bistatic sar imaging using non-linear chirp scaling

20 Dec 2005 Bistatic SAR Imaging using Non-Linear Chirp Scaling1

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

Bistatic SAR imaging using Non-Linear Chirp Scaling

By Y. L. Neo

Supervisor : Prof. Ian Cumming

Industrial Collaborator : Dr. Frank Wong



Agenda

• Bistatic SAR• Bistatic Image Reconstruction Issues• Existing Algorithms• Non-Linear Chirp Scaling Algorithm• Extension to NLCS• Simulation Results• Conclusions



Bistatic SAR

• In a Bistatic configuration, the Transmitter and Receiver are spatially separated and can move along different paths.

• Bistatic SAR is important as it provides many advantages

– Cost savings by sharing active components

– Improved observation geometries

– Passive surveillance and improved survivability



Current Research• Several European radar research institutes - DLR, ONERA,

QinetiQ and FGAN have embarked on bistatic airborne experiments. Majority of the experiments uses two existing monostatic sensors to synthesize bistatic images.

• Satellite missions are also proposed TanDEM – X : proposal for TerraSAR-X single pass interferometry for accurate DEM DTED-3. Interferometric Cartwheel. Excellent paper – Multistatic SAR Satellite Formations: Gerhard Krieger.

• Other research involves the use of Bistatic Parasitic SAR. Where a ground based receiver pairs up with a non-cooperative satellite transmitter.



Agenda




Image Reconstruction Issues

• Bistatic SAR data, unlike monostatic SAR data, is inherently azimuth-variant.

• Difficult to derive the spectrum of bistatic signal due to the double square roots term.

• Traditional monostatic SAR algorithms based on frequency domain methods are not able to focus bistatic SAR imagery, since targets having the same range of closest approach do not necessarily collapse into the same trajectory in the azimuth frequency domain.



Image Reconstruction Issues

• Bistatic SAR has many configurations

– parallel tracks,

– non-parallel tracks,

– stationary receiver etc.

• These different configurations make the derivation of the spectrum difficult – Analytical solution is not available, however approximate

solution exist – Loffeld’s bistatic equation

– Restricted the scope of research to focusing parallel and slightly non-parallel cases



Tra

nsmitte

r Flig

ht Path

Receiver F

light Path

Receiver

Transmitter

Bistatic Angle

Transmitter Beam

Receive

r Beam

RT

RRBaseline

Target

Imaging geometry of bistatic SAR



Agenda




Existing Algorithms

• Time Domain Correlation

• Back Projection Algorithm

• K Algorithm

• Loffeld’s Bistatic Equations– RDA– Rocca’s Smile



Agenda




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

– Limitations of this method is unknown– May be extended to other geometries – parallel

tracks, non-parallel tracks



Advantages

• NLCS can be used to focused bistatic data by NLCS can be used to focused bistatic data by finding the perturbation function for each finding the perturbation function for each bistatic configurationbistatic configuration

• NLCS requires no interpolationNLCS requires no interpolation• NLCS can be used in non-parallel casesNLCS can be used in non-parallel cases• The Linear RCMC step in NLCS eliminates The Linear RCMC step in NLCS eliminates

most of the RCM and the range/azimuth phase most of the RCM and the range/azimuth phase coupling. coupling.

• Computational load is comparable to Computational load is comparable to traditional monostatic algorithms.traditional monostatic algorithms.



Main Processing Steps of NLCS Algorithm

Range Compression Linear RCMC


Azimuth Compression

BasebandSignal

FocusedImage



Monostatic Case

Az

tim

e

Range time

A

B

C

– The trajectories of three point targets in a squinted monostatic case is shown

– Point A and Point B has the same Closest range of approach and the same chirp rate.

– After Range Compression and LRCMC, Point A and Point C now lie in the same range gate. Although they have different chirp rates



Chirp Rate Equalization (monostatic)

CAB

A

B

C

A

B

C

Before LRCMC

Azimuth

Range Range

After LRCMC AB C



• After LRCMC, trajectories at the same range gate do not have the same chirp rates, an equalizing step is necessary

• Once the Azimuth Chirp Rate is equalized, the image can be focused by an azimuth matched filter.

• Chirp rates are equalized by phase multiply with a perturbation function hpert(η) along azimuth time .

– Monostatic Case

• Bistatic Case with Stationary Receiver



Agenda




Research work done

• Added residual QRCMC• Extended the processing to parallel tracks

and non-parallel tracks• Azimuth Frequency Matched filter• Secondary Range Compression• Current work

– Invariance Region Analysis

– Registration to ground plane



• We have added a QRCMC to improve the impulse response

• Residual QRCM Correction can be performed in the range Doppler domain after the Chirp Rate has been equalized

Range CompressionLRCMC / Linear Phase Correction

Azimuth Compression

BasebandSignal

FocusedImage


Residual QRCMC



Residual QRCMC• Uncorrected QRCM will lead to Broadening in Range and Azimuth

• The Cubic RCM is very small compared to Quadratic RCM , can be ignored in most cases

Without residual QRCMC

With residual QRCMCResolution and PSLRImproves



Perturbation Function• We have extended the NLCS algorithm to Non-Parallel Tracks with the Same

Velocity• Using the method similar to the monostatic case and correction of the phase term

up to the cubic term, the perturbation function is found to be a cubic function of azimuth time and the coefficient is found to be

• Limited to short and medium wavelength system



Azimuth Frequency Matched Filter• Initially used time domain matched filter – correlation

(inefficient)• Frequency matched filter is derived using the

reversion of power series

• Linear phase term has to be removed before applying the reversion of power series



Azimuth Matched Filter• Freq matched filter can be obtained by doing a FT of the equalized Az signal

• A relation between azimuth time and azimuth frequency can be obtained by using the Principle of Stationary Phase



Azimuth Matched Filter• The Frequency matched filter is the conjugate of FT signal

• Expansion up to third order phase is necessary- e.g. C band 55deg squint 2m resolution



Limitations • Restriction on patch size, residual RCM difference

< 1 range resolution cell – restrict the range extent• The Non-linear chirp scaling uses some

approximations – leading to restriction in azimuth extent

• Range Doppler Coupling for large QRCM – Secondary Range Compression is necessary

• Algorithm suitable for shorter wavelengths (S, C , X, K band ) and cases where QRCM is not too significant



Invariance Region Analysis

Wavelength (Frequency)

Resolution 0.01m (30GHz) 0.03m (10GHz) 0.06m (5GHz) 0.2m (1.5GHz)

10 m Full size Full size Full size Full size

3 m Full size Full size Full size 3.4 km

1 m Full size 4.5km 2.1km 0.6km

• Bistatic case, Tx imaging at 30 deg squint, Tx slant range of 40km, Bistatic case, Tx imaging at 30 deg squint, Tx slant range of 40km, lateral separation of 20km and squint of 30 deg.lateral separation of 20km and squint of 30 deg.

Wavelength (Frequency)

Resolution 0.01m (30GHz) 0.03m (10GHz) 0.06m (5GHz) 0.2m (1.5GHz)

10 m Full size Full size Full size Full size

3 m Full size Full size Full size 4.0 km

1 m Full size 2.7km 1.3km 0.4km

The range invariance region to keep range and azimuth resolution The range invariance region to keep range and azimuth resolution degradation less than 10% for a 10 km by 10km patch. degradation less than 10% for a 10 km by 10km patch.

• Bistatic case, imaging at broadside with Tx slant range of 40km, Bistatic case, imaging at broadside with Tx slant range of 40km, lateral separation of 20km and a bistatic angle of 9 deg.lateral separation of 20km and a bistatic angle of 9 deg.



Secondary Range Compression• Range Doppler Coupling occurs for large QRCM i.e. longer wavelength

and higher resolution cases• Secondary Range Compression must be performed before Quadratic Range

Cell Migration for these cases• Additional processing required will reduce the efficiency of the algorithm• Still investigating this part. Preliminary results shows that quadratic range

migration of 6 range resolution cells does not produce significant range Doppler coupling

Diagram referenced from “the BOOK” – Digital Processing of Synthetic Aperture Radar Data



Illustration of SRC



Agenda




Non-parallel flight, dissimilar velocityTransmitter squinted at 40 degrees and both platforms moving in a non-parallel configuration with lateral separation of 3km and with Vt = 200m/s and Vr =220m/s1 parallel to Transmitter . It is a C-band system with wavelength = 0.06m, 3dB beamwidth = 1.9degree, PRF = 185Hz. Range bandwidth of 75MHz and Azimuth bandwidth about 160Hz. The imaged area has 25 point targets



Before Registration to Ground Plane



After Registration to Ground Plane



Impulse response



Agenda




Conclusions

• Illustrated the use of NLCS to focus bistatic SAR

• Show the extensions to the NLCS to improve its processing capabilities

• Simulated a non-parallel track example and the results



Future work

• Invariance Region Analysis.

• Secondary Range Compression.

• Registration.

• Comparison with existing algorithms.

• How the existing algorithms relate to one another.



Questions?

bistatic sar imaging using non-linear chirp scaling

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