Fast Factorized Backprojection Algorithm for UWB Bistatic.pdf

Fast Factorized Backprojection

Algorithm for UWB Bistatic

SAR Image Reconstruction

Viet Vu, Thomas Sjögren and Mats Pettersson

Blekinge Institute of Technology, Karlskrona, Sweden.

Outline

• Motivation

• Contribution

• Development from GBP to BiFFBP

– From monostatic GBP to bistatic GBP

– Bistatic FBP development on bistatic GBP

– From bistatic FBP to bistatic FFBP

• Simulation Results and Evaluation

• Conclusion

Motivation

• Algorithms for NB bistatic SAR

– Frequency-domain: Range Doppler (RD), Range

Migration (RM), Chirp Scaling (CS).

– Time-domain: Global Backprojection applied to

bistatic cases (BiGBP).

• Algorithms for UWB monostatic SAR

– Frequency-domain: not recommended [1].

– Time-domain: GBP, Fast Backprojection (FBP), Fast

Factorized Backprojection (FFBP).

[1] V. T. Vu et. al., “A comparison between fast factorized backprojection and

frequency-domain algorithms in UWB low frequency SAR,” in Proc. IEEE

IGARSS’2008, Boston, MA, Jul. 2008, pp. 1293–1296.

Motivation (cont.)

• Algorithms for UWB bistatic SAR

– BiGBP:

• Avaibilable in principal.

• Require huge computational burden.

– BiFBP:

• Shown to work with UWB bistatic SAR data [2].

• Require low computational cost.

– BiFFBP:

• Need to be investigated.

• Supposed to require even lower computational cost.

[2] V. T. Vu et. al., “Fast backprojection algorithm for UWB bistatic SAR,” in Proc.

IEEE RadarCon’2011, Kansas City, MO, May 2011, pp. 431-434.

Contribution

• BiFFBP, a fast time-domain algorithm

– Aim at UWB bistatic SAR systems but available for

NB bistatic SAR systems.

– Inherit time-domain characteristics such as unlimited

scene size, local processing, motion compensation

and so on.

– Tested with different bistatic configurations and

shown to be not limited by any bistatic configuration.

– Low computational cost.

From GBP to BiGBP

• GBP

– Reconstructed either on a slant-range plane or ground

plane.

– Time-domain characteristics.

– Spherical mapping.

– Huge computational burden.

2

2

c,,

i

i

t

t

plnm dtRtvgrxh

From GBP to BiGBP (cont.)

• BiGBP

– Reconstructed only on a ground plane.

– Time-domain chracteristics.

– Ellipsoidal mapping.

– No limitation of bistatic configuration.

– Also huge computational burden.

2

2

c,,,

i

i

t

t

rtnm dtRtvtvgrxh

BiFBP Development on BiGBP

• BiFBP

– Reconstructed only on a ground plane.

– Time-domain chracteristics.

– Ellipsoidal mapping.

– No limitation of bistatic configuration.

– Two processing stages:

• Beam forming.

• Local backprojection

– Low computational cost.

BiFBP Development on BiGBP (cont.)

• Beam forming from radar echoes

– Linear superpositions of radar echoes.

– References for superposition are centers of

• Transmitter subaperture

• Receiver subaperture

• Subimage.

2

2

,

,

c,,

c,,

sl

sl

tt

tt

kllrlt

kllrlt

dtRtvtvg

Rtvtvb

BiFBP Development on BiGBP (cont.)

• Local backprojection from formed beam

– Over elipsoidal mapping.

– Foci determined by centers of subapertures.

– Major axis defined by line connecting foci.

L

l

c

kllrltnm RRtvtvbyxh1

,,,,

From BiFBP to BiFFBP

• BiFFBP

– Reconstructed only on a ground plane.

– Time-domain chracteristics.

– Ellipsoidal mapping.

– No limitation of bistatic configuration.

– More than two processing stages:

• Firtst beam forming.

• ...

• Final beam forming

• Local backprojection

– Lower computational cost than BiFBP.

From BiFBP to BiFFBP (cont.)

• Beam forming from beam previously formed

– Linear superpositions of beam formed in previous

stage. Reconstructed only on a ground plane.

– References for superposition are centers of

• New (longer) transmitter subaperture

• New (longer) receiver subaperture

• New (smaller) subimage.

2

12

2

121

1

1121111

1

1121111

11

,,,1

,,,2

,

,

L

Ll

L

Lll

c

kl

c

klkll

c

kl

c

klkll

RRRtb

RRRtb

From BiFBP to BiFFBP (cont.)

• Mathematical expression for BiFFBP with two

beam forming stages

dtRRRRRtvtvg

yxh

sl

sl

tt

tt

c

kl

c

kl

c

klkllrlt

K

k

K

Kk

K

Kkk

L

l

L

Ll

L

Lll

nm

2

2

,,,,

111

111

2

22

1

11

1

2111

1

1

1

21

1

212

2

2

2

12

2

121

c,,

,

Simulations and Evaluation

Parameter CARABAS-II

(transmitter)

LORA

(receiver)

The maximum frequency 82 MHz

The minimum frequency 22 MHz

Platform speed 𝑣𝑝𝑙 126 m/s 130 m/s

Aperture step 0.9375 m 0.9673 m

Aperture length 3840 m 3950 m

Flight altitude 3700 m 2900 m

Minimum range 𝑟0 5900 m 3000 m

PRF 137 Hz

Bistatic angle 00/00/600

• Simulation parameters

Simulations and Evaluation (cont.)

• Simulated ground scene

– Series of point-like scaterers.

– Equally spaced.

– The same radar cross sections (RCS).

– No noise added.

Simulations and Evaluation (cont.)

• Considered bisatic configurations

– Quasi-monostatic: transmitter and receiver are

mounted on a single platform.

– Azimuth-invariant: transmitter and receiver are

mounted on two different platforms whose flight

tracks are parallel.

– General bistatic: transmitter and receiver are mounted

on two different platforms whose flight tracks are

arbitrary, e.g. 600.

Simulations and Evaluation (cont.)

• Quasi-monostatic:

– Work.

– Similar monostatic

Simulations and Evaluation (cont.)

• Azimuth-invariant:

– Work.

– Beter resolution.

Simulations and Evaluation (cont.)

• General bistatic:

– Work.

– Familiar features

Simulations and Evaluation (cont.)

• Compared to BiGBP

Simulations and Evaluation (cont.)

• Comparison between BiGBP and

– Phase error due to approximations in BiFFBP is

observed.

Phase Error Calculation

• Phase error equation [3]

– Calculate the phase error generated by approximations

in BiFFBP.

– Select subimage and subaperture size.

– Minimize phase error.

[3] V. T. Vu et. al., “Phase error calculation for fast time-domain bistatic SAR

algorithms,” in Proc. IEEE Trans. Aerosp. Electron. Syst., submitted for publication.

Conclusion

• Propose an algorithm BiFFBP.

• Derive BiFFBP analytically.

• Test BiFFBP with simulated UWB bistatic SAR

data.

• Test BiFFBP with different bistatic configurations.

• Compare with BiGBP.

Thanks for your attention!