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D ECIMATIVE S PECTRUM E STIMATION M ETHOD F OR H IGH- R ESOLUTION R ADAR P ARAMETER E STIMATES

D ECIMATIVE S PECTRUM E STIMATION M ETHOD F OR H IGH- R ESOLUTION R ADAR P ARAMETER E STIMATES. A NASTASIOS K ARAKASILIOTIS AND P ANAYIOTIS F RANGOS S CHOOL OF E LECTRICAL AND C OMPUTER E NGINEERING N ATIONAL T ECHNICAL U NIVERSITY OF A THENS GREECE

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D ECIMATIVE S PECTRUM E STIMATION M ETHOD F OR H IGH- R ESOLUTION R ADAR P ARAMETER E STIMATES

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  1. DECIMATIVE SPECTRUM ESTIMATION METHOD FOR HIGH-RESOLUTION RADAR PARAMETER ESTIMATES ANASTASIOSKARAKASILIOTISANDPANAYIOTIS FRANGOS SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL TECHNICAL UNIVERSITY OF ATHENS GREECE Email: anaka@intracom.gr, pfrangos@central.ntua.gr

  2. IN THIS PAPER … … we propose the use of a decimative spectrum estimation method, namely DESED, for the estimation of the parameters of a synthetic radar signal. Practical Use: 1-D scattering center attributes (radial positions & scattering amplitudes) can be employed as feature vectors for radar target classification.

  3. OUTLINE OF PRESENTATION • RADAR SIGNAL MODEL BASED ON GEOMETRICAL THEORY OF DIFFRACTION  GTD MODEL • BASIC CONCEPT OF DECIMATIVE SPECTRAL ANALYSIS • SVDMATH • DESED TECHNIQUE • ADVANTAGES OF DECIMATIVE SPECTRAL ANALYSIS • SIMULATION COMPARISON OF DECIMATIVE TECHNIQUE WITH VARIOUS SUPERRESOLUTION METHODS: • WELL-SEPARATED SCATTERERS • CLOSELY SPACED SCATTERERS

  4. GTD MODEL • PARAMETRIC DESCRIPTION OF SCATTERING BEHAVIOR OF PERFECTLY CONDUCTING TARGET • GTDMODEL EQUATION: [f= fn = fc + n·Δf : stepped frequency of radar waveform] • ACCURACY ATTRIBUTED TO CLOSE RELATION WITH PHYSICS OF ELECTROMAGNETIC SCATTERING • FREQUENCY DEPEDENCE MORE ACCURATE THAN PRONYMODEL, FOR LARGE RELATIVE RADAR BANDWIDTH

  5. Example scattering geometries Geometry parameter value corner diffraction – 1 edge diffraction – ½ ideal point scatterer; doubly curved surface reflection; straight edge specular 0 singly curved surface reflection ½ flat plate at broadside; dihedral 1 GTD MODEL • GEOMETRY PARAMETER

  6. BASIC CONCEPTOFDECIMATIVE SPECTRAL ANALYSIS • DECIMATION: • TAKE ALL POSSIBLE DOWNSAMPLED DATA SEQUENCES • COMPUTE GLOBAL COVARIANCE MATRIX FROM PARTIAL COVARIANCE MATRICES AND PERFORM EIGENANALYSIS • APPLIED TO CLASSICAL SPECTRUM ESTIMATION METHODS (→ ROOT-MUSIC) • SINGULAR VALUE DECOMPOSITION (SVD): • BASIC COMPUTATION FOR DESEDMETHOD • STATE-SPACE DATA MODEL → SVDANALYSIS OF DECIMATED VERSION OF HANKEL MATRIX

  7. SVD MATH • ELEMENTS OF DIAGONAL MATRIX Σ ARE THE SINGULAR VALUES OF MATRIX S • PROVIDES ROBUST SOLUTION OF OVER- AND UNDER-DETERMINED LEAST-SQUARES PROBLEMS • EMPLOYED IN: • SPECTRAL ANALYSIS • FILTER DESIGN • SYSTEM IDENTIFICATION • MODEL ORDER REDUCTION AND ESTIMATION

  8. DESED TECHNIQUE • DAMPED EXPONENTIALS MODEL: p : model order ai , φi , di , fi : amplitude, phase, damping factor and frequency of i-th complex sinusoid • WHITE GAUSSIAN NOISEIS ADDED TO THE SUM OF COMPLEX SINUSOIDS

  9. DESED TECHNIQUE • HANKEL MATRIX FORMULATION FROM DATA RECORD • CONSTRAINTS: • DECIMATED VERSIONS OF HANKEL MATRIX • SD , by deleting top D rows of Hankel matrix S • SD , by deleting bottom D rows of Hankel matrix S

  10. DESED TECHNIQUE • SVD OF MATRIX SD ANDTRUNCATION TO ORDER p, BY RETAINING pLARGEST SINGULAR VALUES OF DIAGONAL MATRIX ΣDAND pCOLUMNS OF UD, VD • COMPUTATION OF TRUNCATED SVD SOLUTION IN THE LEAST-SQUARESSENSE: • FREQUENCY AND DAMPING FACTOR ESTIMATES FROM pLARGEST EIGENVALUES OF MATRIX X • AMPLITUDE AND PHASE ESTIMATES FROM LSSOLUTION TO SIGNAL MODEL EQUATION, AFTER SUBSTITUTING FREQUENCIES AND DAMPING FACTORS

  11. ADVANTAGESOFDECIMATIVE SPECTRAL ANALYSIS • ROBUSTNESS TO ADDITIVE NOISE, ESPECIALLY COLOURED • HIGH-RESOLUTION FREQUENCY ESTIMATES RESULT FROM INCREASED FREQUENCY SPACING (LINEARLY DEPENDENT ON DECIMATION FACTOR D)

  12. SIMULATION SETUP • IDEAL POINT SCATTERERS  ZERO GEOMETRY PARAMETERS IN GTD MODELING OF RADAR SIGNAL • LS-DESED COMPARED AGAINST 2VARIANTS OF ROOT-MUSICSUPERRESOLUTION TECHNIQUE • WITH MODIFIED SPATIAL SMOOTHING PRE-PROCESSING • WITH DECIMATION • 2SIMULATION SCENARIOS • 5 SCATTERERS AT DISTINCT RADIAL POSITIONS: • 4THSCATTERER SPACED FROM 5THSCATTERER BY δr/3

  13. SIMULATION SETUP • RADAR SIGNAL BANDWIDTH B = 400MHz • FOURIER BIN δr = 0.375m • CENTER FREQUENCY fc = 9GHz • RELATIVE RADAR BANDWIDTH γ  0.044 • RADAR FREQUENCY STEP Δf = 2MHz • DATA RECORD LENGTH N = 201 • FREQUENCY ESTIMATES ARE TRANSFORMED TO RANGE POSITION ESTIMATES BY LINKING GTD AND DE MODELS • AVERAGING RMS RANGE/AMPLITUDE ESTIMATION ERRORSOVER 100MONTE-CARLO TRIALS

  14. SIMULATION COMPARISON:WELL-SEPARATED SCATTERERS

  15. SIMULATION COMPARISON:WELL-SEPARATED SCATTERERS

  16. SIMULATION COMPARISON:CLOSELY SPACED SCATTERERS

  17. CONCLUSIONS • DESED OUTPERFORMS ROOT-MUSIC WITH MSSP, IN TERMS OF RANGE/AMPLITUDE ESTIMATION ERRORS, FOR BOTH SIMULATION SCENARIOS • FOR CLOSELY SPACED SCATTERERS, DESED BREAKS DOWN AT SNR=15dB, WHILE ROOT-MUSIC WITH MSSP ATSNR=25dB • DESED AND ROOT-MUSIC WITH DECIMATION EXHIBIT SIMILAR PERFORMANCE, WITH THE FIRST TO HAVE A SLIGHT ADVANTAGE • INCREASINGTHE DECIMATION FACTOR FROM 2 TO 3 RESULTSIN SMALL RESOLUTION IMPROVEMENT, DUE TO THE RELATIVELY SHORT DATA RECORD

  18. QUESTIONS THANK YOU

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