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

I N T HIS P APER … … 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.

O UTLINE OF P RESENTATION  R ADAR S IGNAL M ODEL B ASED ON G EOMETRICAL T HEORY OF D IFFRACTION  GTD M ODEL  B ASIC C ONCEPT OF D ECIMATIVE S PECTRAL A NALYSIS SVD M ATH DESED T ECHNIQUE  A DVANTAGES OF D ECIMATIVE S PECTRAL A NALYSIS  S IMULATION C OMPARISON OF D ECIMATIVE T ECHNIQUE WITH V ARIOUS S UPERRESOLUTION M ETHODS: W ELL- S EPARATED S CATTERERS C LOSELY S PACED S CATTERERS

GTD M ODEL  P ARAMETRIC D ESCRIPTION OF S CATTERING B EHAVIOR OF P ERFECTLY C ONDUCTING T ARGET  GTD M ODEL E QUATION: [f = f n = f c + n·Δf : stepped frequency of radar waveform]  A CCURACY A TTRIBUTED TO C LOSE R ELATION WITH P HYSICS OF E LECTROMAGNETIC S CATTERING  F REQUENCY D EPEDENCE M ORE A CCURATE T HAN PRONY M ODEL, FOR L ARGE R ELATIVE R ADAR B ANDWIDTH

GTD M ODEL  G EOMETRY P ARAMETER 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 reflection½ flat plate at broadside; dihedral 1

B ASIC C ONCEPT OF D ECIMATIVE S PECTRAL A NALYSIS  D ECIMATION : T AKE A LL P OSSIBLE D OWNSAMPLED D ATA S EQUENCES C OMPUTE G LOBAL C OVARIANCE M ATRIX FROM P ARTIAL C OVARIANCE M ATRICES AND P ERFORM E IGENANALYSIS A PPLIED TO C LASSICAL S PECTRUM E STIMATION M ETHODS ( → ROOT - MUSIC )  S INGULAR V ALUE D ECOMPOSITION (SVD): B ASIC C OMPUTATION FOR DESED M ETHOD S TATE- S PACE D ATA M ODEL → SVD A NALYSIS OF D ECIMATED V ERSION OF H ANKEL M ATRIX

SVD M ATH o E LEMENTS OF D IAGONAL M ATRIX Σ A RE THE S INGULAR V ALUES OF M ATRIX S o P ROVIDES R OBUST S OLUTION OF O VER- AND U NDER- D ETERMINED L EAST- S QUARES P ROBLEMS o E MPLOYED IN:  S PECTRAL A NALYSIS  F ILTER D ESIGN  S YSTEM I DENTIFICATION  M ODEL O RDER R EDUCTION AND E STIMATION

DESED T ECHNIQUE  D AMPED E XPONENTIALS M ODEL: p : model order a i, φ i, d i, f i : amplitude, phase, damping factor and frequency of i-th complex sinusoid o W HITE G AUSSIAN N OISE IS A DDED TO THE S UM OF C OMPLEX S INUSOIDS

DESED T ECHNIQUE  H ANKEL M ATRIX F ORMULATION FROM D ATA R ECORD  C ONSTRAINTS:  D ECIMATED V ERSIONS OF H ANKEL M ATRIX S D, by deleting top D rows of Hankel matrix S S D, by deleting bottom D rows of Hankel matrix S

DESED T ECHNIQUE  SVD OF M ATRIX S D AND T RUNCATION TO O RDER p, BY R ETAINING p L ARGEST S INGULAR V ALUES OF D IAGONAL M ATRIX Σ D AND p C OLUMNS OF U D, V D  C OMPUTATION OF T RUNCATED SVD S OLUTION IN THE L EAST- S QUARES S ENSE:  F REQUENCY AND D AMPING F ACTOR E STIMATES FROM p L ARGEST E IGENVALUES OF M ATRIX X  A MPLITUDE AND P HASE E STIMATES FROM LS S OLUTION TO S IGNAL M ODEL E QUATION, AFTER S UBSTITUTING F REQUENCIES AND D AMPING F ACTORS

A DVANTAGES OF D ECIMATIVE S PECTRAL A NALYSIS  R OBUSTNESS TO A DDITIVE N OISE, E SPECIALLY C OLOURED  H IGH -R ESOLUTION F REQUENCY E STIMATES R ESULT FROM I NCREASED F REQUENCY S PACING ( L INEARLY D EPENDENT ON D ECIMATION F ACTOR D)

S IMULATION S ETUP  I DEAL P OINT S CATTERERS  Z ERO G EOMETRY P ARAMETERS IN GTD M ODELING OF R ADAR S IGNAL  LS-DESED C OMPARED AGAINST 2 V ARIANTS OF ROOT-MUSIC S UPERRESOLUTION T ECHNIQUE WITH M ODIFIED S PATIAL S MOOTHING P RE- P ROCESSING WITH D ECIMATION  2 S IMULATION S CENARIOS 5 S CATTERERS AT D ISTINCT R ADIAL P OSITIONS: 4 TH S CATTERER S PACED FROM 5 TH S CATTERER BY δr/3

S IMULATION S ETUP  R ADAR S IGNAL B ANDWIDTH B = 400MHz  F OURIER B IN δr = 0.375m  C ENTER F REQUENCY f c = 9GHz  R ELATIVE R ADAR B ANDWIDTH γ   R ADAR F REQUENCY S TEP Δf = 2MHz  D ATA R ECORD L ENGTH N = 201  F REQUENCY E STIMATES A RE T RANSFORMED TO R ANGE P OSITION E STIMATES BY L INKING GTD AND DE M ODELS  A VERAGING RMS R ANGE/ A MPLITUDE E STIMATION E RRORS OVER 100 M ONTE- C ARLO T RIALS

S IMULATION C OMPARISON: W ELL- S EPARATED S CATTERERS

S IMULATION C OMPARISON: C LOSELY S PACED S CATTERERS

C ONCLUSIONS  DESED O UTPERFORMS ROOT-MUSIC WITH MSSP, IN T ERMS OF R ANGE/ A MPLITUDE E STIMATION E RRORS, FOR B OTH S IMULATION S CENARIOS  F OR C LOSELY S PACED S CATTERERS, DESED B REAKS D OWN AT SNR=15dB, W HILE ROOT-MUSIC WITH MSSP AT SNR=25dB  DESED AND ROOT-MUSIC WITH D ECIMATION E XHIBIT S IMILAR P ERFORMANCE, WITH THE F IRST TO H AVE A S LIGHT A DVANTAGE  I NCREASING THE D ECIMATION F ACTOR FROM 2 TO 3 R ESULTS IN S MALL R ESOLUTION I MPROVEMENT, D UE TO THE R ELATIVELY S HORT D ATA R ECORD

QUESTIONS THANK YOU