Fast Factorized Backprojection Algorithm for UWB Bistatic.pdf

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Fast Factorized Backprojection Algorithm for UWB Bistatic.pdf

  1. 1. Fast Factorized BackprojectionAlgorithm for UWB BistaticSAR Image ReconstructionViet Vu, Thomas Sjögren and Mats PetterssonBlekinge Institute of Technology, Karlskrona, Sweden.
  2. 2. 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
  3. 3. 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.
  4. 4. 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.
  5. 5. 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.
  6. 6. From GBP to BiGBP• GBP – Reconstructed either on a slant-range plane or ground plane. – Time-domain characteristics. – Spherical mapping. – Huge computational burden. ti   g v t , c  R dt 2 hxm , rn   pl ti  2
  7. 7. 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. ti  2 hxm , rn    g v t , v t , c  R dt t r ti  2
  8. 8. 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.
  9. 9. 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. bvt tl , vr tl , c  Rl ,k  ts tl  2   g v t , v t , c  R dt ts t l r l l ,k tl  2
  10. 10. 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.   Lhxm , yn    b vt tl , vr tl , R  Rlc,k l 1
  11. 11. 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.
  12. 12. 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.  b2 tl1 ,   Rl1 ,k1  Rlc ,k2  Rlc1,k1  1 1 L1 l2    L2  b1 tl1 ,   Rl1 ,k1  Rlc ,k2  Rlc1,k1 L1 1 1l1 1 l2 1 L2
  13. 13. From BiFBP to BiFFBP (cont.)• Mathematical expression for BiFFBP with two beam forming stages K2 L1 k1 l2 K1 K1 L2 L2h  xm , y n       k1 1 K 2 l2 1 L k 2 1  k1 1 l1 1 l2 1 1 K1 L2 ts tl    2  g vt tl , vr tl , c  Rl1 ,k1  Rlc1,k2  Rlc1,k1  R  Rlc22,k2 dt 1 1 ts tl  2
  14. 14. Simulations and Evaluation• Simulation parameters Parameter CARABAS-II LORA (transmitter) (receiver) The maximum frequency 82 MHz The minimum frequency 22 MHz Platform speed 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 0 5900 m 3000 m PRF 137 Hz Bistatic angle 00/00/600
  15. 15. Simulations and Evaluation (cont.)• Simulated ground scene – Series of point-like scaterers. – Equally spaced. – The same radar cross sections (RCS). – No noise added.
  16. 16. 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.
  17. 17. Simulations and Evaluation (cont.)• Quasi-monostatic: – Work. – Similar monostatic
  18. 18. Simulations and Evaluation (cont.)• Azimuth-invariant: – Work. – Beter resolution.
  19. 19. Simulations and Evaluation (cont.)• General bistatic: – Work. – Familiar features
  20. 20. Simulations and Evaluation (cont.)• Compared to BiGBP
  21. 21. Simulations and Evaluation (cont.)• Comparison between BiGBP and – Phase error due to approximations in BiFFBP is observed.
  22. 22. 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.
  23. 23. 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.
  24. 24. Thanks for your attention!

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