1. 1 ASU MAT 591: Opportunities in Industry! ASU MAT 591: Opportunities In Industry!

2. 2 ASU MAT 591: Opportunities in Industry! Advanced MTI Algorithms Howard Mendelson Principal Investigator 21 August 2000

3. 3 ASU MAT 591: Opportunities in Industry! Problem Advanced MTI Algorithms l SAR systems provide excellent intelligence concerning status of fixed installations (assuming no electronic countermeasures (ECM) are employed) l Warfighter requires precise information describing MOVING formations of troops and weapons –Formations may be slow moving and thus difficult to distinguish from background clutter –Formations (as well as fixed targets) may be screened by ECM l Our customers now specify high fidelity moving target indication (MTI) and fixed target indication (FTI) with interference rejection capabilities for their battlefield surveillance systems. l These issues make it imperative for us to develop the techniques necessary to provide these capabilities

4. 4 ASU MAT 591: Opportunities in Industry! STATE OF THE ART Advanced MTI Algorithms l DPCA –Not data adaptive l ADSAR –Data adaptive but not jammer resistant l SPACE TIME ADAPTIVE PROCESSING (STAP) –No Fielded GMTI Systems –Computationally Intensive –Traditional SMI Approach Produces Large Numbers of False Alarms

5. 5 ASU MAT 591: Opportunities in Industry! Approach Advanced MTI Algorithms l Develop Post Doppler Eigenspace Analysis Techniques –Advantages  Lower false alarm rate than traditional SMI approach  Simultaneous SAR and MTI in the presence of ECM  Common processing framework for clutter and jammer suppression  Higher Signal-to-Background Ratio (SBR) after interference suppression  Smaller training data set required for STAP algorithms  Computational Efficiency

6. 6 ASU MAT 591: Opportunities in Industry! Sample Matrix Inversion (SMI) Interference Suppression Algorithm Sample Matrix Inversion (SMI) Interference Suppression Algorithm Advanced MTI Algorithms Beamform Form Covariance Estimates Invert Covariance Matrix Apply Inverse Input Data (N channels) Detection Processing

7. 7 ASU MAT 591: Opportunities in Industry! Advanced MTI Algorithms Eigendecomposition Interference Suppression Algorithm Eigendecomposition Project Data Orthogonally to Interference Subspace Form Covariance Estimates Perform Eigendecomposition Determine No. of Interference Sources Input Data (N channels) Detection Processing Beamform

8. 8 ASU MAT 591: Opportunities in Industry! Covariance Estimation X1...XNX1...XN H is complex conjugate transpose N/2 Rng Cells Channel N Guard Cells Guard Cells N/2 Rng Cells Cell of Interest Channel 2 Channel 1 N/2 Rng Cells Guard Cells Guard Cells N/2 Rng Cells Cell of Interest No. of range cells used for Eigen processing is typically 1.5 x No.of channels (Higher for SMI) Covariance estimate is computed in sliding window at every pixel No. of guard cells depends on range resolution N/2 Rng Cells Guard Cells Guard Cells N/2 Rng Cells Cell of Interest

9. 9 ASU MAT 591: Opportunities in Industry! Weight Calculation (SMI) Sample Matrix Inversion (SMI) subject to  R C f w Sample Covariance Matrix Constraint Matrix Coefficient Vector WeightVector Hermitian adjoint (conjugate transpose) H

10. 10 ASU MAT 591: Opportunities in Industry! Weight Calculation (MNE) Minimum Norm Eigencancler (MNE) subject toand Q C f w r Matrix of eigenvectors of estimated covariance matrix associated with interference Constraint Matrix Coefficient Vector Weight Vector

11. 11 ASU MAT 591: Opportunities in Industry! LM M&DS – ISRS IR&D SAR Testbed flight 24” adjustable 7” Channel 0 Receive Channel 2 Receive Channel 1 Transmit/Receive

12. 12 ASU MAT 591: Opportunities in Industry! Controlled Mover in Clutter (Eigendecomposition) Advanced MTI Algorithms Controlled Moving Target

13. 13 ASU MAT 591: Opportunities in Industry! Controlled Mover in Clutter (SMI) Advanced MTI Algorithms

14. 14 ASU MAT 591: Opportunities in Industry! PRI Stagger Algorithm Advanced MTI Algorithms FFT STAPSTAP Elements (or beams) 1 2 3... P - 1 P

15. 15 ASU MAT 591: Opportunities in Industry! Covariance Estimation X 10n. X LNstg-1n H is complex conjugate transpose N/2 Rng Cells Channel L Stagger N stg - 1 Guard Cells Guard Cells N/2 Rng Cells Cell of Interest Channel 2 Stagger 0 Channel 1 Stagger 0 N/2 Rng Cells Guard Cells Guard Cells N/2 Rng Cells Cell of Interest No. of range cells used for Eigen processing is typically 1.5 x No.of channels x No. of staggers (Higher for SMI) Covariance estimate is computed in sliding window at every pixel No. of guard cells depends on range resolution N/2 Rng Cells Guard Cells Guard Cells N/2 Rng Cells Cell of Interest

16. 16 ASU MAT 591: Opportunities in Industry! Data Collect Radar Image Tactical Targets

17. 17 ASU MAT 591: Opportunities in Industry! Data Collect Tactical Targets Eigendecomposition ProcessingSMI Processing Unprocessed Image

18. 18 ASU MAT 591: Opportunities in Industry! CFAR DETECTORS (GMTI) H1 > < H2  AMF H1 > < H2  GLRT H1 > < H2  PC Adaptive Matched Filter (SMI) Generalized Likelihood Ratio Test (SMI) Eigendecompsition Likelihood Ratio Test

19. 19 ASU MAT 591: Opportunities in Industry! Detection Performance (P fa = 10 -6 ) Unprocessed ImageSMI - AMF Detection Reports SMI - GLRT Detection ReportsLRT - Eigendecomposition Detection Reports

20. 20 ASU MAT 591: Opportunities in Industry! Detection Performance P fa = 10 -6 Unprocessed ImageSMI - AMF Detection Reports SMI - GLRT Detection ReportsLRT - Eigendecomposition Detection Reports

21. 21 ASU MAT 591: Opportunities in Industry! RELOCATION ALGORITHM l Uses Channel-to-Channel Phase Differences to Obtain Target Direction of Arrival (DOA) l Originally Developed for Three Channel “Uniformly” Spaced Array Without PRI Stagger l Assumed Clutter as only Interference Source –Insufficient number of degrees of freedom available to deal with more than one interfering source l Can be extended –No. of channels greater than 3 –Multiple interfering sources –Non-uniform spacing

22. 22 ASU MAT 591: Opportunities in Industry! RELOCATION ALGORITHM Assumed Signal Model

23. 23 ASU MAT 591: Opportunities in Industry! RELOCATION ALGORITHM Phase of target vector can now be found by solving for roots of quadratic Solution which provides largest return after beamforming is assumed correct   e e 1 2 = First eigenvectororthoganal to clutter direction Second eigenvector orthoganal to clutter direction Same eigenvectors computed during interference suppression and detection processing = y y Tgt 111 222 =  = ( ,)( ,) ( ,)( ,) eses eses   

24. 24 ASU MAT 591: Opportunities in Industry! Relocation Algorithm - Example Original Target Detections Relocated Targets

25. 25 ASU MAT 591: Opportunities in Industry! RELOCATION ALGORITHM - 2 Assumed Signal Model Complex images from each channel are assumed to have been relocated to a common point

26. 26 ASU MAT 591: Opportunities in Industry! RELOCATION ALGORITHM - 2 (cont.) Phase of target vector can now be found by solving for roots of quadratic Solution which provides largest return after beamforming is assumed correct y y Tgt 111 222 =  = ( ,)( ,) ( ,)( ,) eses eses      e e 1 2 = First eigenvectororthoganal to clutter direction Second eigenvector orthoganal to clutter direction Same eigenvectors computed during interference suppression and detection processing =

27. 27 ASU MAT 591: Opportunities in Industry! Geolocation Accuracy Cramer Rao bound of interferometer measurement accuracy used to estimate cross range error

28. 28 ASU MAT 591: Opportunities in Industry! Target Reports SMI based STAPEigenanalysis based STAP Known Targets

29. 29 ASU MAT 591: Opportunities in Industry! Target Reports Unprocessed Target DetectionsRelocated Target Detections Relocated Targets Original Detections

30. 30 ASU MAT 591: Opportunities in Industry! Multi-Stage False Alarm Reduction Processing Multichannel Complex Image Data Detection reports Location, Speed and Heading Estimates Covariance Estimate Find Eigenvalues and Eigenvectors Form Interference Suppression Projections Find Noise Subspace Dimension Form Estimated Steering Vector Compute Cancellation Ratios of Threshold Crossings Produce Low Resolution SAR Image Produce Interference Suppressed Data Field Perform CFAR Thresholding Determine AOA Consistency of Estimates of Possible Detections Compute AOA (Radial Speed) Estimates Form Image Projections

31. 31 ASU MAT 591: Opportunities in Industry! SUMMARY l Multiple post-Doppler STAP algorithms studied and evaluated for clutter suppression and target detection –Eigenanalysis, SMI –Single Doppler bin, adjacent Doppler bin, PRI stagger l “Mono-pulse” location algorithm developed and tested on collected data l Work ongoing to develop algorithm upgrades