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x
yO
z
Equator plane
0y0
z
0x
0S
kS
k
kr
0r
Figure 1 Satellite formation flying
Signal Processing Method for Distributed SAR
Imaging Improvement
Zuo Yanjun Yang Ruliang
Institute of Electronics, Chinese Academy of SciencesBeijing,
China
Email: [email protected]: A commonly known design
requirement for
synthetic aperture (SAR) systems is the minimum SAR
antenna area constraint, and there are range-Doppler
ambiguities. So in conventional SAR, there is a well
known trade-off between unambiguous swathwidth and
resolution. However, if spatial sampling is added, the
maximum unambiguous illumination area will increase
with the number of receivers; through this method
multiple beams can be formed to reject range-Doppler
ambiguities. As is well known, multistatic syntheticaperture
radar operates with multiple receive atennas
distributed among different platforms which can be
used to increase the special sampling. And
constellat ions of formation-flyi ng microsatelli tes are
currently under study in the field of remote sensing.
Basing on this multistatic modes, this paper is intended
to study signal processing method of SAR Doppler
ambiguities resolving to improve image quality.
Key words: Distributed SAR; Range-Doppler Ambiguities;Imaging
Improvement
I. INTRODUCTION
It is desirable for SAR to have high resolution and alarge
spotlight area or wide swathwidth. Instantaneouslyilluminating a
large area is advantageous for applicationsthat require immediate
access to the information that SARprovides. For dynamic remote
sensing applications, such assoil moisture measurement, that
require wide coverage andmonitoring over time, increased
illumination area translatesto fewer orbits necessary for imaging a
wide area.Unfortunately, a commonly known design requirement
thatlimits SAR illumination area is the minimum SAR antennaarea
constraint. So there exits range ambiguities, Dopplerambiguities,
or both .There are a number of ways to resolveambiguities of a
distributed SAR systems: One way is to
operate Doppler unambiguous but allow range ambiguities,and use
some measures to reject the range ambiguities. Asecond way is to
let Doppler ambiguous and rangeunambiguous and adopt STAP
processing to resolveDoppler ambiguities. The last way is operate
Doppler andrange all ambiguous and use signal processing approach
toresolve the Doppler and range ambiguities. Basing on thesecond
way, theoretical derivation, performance analysis,and simulation
are studied in the paper.
II. DISTRIBUTED MICRO SATELLITES FORMATIONFLYING ORBIT
ANALYSIS
There two coordinate systems shown in Fig.1.
1) inertial coordinate system oxyz ;2) relative motion
coordinate system
0 0 0 0s x y z ;
Theoretically, the formation configuration ofdistributed micro
satellites can be designed on demand atdiscretion. At present, the
formation orbit problem isstudied by Hill equation in most
literatures, and thismethod needs to know the initial position and
velocity ofchase satellites in relative motion coordinate
system,
which cant educe analytical result. So, it is inapplicable
to
the orbit design of distributed SAR satellites. In this
paper,based on satellite trajectories the formula of distributedSAR
satellites orbit parameters is deduced.
Suppose the trajectories of the reference satellite0S
is: ( , , , , , )pka e i t , the trajectories of satellite
kS is: ( , , , , , )k k k k k pk a e i t and ka a= , k ki i i= +
,
k k k = + ,
k k = + , k is the initial phase angleof
kS in the satellite formation. And
k s pk t = . Where,
pkt is the perigee time of
kS , s is the mean angular
velocity of satellites formation.
The true anomaly of SatellitekS is:
1
( ) ( ) sin[ ( )]k k n k n
f t M t g n M t
=
= + (1)
Where, ( )kf t denotes the true anomaly, ( )kM t denotes
mean anomaly, ng is the coefficient of fourier series,e is
orbital eccentricity.
Let the perigee time, perigee angular and the
ascending node angular of0
S are respectively: 0pt = ,
0 = , ( ) su t t= ; then the ascending node angular
ofsatellite
kS ( ) ( ) ( ) ( )k k k k u t f t u t u t = + = + ,
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( ( 0), (0))k k kS y z
0S
0y
y
z
maxkz
maxky 0ky
Figure 2 Five parameters of relative orbit
sin
df
o
Figure 3(a) Relation between df and
where,
1
( ) sin[ ( )]k n k k
n
u t g nM t
=
= + (2)
and ( )k s kM t t = , 0k kM = .
0kM denotes the mean anomaly at formation initial
time 0pkt = .
In inertial coordinate system, the position vectors ofchase
satellites and reference satellite are respectively:
cos( )cos( ) sin( )sin( )cos( )
sin( )cos( ) cos( )sin( )cos( )
sin( )sin( )
k k k k k
k k k k k k k
k k
u u i
E r u u i
u i
=
cos( ) cos( ) sin( ) sin( ) cos( )
sin( ) cos( ) cos( ) sin( ) cos( )sin( ) sin( )
u u i
E r u u iu i
=
Then the relative position vector between the chase
satellites and reference satellite k is:
k kE E = (3)
Where,2(1 )
( )1 cos[ ( )]
a er t
e f t
=
+,
2(1 )( )
1 cos[ ( )]
k
kk k
a er t
e f t
=
+.
Suppose the reference satellite orbit is circular, i.e.
0e= . Ignore all high order infinitesimals ofk
ku
ki in equation (3), then:
0
cos( )
sin( )
cos( )
k k p
k k k p k
k k p k k
x a e nt nt
y y A a nt nt
z B nt nt
=
= + + = + +
(4)
Where, k, ky and kz denote the position coordinateof chase
satellites in the relative orbit reference frame.
0
2 2
0 0
2 2
1
1
( cos )
2 2 cos( )
( sin ) ( )
sin( ) sin( )tan
cos( ) sin( )
tansin
k k pk k
k k k pk
k k k
p k pk
k
k pk p
kk
k
y a nt i
A a e e e e n t
B a i i
e nt e nt
e nt e nt
i
i
= + = +
= + =
=
(5)
For observation satellite formation, its most care is the
geometry relation on0 0
y z plane in relative orbit reference
frame, see Fig.2. Commonly, the relative motion between
the
reference satellite and chase satellites on0 0
y z plane is
elliptical; their relationship is shown in Fig.2 in detail.
max
max
k k
k k
y A
z B
= =
(6)
III. MICRO SATELLITES ECHO SIGNAL AMBIGUTIESAANALYSIS
For space borne SAR, the relationship between
Doppler frequency df of ground echo signal and azimuth
angle is:
2sin cosd
vf
= (7)
Where, is downwards angle of visibility. For sidemode, let
azimuth beam width is , main satellitevelocity isv , radar
wavelength is, 0 = o ;
Suppose 0.015rad = , 7000 /v m s= , 3cm = ,then the spectrum
range of the ground echo signal mainlobe can be calculated based on
the formula (7), which is
7000Hz. And the relation between df and sin is shownin Fig 3(a).
In order to avoid the range ambiguities, thelower PRF is adopted,
for example PRF=1400Hz. Soactually there exits five Doppler
ambiguities, which is
shown in Fig.3(b).
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Figure 6 the construct between ambiguous image and unambiguous
one
AcknowledgmentThe authors would like to thank my tutor
Professor
Yang Ruliang for his helpful comments and suggestions.The
authors would also like to thank my schoolfellows forhelpful
discussions during the execution of some of thework summarized in
this paper.
REFERENCES
[1] Krieger G, Fiedler H, Mittermayer J, et al. Analysis of
multistaticconfigurations for spaceborne SAR interferometry.
IEE
Proceedings Radar Sonar Navigation, 2003, 150(3): 87-96
[2] Goodman N, SAR and MTI processing of sparse satellite
clusters, Doctoral thesis, The University of Kanasas, 2002.
[3] Goodman N,Rajakrishna D, et al. Wide swath, high resolution
SAR
using multiple receive apertures. IEEE International
Geoscienceand Remote sensing Symposium, Hamburg Germany, pp.
1767-
1769.
[4] Goodman N, Lin S, et al. Processing of
multiple-receiverspaceborne arrays for wide-area SAR. IEEE
Transaction on
Geoscience and Remote sensing, 2002, 40(4): 841-852.
[5] K. Tomiyasu, "Image processing of synthetic aperture radar
range
ambiguous signals," IEEE Trans. Geosci. Remote Sensing, vol.
32,no. 5, pp. 1114-1117, Sept., 1994.
[6] K. Tomiyasu, "Conceptual performance of a satellite borne,
wide
swath synthetic aperture radar," IEEE Trans. Geosci.
RemoteSensing, vol. GE-19, no. 2, pp. 108-116, April, 1981.
