Extra Illustrations
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Transcript of Extra Illustrations
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Extra Illustrations
By Y. L. Neo
Supervisor : Prof. Ian Cumming
Industrial Collaborator : Dr. Frank Wong
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Azimuth Invariance
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Bistatic SAR signal
range
azimuth
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
A point target signal
• Two-dimensional signal in time and azimuth• Simplest way to focus is using two-
dimensional matched filtering
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Overview of Existing Algorithms
• Time domain algorithms are accurate but slow – BPA, TDC
• Monostatic algorithms make use– Azimuth-Invariance
– Efficiency achieved in azimuth frequency domain
• Traditional monostatic frequency domain algorithms– RDA, CSA and ωKA
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Simple Illustration of Frequency based algorithms
Rg time
Az
tim
eA
z fr
eqA
z T
ime
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
POSP
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Principle of Stationary Phase (POSP)
• 1.) Want to find spectrum S(f)• 2.) POSP takes note of contribution to integral of
rapidly changing signal is zero.• 3.) Most of the contribution is near the stationary
point where phase do not change rapidly.• 4.) Therefore we are interested in the azimuth times
where d/d=0, i.e. at solution to the stationary phase (f)
• 5.) Expanding around this solution (f) we end up with the result given next
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
POSPAnalytical SpectrumDifficult to derive directly
Most of the contributionof integral comes fromaround stationary point
Expanding around stationary point, the analytical spectrum can be derived
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
SRC
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Cross Coupling
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
LBF
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
LBF
Expand around individual stationary phase
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
LBF• Make use of the fact
that sum of 2 quadratic functions is another scaled and shifted quadratic function.
• Apply POSP, we get approximate stationary phase solution
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
LINK between MSR, LBF and DMO
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Typical example
• X band example
• Squint angles θsqT = -θsqR
• Large baseline to rangeRatio of 2h/R = 0.83
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Summary • MSR is the most general of the three spectra –
MSR, DMO and LBF• DMO is accurate when short baseline/Range ratio
• LBF is accurate under conditions – higher order bistatic deformation terms are negligible and
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
DMO
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
DMO
• Pre-processing technique – transform bistatic data to monostatic data
• Technique from seismic processing
• Transform special bistatic configuration (Tandem Configuration or Leader-Follower) to monostatic
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
DMO (seismic processing)
Tx Rx
θd
Monosurvey
tb
tm
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
θd
Tx Rx
θd
MonoSAR
θsq
tbtm
DMO applied to SAR
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
DMO Operator for bistatic SAR to Monostatic SAR transformation
Phase modulator Migration operator
DMO operator transform
Bistatic Trajectoryto
Monostatic trajectoryMonostatic trajectory
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Bistatic RDA/Approximate bistatic RDA
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Phase terms of spectrum
• Range Modulation – range chirp
• Range Doppler Coupling – removed in the 2D frequency domain, evaluated at the reference range. For wider scene, requires range blocks.
• Range Cell Migration term – linear range frequency term, removed in the range Doppler domain
• Azimuth Modulation – removed by azimuth matched filter in range Doppler domain
• Residual phase – range varying but can be ignored if magnitude is the final product
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Approximate RDA• For coarse range resolution and lower squint, the range Doppler
coupling has only a small dependency on azimuth frequency. • Thus, SRC is evaluated at Doppler centroid and can be combined
with Range Compression (as in Monostatic Case).
Range FT Azimuth FT
Azimuth CompressionWith Azimuth IFT
Baseband Signal
Focused Image
Range CompressionAnd SRC
Range IFT
RCMC
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
NLCS (parallel)
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Non-Linear Chirp Scaling
• Existing Non-Linear Chirp Scaling
– Based on paper by F. H. Wong, and T. S. Yeo, “New Applications of Nonlinear Chirp Scaling in SAR Data Processing," in IEEE Trans. Geosci. Remote Sensing, May 2001.
– Assumes negligible QRCM (for SAR with short wavelength)
– shown to work on Monostatic case and the Bistatic case where receiver is stationary
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
NLCS
• We have extended NLCS to handle non parallel tracks cases
• Able to higher resolutions, longer wavelength cases
• Correct range curvature, higher order phase terms and SRC
• Develop fast frequency domain matched filter using MSR
• Registration to Ground Plane
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Applying QRCMC and SRC
Range compressionLRCMC / Linear phase removal
Azimuth compression
BasebandSignal
FocusedImage
Non-Linear Chirp Scaling
Residual QRCMC
The scaling function is a
polynomial function of azimuth time
• NLCS applied in the time domain• SRC and QRCMC --- range Doppler/2D freq domain• Azimuth matched filtering --- range Doppler domain
Residual QRCMCand SRC
Non-Linear Chirp Scaling
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Monostatic Case
Az
tim
e
Range time
A
B
C FM Rate Difference
– The trajectories of three point targets in a squinted monostatic case is shown
– Point A and Point B have the same closest range of approach and the same FM rate.
– After range compression and LRCMC, Point B and Point C now lie in the same range gate. Although they have different FM rates
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
• After LRCMC, trajectories at the same range gate do not have the same chirp rates, an equalizing step is necessary
• This equalization step is done using a perturbation function in azimuth time
• Once the azimuth chirp rate is equalized, the image can be focused by an azimuth matched filter.
FM Rate Equalization (monostatic)
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
FM Rate Equalization (monostatic or nonparallel case) – cubic perturbation function
CAB
A
B
C
A
B
C
Before LRCMC
Azimuth
Range Range
After LRCMC AB C
Azimuth
Azimuth
Phase
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Longer wavelength experiment
Without residual QRCMC(20 % range and azimuth broadening)
With residual QRCMC,resolution and PSLRimproves
• Uncorrected QRCM will lead to broadening in range and azimuth
• QRCMC is necessary in longer wavelength cases
• Higher order terms can be ignored in most cases
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Expansion of phase up to third order necessary- e.g. C band 55deg squint 2m resolution
•Azimuth Frequency Matched Filter •Accuracy is attained by including enough terms.
Second order Third order
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Requirement for SRC
• L-band
• 1 m resolution
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Simulation results
• C-band• Non-parallel tracks
range resolution of 1.35m and azimuth resolution of 2.5m
• Unequal velocities Vt = 200 m/s
Vr = 221 m/s
• track angle difference 1.3 degree
• 30° and 47.3° squint
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Simulation results with NLCS processing
Accurate compression Registration to ground plane
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
NLCS (Stationary Receiver)
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
NLCS (Stationary Receiver)
D
F’
E’
– Data is inherently azimuth-variant
– Targets D E’ F’ lie on the same range gate but have different FM rates
– Point E’ and Point F’ have the same closest range of approach and the same FM rate but different from Point D
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
FM Rate Equalization (stationary receiver case) – quartic perturbation function
Azimuth
Phase
F’DE’
D
E’
F’
Stationary Receiver
Azimuth
Range
DE’ F’
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Simulation Experiment
• S-band • Transmitter at broadside• Range resolution of 2.1m and azimuth resolution of 1.4m• Unequal velocities Vt = 200 m/s Vr = 0 m/s
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T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A
University of Siegen
Simulation results with NLCS processing
Focused Image Registration to Ground plane