a stochastic model-based approach to sar atr lee montagnino electronic systems and signals research...

A Stochastic Model-Based Approach to SAR ATR

Lee Montagnino

Electronic Systems and Signals Research Laboratory

Department of Electrical and Systems Engineering

Washington University

St. Louis, Missouri

Supported in part by ONR grant N00014-98-1-06-06

February 6, 2004 Montagnino: SAR ATR 2

Presentation Overview

Problem DefinitionLikelihood Approach to ATRConditionally Gamma ModelConditionally K distributionAzimuth Correlation ModelConclusions


Problem Definition

Typical Recognition Scenario

Imaging Platform

Target Classifier

Orientation Estimator

65ˆ

72ˆ Ta


Problem Definition

Model-Based Recognition

65ˆ

72ˆ TaTarget Classifier

Orientation Estimator

form)Simply Unior (Known ClassTarget on Prior -

form)Simply Unior (Known n Orientatioon Prior -

Model Data lConditiona - ,,

ap

ap

ap

A

A

A

rR


Problem Definition

Model-Based Recognition

Functional Estimation

Training Data

Scene and Sensor Physics

ProcessingImage

Inference ,aL r 72Tˆ a


Problem Definition

Use Modular Software Test Bed to Perform: Direct comparisons of different

stochastic models Performance analysis under a wide

range of testing and training scenarios Detailed study of performance vs.

models and model parameters


Likelihood Approach to ATR

Target Class and Pose Estimates

,,ˆminargˆ

,maxargˆ

2

HSˆHS

,Bayes

aOOEa

dapapaPa AAa

rr

rr R

cossin

sincos

where

O


Likelihood Approach to ATR

Generalized Likelihood Ratio Test and Maximum-A-Posteriori Estimation

,ln,lnmaxargˆ

ln ln,lnmaxmaxargˆ

,MAP

,GLRT

apapa

Apapapa

AA

AAa

rr

rr

R

R


MSTAR DATA SET

A collection of spotlight mode SAR images from a number of target classes Using 4 target classes from the public

release set Using 10 target classes from the public

release set MSTAR Program sponsored by DARPA and

Wright Laboratory


MSTAR Data Set

Partitioned into two subsets: 17 ° depression images used for

estimating likelihood functions 15 ° depression images used for

experimentally assessing performance

For testing, we assume a uniform prior on orientation and target class


Gamma Distribution

Multi-parameter distributionRelaxation of the quarter-power

normal modelRelates to Work in MSTAR Program

at WPAFB

,/

1,

1GAMMA ,,,

1, ar

a

i

in

i ii

ii

i

ea

r

aaap

r


Gamma Estimates

Maximum Likelihood Estimates

where

ii

ii

AG

A

ˆˆ

lnˆˆln

) of derivative ic(logarithmfunction digamma theis

and , ,/1/1

11

nn

i i

n

i i rGrnA


Gamma Results

Percentage of Correct Classification and Orientation Estimation Error


K Distribution

Multi-ParameterMixture modelModels Specular and Diffuse

Reflectivity

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i iiaa

ii

aai

arK

aa

rap

ii

ii

11,2/1,

2/,3,

K ,

2

,,

2,

r


K Estimates

Expectation-Maximization

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ki

kik

i

ki

ki

ki

kik

iki

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G

A

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,ˆ,ˆ

,ˆ,ˆlnˆˆln

1

11

r

r

r

n

iki

ki

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ii

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i

iki

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/1

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ˆ1

ˆ

ˆ2

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ˆ2

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ˆ2

1,ˆ,ˆ

rr


K Results



Azimuth Correlation

Radar data correlated in azimuth

M

Mmmm wZ R

mlo

M

Mlml

M

Mmml NZZERREK ,212121,

mlo

M

Mlml

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Mmm NK ,212

21,

2/12

2sin

122

21

sin

122

1

Mm

Mm

M

Mm


Azimuth Correlation Functions

EM Algorithm to Find Estimates of

pm

p

m

p

m

p

m

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MmNom

p

mp

EK

KKKE

INKK

traceˆˆˆ

ˆˆˆ

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22212

11

2

rr

2ˆm


Azimuth Correlation Covariance Images


Azimuth Correlation Results



Conclusions

Gamma Distribution Model low recognition rates poor orientation estimation

K distribution model comparable recognition rates to the

zero-mean conditionally Gaussian presented by DeVore


Conclusion

Azimuth Correlation comparable recognition rates to the

zero-mean conditionally Gaussian model presented by DeVore

best orientation estimation error rates of any distribution

correlation models don’t match actual data


Questions


References

a stochastic model-based approach to sar atr lee montagnino electronic systems and signals research...

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