ASU MAT 591: Opportunities In Industry!kuang/LM/031021.pdf5 ASU MAT 591: Opportunities in Industry!...

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ASU MAT 591: Opportunities in Industry!

ASU MAT 591: Opportunities In ASU MAT 591: Opportunities In Industry!Industry!

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Advanced MTIAlgorithms

L O C K H E E D M A R T I N

Howard MendelsonPrincipal Investigator

21 August 2000

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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 MOVINGformations 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 techniquesnecessary to provide these capabilities

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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

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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

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Sample Matrix Inversion (SMI)

Interference Suppression Algorithm

Sample Matrix Inversion Sample Matrix Inversion (SMI)(SMI)

Interference Suppression Interference Suppression AlgorithmAlgorithm

Advanced MTI Algorithms

Beamform

Form Covariance Estimates

Invert CovarianceMatrix

Apply Inverse

Input Data (N channels)

Detection Processing

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Advanced MTI Algorithms

EigendecompositionInterference Suppression

Algorithm

EigendecompositionEigendecompositionInterference SuppressionInterference Suppression

AlgorithmAlgorithm

Project Data Orthogonallyto Interference Subspace

Form Covariance Estimates

Perform Eigendecomposition

Determine No. ofInterference Sources

Input Data (N channels)

Detection Processing

Beamform

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Covariance Estimation

Hn

N

nn

rc

rc

NxxR rr∑

=

∧

≡1

1

=nxrX1

.

.

.XN

H is complex conjugate transpose

N/2 Rng Cells

Channel NGuardCells

GuardCells

N/2 Rng Cells Cell ofInterest

Channel 2

Channel 1

N/2 Rng CellsGuardCells

GuardCells


No. of range cells used for Eigen processing is typically1.5 x No.of channels(Higher for SMI)Covariance estimate is computedin sliding window at every pixelNo. of guard cells depends on rangeresolution


GuardCells


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Weight Calculation (SMI)

Sample Matrix Inversion (SMI)

m in $w

w R wH subject to fwC =H

fCRCCRw 111 )ˆ(ˆ −−−= H

SMI

$RCfw

Sample Covariance MatrixConstraint MatrixCoefficient VectorWeight VectorHermitian adjoint (conjugate transpose)H

≡≡≡≡≡

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Weight Calculation (MNE)

Minimum Norm Eigencancler (MNE)

fCQQICCQQIw 1))(()( −−−= Hrr

HHrrMNE

minw

w wH subject to and 0wQ =H

rfwC =H

Q

C

f

w

r Matrix of eigenvectors of estimated covariance matrixassociated with interference

Constraint Matrix

Coefficient Vector

Weight Vector

≡≡≡≡

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LM M&DS – ISRSIR&D SAR Testbed

flight

24”

adjustable7”

Channel 0Receive

Channel 2Receive

Channel 1Transmit/Receive

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Controlled Mover in Clutter (Eigendecomposition)Advanced MTI Algorithms

Controlled Moving Target

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Controlled Mover in Clutter (SMI)Advanced MTI Algorithms

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PRI Stagger AlgorithmAdvanced MTI Algorithms

FFT

FFT

FFT

FFT

FFT

FFT

STAP

Elem

ents

(or b

eam

s)

1 2 3 . . . P - 1 P

1 2 3 . . . P - 1 P

1 2 3 . . . P - 1 P

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Covariance Estimation

= nXr X10n

.

.

.XLNstg-1n

H is complex conjugate transpose

N/2 Rng Cells

Channel L Stagger Nstg - 1GuardCells

GuardCells


Channel 2 Stagger 0

Channel 1 Stagger 0


GuardCells


No. of range cells used for Eigen processing is typically1.5 x No.of channels x No. of staggers(Higher for SMI)Covariance estimate is computedin sliding window at every pixelNo. of guard cells depends on rangeresolution


GuardCells


Hn

N

nn

rc

rc

NxxR rr

∑≡=

∧

1

1

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Data Collect Radar Image Tactical Targets

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Data Collect Tactical Targets

Eigendecomposition ProcessingSMI Processing

Unprocessed Image

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CFAR DETECTORS(GMTI)

sRsxRs1

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ˆˆ

−

−

H

H H1

><H2

αAMF

)ˆ

1(ˆ

ˆ1

1

21

K

HH

H

xRxsRs

xRs−

−

−

−

H1

><H2

αGLRT

s Pxs P R P s

T

T

2

)H1

><H2

αPC

Adaptive MatchedFilter (SMI)

Generalized LikelihoodRatio Test (SMI)

Eigendecompsition LikelihoodRatio Test

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Detection Performance (Pfa = 10-6 )

Unprocessed Image SMI - AMF Detection Reports

SMI - GLRT Detection Reports LRT - Eigendecomposition Detection Reports

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Detection Performance Pfa = 10-6

Unprocessed Image SMI - AMF Detection Reports

SMI - GLRT Detection Reports LRT - Eigendecomposition Detection Reports

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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

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+

=

ψ

ψ

φ

φ

i

i

i

i

eeb

eea

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1

1 sr

Assumed Signal Model

frequencycenter ofth Waveleng spacingnt Intereleme

sin2

channel 1 torelativereturn clutter of Phase

sin2

channel 1 torelativereturn target of Phase

returnclutter of amplitudeComplex returntarget ofamplitudeComplex

st

st

==

=

=

=

=

==

λ

λθπ

ψλ

θπφ

d

d

d

ba

clut

tgt

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Phase of target vector can now be foundby solving for roots of quadraticSolution which provides largest returnafter beamforming is assumed correct

$

$

ee

1

2=

First eigenvector orthoganal to clutter directionSecond eigenvector orthoganal to clutter direction

Same eigenvectors computed during interference suppressionand detection processing

=

yy

Tgt

Tgt

1 1 1

2 2 2

= ≅

=

( $ , ) ( $ , )( $ , ) ( $ , )e s e se s e s

r r

r r≅

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Relocation Algorithm - Example

Original Target Detections

Relocated Targets

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RELOCATION ALGORITHM - 2

Assumed Signal Model

Complex images from each channel are assumed to have been relocated to a common point

+

=

111

1

2

beea

i

i

φ

φsr

frequencycenter ofth Waveleng spacingnt Intereleme

v2

channel 1 torelativereturn clutter of Phase

v2

channel 1 torelativereturn target of Phase

returnclutter of amplitudeComplex returntarget ofamplitudeComplex

platform

.

st

platform

.

st

==

=

=

=

=

==

λ

λπ

ψ

λπ

φ

d

rd

rd

ba

clut

tgt

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RELOCATION ALGORITHM - 2 (cont.)

Phase of target vector can now be foundby solving for roots of quadraticSolution which provides largest returnafter beamforming is assumed correct

yy

Tgt

Tgt

1 1 1

2 2 2

= ≅

=

( $ , ) ( $ , )( $ , ) ( $ , )e s e se s e s

r r

r r≅

$

$

ee

1

2=

First eigenvector orthoganal to clutter directionSecond eigenvector orthoganal to clutter direction

Same eigenvectors computed during interference suppressionand detection processing

=

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Geolocation Accuracy

SINRdRR s

c 2πλ =∆

on)cancellati(post ratio noise plus ceinterferen to signalElement centers phaseoutermost between Distance frequency center withassociated th Waveleng

RangeSlant tmeasuremen range cross of deviation Standard

≡≡≡≡≡∆

SINRd

RR

s

c

λ

Cramer Rao bound of interferometer measurement accuracyused to estimate cross range error

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Target Reports

SMI based STAP Eigenanalysis based STAP

Known Targets

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Target Reports

Unprocessed Target Detections Relocated Target Detections

Relocated Targets

Original Detections

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Multi-Stage False Alarm Reduction Processing

MultichannelComplexImage Data

Detection reportsLocation, Speed

and Heading Estimates

CovarianceEstimate

Find Eigenvaluesand Eigenvectors

Form InterferenceSuppressionProjections

Find Noise SubspaceDimension

Form EstimatedSteering Vector

Compute Cancellation

Ratios ofThreshold Crossings

Produce LowResolution SAR

Image

ProduceInterference

Suppressed Data Field

Perform CFARThresholding

Determine AOA Consistencyof Estimatesof PossibleDetections

Compute AOA(Radial Speed)Estimates

Form ImageProjections

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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

ASU MAT 591: Opportunities In Industry!kuang/LM/031021.pdf5 ASU MAT 591: Opportunities in Industry!...

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