10], [11] in order
to compensate deviations of the aircraft trajectory
from a straight line. The problem is that the motion
compensation and the conventional FFT-based
processing cannot be used in the case of signi-
ficant deviations from the reference flight line.
Alternative SAR processing algorithms for ima-
ging from curvilinear trajectories are considered
in [12]. Running ahead we should say that the
algorithm of the built-in geometric correction pro-
posed in this paper belongs to streaming algorithms
and works despite significant motion errors.
The described SAR algorithm is effective for
building moderate-resolution SAR images when
the convolution is not too long. The advantage
of the algorithm is its ability to build each pixel
of the SAR image with a particular reference
SAR Processing Algorithm with Built-In Geometric Correction
101Радиофизика и радиоастрономия, 2011, т. 16, №1
function and migration curve, in contrast to the
FFT-based SAR algorithms. It means that the
algorithm works well for time-varying and range-
dependent Doppler centroid and Doppler rate,
which is the case of SAR systems installed on
small aircrafts.
3. Multi-Look Processing in Time Domain
Multi-look processing is implemented in most
modern SAR systems. According to this technique,
several SAR images of the same ground scene,
called SAR looks, are produced from the radar
data collected on conjugated segments of the air-
craft trajectory. To suppress speckle noise, the SAR
look images are summed up non-coherently re-
sulting in a multi-look SAR image of higher quality
[1], [13]. Multi-look imaging is also used for other
applications, for example, for measuring the Dop-
pler centroid with high accuracy and high spatial
resolution [14].
The multi-look processing in time domain is
usually performed directly following the defini-
tion, as illustrated in Fig. 2(a) and Fig. 3(a). Namely,
the reference functions and range migration curves
are built for the long interval of synthesis max ,ST
which is the time required for the ground target
to cross the antenna footprint. The multi-look pro-
cessing is performed by splitting the long interval
maxST of the coherent summation (5) on several
integrals on sub-intervals ,ST thus forming the
multiple synthetic beams pointed to the same point
on the ground. The number of looks for a scheme
with half-overlapped sub-intervals is given by
maxint 1.
2
S
L
S
TN
T
⎧ ⎫
= −⎨ ⎬
⎩ ⎭
(12)
It will be observed that in the case of many looks,
the interval of synthesis maxST could become
so long that the quadratic approximation of the
slant range law (7) will be inaccurate, and we
should use a cubic approximation or the precise
square-root law for the slant range instead.
In order to use the described time-domain multi-
look processing approach successfully, we should
guarantee that there are no significant uncompen-
sated phase errors during the long coherent pro-
cessing time. However, as a matter of fact, in
order to achieve the desired azimuth resolution
for one SAR look it is sufficient to perform cohe-
rent processing on the short time interval ST ac-
cording to Eq. (10). This consideration turns us
to another approach, which is more preferable
in the case of significant motion errors. The idea
is to process the data collected during the short
time of synthesis ST with a set of different refe-
rence functions and migration curves to form multi-
look SAR beams. We have called this approach
Fig. 2. The conventional multi-look processing (a)
and the multi-look processing on a single-look interval
of synthesis (b): the antenna footprint consideration
O. O. Bezvesilniy, I. M. Gorovyi, S. V. Sosnytskiy, V. V. Vynogradov, and D. M. Vavriv
102 Радиофизика и радиоастрономия, 2011, т. 16, №1
“the multi-look processing on a single-look inter-
val of synthesis”. The question is how to build
these reference functions. The answer can be
obtained from the consideration of central fre-
quencies of SAR looks.
Considering the multi-look processing we may
say that the splitting of a long interval of synthesis
on several sub-intervals for coherent summation
in time domain corresponds to the dividing of the
whole azimuth Doppler bandwidth
max maxD DR SF F TΔ = (13)
on several sub-bands in frequency domain for
separate matched filtering. For multi-look
processing scheme with the half-overlapped sub-
bands (12), the central frequencies and the width
of the sub-bands are given by
( , ) ( ) ,
2
D
C L DC L
FF R n F R n Δ= − (14)
max ,
( 1) 2
D
D
L
FF
N
ΔΔ =
+
(15)
where 2, ..., 2 1L L Ln N N= − − is the SAR look
index. The SAR look sub-intervals are numerated
from left to right both in time and in frequency
domains. However, since the Doppler rate is al-
ways negative (9), the first sub-interval in time
domain corresponds to the last sub-interval in fre-
quency domain. Therefore, we write the “minus”
sign in Eq. (14) in order to use the same “left-
right” SAR look index in both domains, for con-
venience.
Taking into account the relation (10) for the azi-
muth resolution and Eqs. (13), (15), the central fre-
quencies of the SAR looks (14) can be written as
( , ) ( ) .
2
w x
C L DC L
X
K VF R n F R nΔ = −
ρ
(16)
Thus, we should process the same radar data
on the short interval of synthesis ST with a set
of different reference functions, which central
Doppler frequencies are given by the relation (16).
The proposed approach is illustrated in Fig. 2(b)
and Fig. 3(b). According to the principle of SAR
processing in time domain, in order to aim
the SAR beam at any particular point ( , )x y
we should perform processing with the corre-
sponding range migration curve (7), the Dop-
pler centroid ( )DCF R (8), and the Doppler rate
( )DCF R (9). Considering in backward direction,
the SAR look beam formed with the central fre-
quencies ( , )C LF R nΔ (16) will be pointed to some
points ( )( , ), ( , )R L R Lx R n y R n+ ξ +η which ap-
pear at the same slant range R at the center of the
interval of synthesis (see Fig. 2(b) and Fig. 3(b)).
Let us find the coordinates of these points.
Fig. 3. The conventional multi-look processing (a) and the multi-look processing on a single-look interval
of synthesis (b): the raw data buffer consideration
SAR Processing Algorithm with Built-In Geometric Correction
103Радиофизика и радиоастрономия, 2011, т. 16, №1
First, since the signals from these points have
appeared at the slant range R when the aircraft
is at the center of the synthetic aperture, we can
write
2 2 2
R Rx y H+ +
( ) ( )2 2 2( , ) ( , ) ,R L R Lx R n y R n H= + ξ + +η +
(17)
( ) ( )2 22 2 ( , ) ( , ) .R R R L R Lx y x R n y R n+ = + ξ + +η
Second, the position of the point in the azimuth
direction is related to its Doppler centroid (8), so
we can write
( )( , )2( , ) .R L x z
C L
x R n V HV
F R n
R
+ ξ −
Δ =
λ
(18)
Substituting the relation (16) in Eq. (18), we obtain
( )( , )2( ) ,
2
R L x zw x
DC L
X
x R n V HVK VF R n
R
+ ξ −
− =
ρ λ
(19)
( , ) .
4
w
L L
X
KR n n Rλξ = −
ρ
Now, we can calculate the coordinate ( , )LR nη
from Eq. (17) as
2 2 2( , ) ( ( , )) .L R R R L RR n x y x R n yη = + − + ξ −
(20)
Thus, in order to form the set of SAR looks for
the slant range R with central frequencies (16)
we should first calculate the corresponding points
( )( , ), ( , )R L R Lx R n y R n+ ξ +η on the ground from
Eq. (19) and Eq. (20) and then process the same
raw data on the interval of synthesis ST with the
appropriate range migration curves (7), Doppler
centroids (8) and Doppler rates (9).
It will be observed that all SAR look beams
are aimed at different points on the ground.
It means that the obtained SAR look images are
sampled on different grids. Therefore, the SAR
look images should be first re-sampled to the same
ground grid and only then they can be averaged
to produce the multi-look image. The deviations
of the aircraft trajectory introduce further com-
plexity into the re-sampling process. An efficient
approach to solve this problem called “built-in
correction of geometric distortions” is proposed
in the next section.
4. Built-In Correction
of Geometric Distortions
In order to perform the multi-look processing
on a single-look interval of synthesis and, at the
same time, to avoid complicated re-sampling
of the SAR look images to the rectangular grid
(including the correction of geometric errors),
we have proposed an algorithm of “built-in cor-
rection of geometric distortions”. The idea of the
built-in geometric correction is to point the multi-
look SAR beams exactly to the nodes of the rect-
angular grid on the ground plane as early as at the
stage of synthesis. In this way, we immediately
obtain geometrically correct SAR look images
and avoid the interpolation post-processing step.
In order to define the rectangular grid on the
ground plane, we should determine the following
reference (constant) parameters: the reference
flight direction, the reference aircraft flight alti-
tude 0H and velocity 0,V the reference orienta-
tion of the antenna beam with the antenna pitch
and yaw angles 0α and 0 ,β as well as the re-
ference pulse repetition period 0.T These para-
meters determine the reference flight line which
is close to the actual curvilinear flight trajectory
of the aircraft.
We shall define the scene coordinate system
( , , )X Y Z so that the reference flight line goes
exactly above the X axis. The rectangular grid
for SAR processing is the coordinate grid of
the ground plane ( , ).X Y The scene coordinate
system is shown in Fig. 4 together with the actual
local coordinate system ( , , ),x y z which slides
along the real aircraft flight trajectory, and the
reference local coordinate system ( , , ),ref ref refx y z
which slides along the reference flight line, that
is along the X axis. The current flight direction
O. O. Bezvesilniy, I. M. Gorovyi, S. V. Sosnytskiy, V. V. Vynogradov, and D. M. Vavriv
104 Радиофизика и радиоастрономия, 2011, т. 16, №1
is described by the angle Vϕ between the hori-
zontal component of the velocity vector XYV and
the X axis. The coordinates ( , )x y are related to
the coordinates ( , )ref refx y as follows
0( ) cos ( )ref A Vx x X t V t t⎡ ⎤= − + ϕ⎣ ⎦
( ) sin ( ),ref A Vy Y t t⎡ ⎤+ − ϕ⎣ ⎦ (21)
0( ) sin ( )ref A Vy x X t V t t⎡ ⎤= − − + ϕ⎣ ⎦
( ) cos ( ).ref A Vy Y t t⎡ ⎤+ − ϕ⎣ ⎦ (22)
Notice here that formulas (1)-(4) of the de-
scribed time-domain SAR processing algorithm
and formulas (19), (20) of the multi-look proces-
sing are valid with respect to the actual local
coordinate system. It means that in order to aim
the synthetic beam at a point with the scene
coordinates ( , )X Y or the reference local coordi-
nates ( , )ref refx y we should calculate the corre-
sponding actual local coordinates ( , )x y (21), (22)
of this point to use them in calculation of the
Doppler centroid (8), the Doppler rate (9) and the
migration curve (7). For the aircraft velocity we
have simply x XYV V= and .z ZV V= The aircraft
position and velocity vector are measured with
a simple GPS receiver.
There are several important requirements for
the grid steps in azimuth and ground range direc-
tions, GxΔ and .GyΔ The first one is that the grid
steps should be smaller than the corresponding
resolutions just to have at least one image sample
per resolution cell:
,G X Xx kΔ = ρ 1;Xk ≥ ,G R Yy kΔ = ρ 1.Yk ≥
(23)
Typically, the sampling factors Xk and Yk are
approximately equal to 2 (two samples per reso-
lution cell). Also, it is convenient to choose the
same grid step in azimuth and in ground range,
.G Gx yΔ ≈ Δ
The second requirement to the grid step
in azimuth comes from peculiarities of the time-
domain SAR processing algorithm. As aforesaid,
when we move from the one step of synthesis
to the next step, we update the radar data buffer
with SARK new pulses (11). The grid step in azi-
muth should be equal exactly to this number
of pulses, viz.
0 0( ).G SAR SARx x K V TΔ = Δ = (24)
The grid nodes to which the multi-look SAR
beams should be pointed can be found as follows.
The reference parameters are used to calculate
the Doppler centroid values ( ),DCF R the central
Doppler frequencies ( , )C LF R n of the SAR looks,
and the coordinates of the corresponding points
on the ground in the reference local coordinate
system, viz.
{ }( , ), ( , ) ,ref R L ref R Lx n n y n n
{ }( ) ( , ), ( , ) .
R R RR n n L R n Lx R R n y R n+ ξ + η
These computations are performed for all range
gates, 0 ,
Rn RR R n R= + Δ 0, 1, ..., 1R Rn N= − is
the slant range gate index, RN the number of
the range gates within the swath, 0R the near
slant range of the swath, and RΔ the slant range
sampling interval. The found points are shown
in Fig. 5 by circles and are situated on the central
frequency lines which are similar to the Doppler
Fig. 4. The scene coordinate system, the reference local
coordinate system, and the actual local coordinate
system
SAR Processing Algorithm with Built-In Geometric Correction
105Радиофизика и радиоастрономия, 2011, т. 16, №1
centroid line AB in Fig. 1. By using interpolation,
we find the points situated on the ground-range
grid lines
{ }( , ), ( , ) ,node
ref Y L ref Y Lx n n y n n
0( , ) .node
ref Y L Y Gy n n y n y= + Δ
Here Yn is the ground range index of the grid, 0y
the near ground range of the swath. Finally, roun-
ding the x-coordinates, we find the closest nodes
of the grid,
{ }( , ), ( , ) ,node node
ref Y L ref Y Lx n n y n n
( , ) round ( , ) ,node
ref Y L ref Y Lx n n x n n⎡ ⎤= ⎣ ⎦
indicated by triangles in Fig. 5.
Here the third requirement to the grid step
in azimuth arises. If the coordinates of the no-
des of the adjacent looks ( , )node
ref Y Lx n n and
( , 1)node
ref Y Lx n n + are closer than the grid step ,GxΔ
these nodes will coincide. To prevent such a si-
tuation we should decrease the grid step GxΔ
and, consequently, increase the sampling factor
Xk (23) so that
( , 1) ( , ) .node node
ref Y L ref Y L Gx n n x n n x+ − ≥ Δ (25)
Thus, the grid steps should satisfy the require-
ments (23), (24) and (25).
Moving from the one step of synthesis to the
next step, the data buffer is updated with SARK
new radar data pulses ( 5SARK = in Fig. 5), we
move up to the next reference local coordinate
system, from ( , )ref refx y′ ′ to ( , ),ref refx y′′ ′′ and the
next neighbor grid nodes indicated by squares in
Fig. 5 are used for pointing the SAR look beams.
In order to point the SAR look beams to par-
ticular grid nodes, we should recalculate the coor-
dinates of these nodes from the reference local
coordinate system to the actual local coordinate
system by using Eqs. (21), (22), taking into ac-
count the actual aircraft position and orientation
of the aircraft velocity vector. This recalculation
Fig. 5. Grid nodes in the built-in geometric correction algorithm
O. O. Bezvesilniy, I. M. Gorovyi, S. V. Sosnytskiy, V. V. Vynogradov, and D. M. Vavriv
106 Радиофизика и радиоастрономия, 2011, т. 16, №1
is performed at each step of the synthesis. Thus,
we obtain geometrically-correct SAR image sam-
pled at the grid nodes of a rectangular grid on the
ground plane.
The proposed built-in geometric correction
algorithm cannot be combined with the clutter-
lock technique – the SAR beams do not follow
the orientation of the real antenna beam. There-
fore, the algorithm works well without additional
radiometric correction only for a wide-beam an-
tenna and only for the central SAR looks. In order
to use all possible SAR looks to form the multi-
look SAR image without radiometric errors, we
have proposed an effective radiometric correc-
tion technique based on multi-look processing with
extended number of looks [5].
5. Results
The geometric correction is illustrated in Fig. 6.
The SAR image shown in Fig. 6(a) was built by
using the clutter-lock technique. One can see the
geometric distortions caused by instabilities of
antenna orientation. The correct SAR image
shown in Fig. 6(b) was formed by using the algo-
rithm with the built-in geometric correction. Both
images have 3-m resolution and were built using
3 looks.
The accuracy of the geometric correction is
illustrated in Fig. 7, where the SAR image com-
posed of 45 looks and formed by using the built-
in geometric correction is imposed on the Google
Map image of the scene. One can see that the
SAR processing algorithm with the built-in cor-
rection of geometric distortions proposed in this
paper allows building high-quality multi-look SAR
images.
The obtained results prove that the proposed
algorithm can be effectively used for a SAR
system installed onboard a light-weight aircraft
with a non-stabilized antenna. An important ad-
vantage of the algorithm is that the produced
SAR images are already geometrically correct
immediately after synthesis, and there is no need
in any additional interpolation. Another impor-
tant advantage of the algorithm is the reduced
requirements for the SAR navigation system.
Although the aircraft velocity vector should be
measured quite accurately to aim the synthetic
beams at proper points on the ground, the air-
craft trajectory should be measured and com-
pensated with the high accuracy of a fraction of
the radar wavelength only during the short time
of synthesis of one look. There is no need to
keep so high accuracy during the long time of
data acquisition for all looks. In order to combine
all SAR looks into one multi-look image, it
is sufficient to measure the trajectory with the
accuracy of a fraction of the SAR resolution.
The algorithm requires lots of computations
in the case of SAR imaging with very high reso-
lution because of the long time-domain convolu-
tion, and this is its disadvantage. Other SAR pro-
cessing methods could be more efficient in com-
putations, however the SAR system must be
equipped with a stabilized antenna and good na-
vigation system, and full motion error compensa-
tion should be performed, too.
Fig. 6. Illustration of geometric correction: a 3-look
SAR image built by using the clutter-lock technique
(a), and a 3-look SAR image formed by using the built-
in geometric correction (b)
SAR Processing Algorithm with Built-In Geometric Correction
107Радиофизика и радиоастрономия, 2011, т. 16, №1
References
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Fig. 7. A 45-look SAR image formed by using the built-in geometric correction (a) is imposed on the Google Maps
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108 Радиофизика и радиоастрономия, 2011, т. 16, №1
Алгоритм со встроенной
геометрической коррекцией
для обработки данных РСА
А. А. Безвесильный, Е. Н. Горовой,
С. В. Сосницкий, В. В. Виноградов,
Д. М. Ваврив
Радиолокационные системы с синтезирован-
ной апертурой (РСА), установленные на неболь-
ших самолетах, подвержены влиянию отклоне-
ний траектории и нестабильности ориентации
антенны. Такие ошибки движения приводят
к значительным геометрическим искажениям
на радиолокационных изображениях (РЛИ).
Чтобы исправить эти искажения, мы пред-
лагаем алгоритм многовзглядовой обработки
со встроенной геометрической коррекцией,
работающий во временной области и предназ-
наченный для РСА бокового обзора. В этом
алгоритме азимутальные опорные функции
и кривые миграции строятся таким образом,
чтобы получать РЛИ сразу на прямоугольной
сетке в плоскости земли. Предложенный ме-
тод был успешно испытан с использованием
самолетного РСА сантиметрового диапазона
длин волн, установленного на легком самолете.
Алгоритм з вбудованою геометричною
корекцією для обробки даних РСА
О. О. Безвесільний, Є. М. Горовий,
С. В. Сосницький, В. В. Виноградов,
Д. М. Ваврів
Радіолокаційні системи з синтезованою
апертурою (РСА), встановлені на невеликих
літаках, зазнають впливу відхилень траєкторії
і нестабільності орієнтації антени. Такі помил-
ки руху призводять до значних геометричних
спотворень на радіолокаційних зображеннях
(РЛЗ). Аби виправити ці спотворення, ми про-
понуємо алгоритм багатопоглядової обробки
з вбудованою геометричною корекцією, який
працює у часовому просторі та призначений
для РСА бічного огляду. У цьому алгоритмі
азимутальні опорні функції та криві міграції
формуються таким чином, щоб отримувати
РЛЗ одразу на прямокутній сітці в площині
землі. Запропонований метод було успішно
випробувано з використанням РСА сантимет-
рового діапазону довжин хвиль, встановлено-
му на легкому літаку.
|
| id | nasplib_isofts_kiev_ua-123456789-98205 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1027-9636 |
| language | English |
| last_indexed | 2025-12-07T18:57:08Z |
| publishDate | 2011 |
| publisher | Радіоастрономічний інститут НАН України |
| record_format | dspace |
| spelling | Bezvesilniy, O.O. Gorovyi, I.M. Sosnytskiy, S.V. Vavriv, D.M. Vynogradov, V.V. 2016-04-10T16:13:31Z 2016-04-10T16:13:31Z 2011 SAR Processing Algorithm with Built-In Geometric Correction / O.O. Bezvesilniy, I.M. Gorovyi, S.V. Sosnytskiy, V.V. Vynogradov, D.M. Vavriv // Радиофизика и радиоастрономия. — 2011. — Т. 16, № 1. — С. 98-108. — Бібліогр.: 14 назв. — англ. 1027-9636 https://nasplib.isofts.kiev.ua/handle/123456789/98205 Synthetic aperture radar (SAR) systems onboard small aircrafts suffer from trajectory deviations and
 instabilities of antenna orientation. These kinds of motion errors lead to significant geometric distortions
 in SAR images. In order to correct the distortions, we propose a time-domain multi-look stripmap SAR
 processing algorithm with built-in geometric correction. In the algorithm, the azimuth reference functions
 and range migration curves are designed to produce SAR images directly on a correct rectangular grid
 on the ground plane. The proposed technique has been successfully tested by using a Ku-band airborne
 SAR system installed onboard light-weight aircraft. Радиолокационные системы с синтезированной апертурой (РСА), установленные на небольших самолетах, подвержены влиянию отклонений траектории и нестабильности ориентацииантенны. Такие ошибки движения приводят
 к значительным геометрическим искажениям на радиолокационных изображениях (РЛИ). Чтобы исправить эти искажения, мы предлагаем алгоритм многовзглядовой обработки со встроенной геометрической коррекцией,
 работающий во временной области и предназначенный для РСА бокового обзора. В этом алгоритме азимутальные опорные функции и кривые миграции строятся таким образом, чтобы получать РЛИ сразу на прямоугольной сетке в плоскости земли. Предложенный метод был успешно испытан с использованием самолетного РСА сантиметрового диапазона длин волн, установленного на легком самолете. Радіолокаційні системи з синтезованою апертурою (РСА), встановлені на невеликих
 літаках, зазнають впливу відхилень траєкторії і нестабільності орієнтації антени. Такі помилки руху призводять до значних геометричних спотворень на радіолокаційних зображеннях (РЛЗ). Аби виправити ці спотворення, ми пропонуємо алгоритм багатопоглядової обробки з вбудованою геометричною корекцією, який
 працює у часовому просторі та призначений для РСА бічного огляду. У цьому алгоритмі азимутальні опорні функції та криві міграції формуються таким чином, щоб отримувати РЛЗ одразу на прямокутній сітці в площині землі. Запропонований метод було успішно випробувано з використанням РСА сантиметрового діапазону довжин хвиль, встановленому на легкому літаку. en Радіоастрономічний інститут НАН України Радиофизика и радиоастрономия Радиофизические аспекты радиолокации, радионавигации, связи и дистанционного зондирования SAR Processing Algorithm with Built-In Geometric Correction Алгоритм со встроенной геометрической коррекцией для обработки данных РСА Алгоритм з вбудованою геометричною корекцією для обробки даних РСА Article published earlier |
| spellingShingle | SAR Processing Algorithm with Built-In Geometric Correction Bezvesilniy, O.O. Gorovyi, I.M. Sosnytskiy, S.V. Vavriv, D.M. Vynogradov, V.V. Радиофизические аспекты радиолокации, радионавигации, связи и дистанционного зондирования |
| title | SAR Processing Algorithm with Built-In Geometric Correction |
| title_alt | Алгоритм со встроенной геометрической коррекцией для обработки данных РСА Алгоритм з вбудованою геометричною корекцією для обробки даних РСА |
| title_full | SAR Processing Algorithm with Built-In Geometric Correction |
| title_fullStr | SAR Processing Algorithm with Built-In Geometric Correction |
| title_full_unstemmed | SAR Processing Algorithm with Built-In Geometric Correction |
| title_short | SAR Processing Algorithm with Built-In Geometric Correction |
| title_sort | sar processing algorithm with built-in geometric correction |
| topic | Радиофизические аспекты радиолокации, радионавигации, связи и дистанционного зондирования |
| topic_facet | Радиофизические аспекты радиолокации, радионавигации, связи и дистанционного зондирования |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/98205 |
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