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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Azimuth Invariance

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Bistatic SAR signal

range

azimuth

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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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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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Simple Illustration of Frequency based algorithms

Rg time

Az

tim

eA

z fr

eqA

z T

ime

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POSP

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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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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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SRC

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Cross Coupling

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LBF

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LBF

Expand around individual stationary phase

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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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LINK between MSR, LBF and DMO

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Typical example

• X band example

• Squint angles θsqT = -θsqR

• Large baseline to rangeRatio of 2h/R = 0.83

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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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DMO

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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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DMO (seismic processing)

Tx Rx

θd

Monosurvey

tb

tm

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θd

Tx Rx

θd

MonoSAR

θsq

tbtm

DMO applied to SAR

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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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Bistatic RDA/Approximate bistatic RDA

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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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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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NLCS (parallel)

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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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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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Applying QRCMC and SRC

Range compressionLRCMC / Linear phase removal

Azimuth compression

BasebandSignal

FocusedImage


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


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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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• 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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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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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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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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Requirement for SRC

• L-band

• 1 m resolution

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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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Simulation results with NLCS processing

Accurate compression Registration to ground plane

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NLCS (Stationary Receiver)

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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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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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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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Simulation results with NLCS processing

Focused Image Registration to Ground plane

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