ASU MAT 591: Opportunities In Industry!

1. ASU MAT 591: Opportunities In Industry!

2. Advanced MTI Algorithms Howard Mendelson Principal Investigator 21 August 2000

3. ProblemAdvanced MTI Algorithms • SAR systems provide excellent intelligence concerning status of fixed installations (assuming no electronic countermeasures (ECM) are employed) • 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 • Our customers now specify high fidelity moving target indication (MTI) and fixed target indication (FTI) with interference rejection capabilities for their battlefield surveillance systems. • These issues make it imperative for us to develop the techniques necessary to provide these capabilities

4. STATE OF THE ARTAdvanced MTI Algorithms • DPCA • Not data adaptive • ADSAR • Data adaptive but not jammer resistant • SPACE TIME ADAPTIVE PROCESSING (STAP) • No Fielded GMTI Systems • Computationally Intensive • Traditional SMI Approach Produces Large Numbers of False Alarms

5. ApproachAdvanced MTI Algorithms • 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. Advanced MTI Algorithms Sample Matrix Inversion (SMI) Interference Suppression Algorithm Input Data (N channels) Invert Covariance Matrix Apply Inverse Form Covariance Estimates Detection Processing Beamform

7. Eigendecomposition Interference SuppressionAlgorithm Advanced MTI Algorithms Input Data (N channels) Perform Eigendecomposition Determine No. of Interference Sources Form Covariance Estimates Project Data Orthogonally to Interference Subspace Detection Processing Beamform

8. Covariance Estimation Channel 1 N/2 Rng Cells Guard Cells Cell of Interest Guard Cells N/2 Rng Cells Channel 2 N/2 Rng Cells Guard Cells Cell of Interest Guard Cells N/2 Rng Cells X1 . . . XN Channel N N/2 Rng Cells Guard Cells Cell of Interest Guard Cells N/2 Rng Cells 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 His complex conjugate transpose

9. Weight Calculation (SMI) Sample Matrix Inversion (SMI) subject to $ R Sample Covariance Matrix C Constraint Matrix f Coefficient Vector w Weight Vector Hermitian adjoint (conjugate transpose) H

10. subject to and Matrix of eigenvectors of estimated covariance matrix associated with interference Q r C Constraint Matrix f Coefficient Vector w Weight Vector Weight Calculation (MNE) Minimum Norm Eigencancler (MNE)

11. LM M&DS – ISRSIR&D SAR Testbed 24” 7” adjustable Channel 2 Receive Channel 1 Transmit/Receive Channel 0 Receive flight

12. Controlled Mover in Clutter (Eigendecomposition)Advanced MTI Algorithms Controlled Moving Target

13. Controlled Mover in Clutter (SMI)Advanced MTI Algorithms

14. PRI Stagger AlgorithmAdvanced MTI Algorithms FFT 1 2 3 . . . P - 1 P FFT S T A P FFT 1 2 3 . . . P - 1 P Elements (or beams) FFT FFT 1 2 3 . . . P - 1 P FFT

15. Covariance Estimation Channel 1 Stagger 0 N/2 Rng Cells Guard Cells Cell of Interest Guard Cells N/2 Rng Cells Channel 2 Stagger 0 N/2 Rng Cells Guard Cells Cell of Interest Guard Cells N/2 Rng Cells X10n . . . XLNstg-1n Channel L Stagger Nstg - 1 N/2 Rng Cells Guard Cells Cell of Interest Guard Cells N/2 Rng Cells 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 His complex conjugate transpose

16. Data Collect Radar Image Tactical Targets

17. Unprocessed Image SMI Processing Eigendecomposition Processing Data Collect Tactical Targets

18. CFAR DETECTORS(GMTI) Adaptive Matched Filter (SMI) H1 > < H2 aAMF H1 > < H2 Generalized Likelihood Ratio Test (SMI) aGLRT H1 > < H2 Eigendecompsition Likelihood Ratio Test aPC

19. Detection Performance (Pfa = 10-6 ) Unprocessed Image SMI - AMF Detection Reports SMI - GLRT Detection Reports LRT - Eigendecomposition Detection Reports

20. Unprocessed Image SMI - AMF Detection Reports SMI - GLRT Detection Reports LRT - Eigendecomposition Detection Reports Detection Performance Pfa = 10-6

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

22. RELOCATION ALGORITHM Assumed Signal Model

23. r r y ( e , s ) ( e , s ) $ $ = @ 1 1 1 Tgt r r y ( e , s ) ( e , s ) $ $ = @ 2 2 2 Tgt = e First ei genvector orthoganal to clutte r directio n $ 1 = e Second e igenvector orthogana l to clutt er directi on $ 2 Same eigen vectors co mputed dur ing interf erence sup pression and detect ion proces sing 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

24. Relocation Algorithm - Example Relocated Targets Original Target Detections

25. RELOCATION ALGORITHM - 2 Assumed Signal Model Complex images from each channel are assumed to have been relocated to a common point

26. r r y ( e , s ) ( e , s ) $ $ = @ 1 1 1 Tgt r r y ( e , s ) ( e , s ) $ $ = @ 2 2 2 Tgt = e First ei genvector orthoganal to clutte r directio n $ 1 = e Second e igenvector orthogana l to clutt er directi on $ 2 Same eigen vectors co mputed dur ing interf erence sup pression and detect ion proces sing 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

27. Geolocation Accuracy Cramer Rao bound of interferometer measurement accuracy used to estimate cross range error

28. Target Reports Known Targets SMI based STAP Eigenanalysis based STAP

29. Target Reports Original Detections Relocated Targets Unprocessed Target Detections Relocated Target Detections

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

31. SUMMARY • Multiple post-Doppler STAP algorithms studied and evaluated for clutter suppression and target detection • Eigenanalysis, SMI • Single Doppler bin, adjacent Doppler bin, PRI stagger • “Mono-pulse” location algorithm developed and tested on collected data • Work ongoing to develop algorithm upgrades