A Stochastic Model-Based Approach to SAR ATR

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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

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Presentation Overview

• Problem Definition
• Likelihood Approach to ATR
• Conditionally Gamma Model
• Conditionally K distribution
• Azimuth Correlation Model
• Conclusions

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Problem Definition

• Typical Recognition Scenario

Imaging Platform
Target Classifier
Orientation Estimator
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Problem Definition

• Model-Based Recognition

Target Classifier
Orientation Estimator
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Problem Definition

• Model-Based Recognition

Training Data
Functional Estimation
Scene and Sensor Physics
Image
Processing
Inference
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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

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Likelihood Approach to ATR

• Target Class and Pose Estimates

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Likelihood Approach to ATR

• Generalized Likelihood Ratio Test and
  Maximum-A-Posteriori Estimation

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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

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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

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Gamma Distribution

• Multi-parameter distribution
• Relaxation of the quarter-power normal model
• Relates to Work in MSTAR Program at WPAFB

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Gamma Estimates

• Maximum Likelihood Estimates
• where

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Gamma Results

• Percentage of Correct Classification and
  Orientation Estimation Error

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K Distribution

• Multi-Parameter
• Mixture model
• Models Specular and Diffuse Reflectivity

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K Estimates

• Expectation-Maximization

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K Results

• Percentage of Correct Classification and
  Orientation Estimation Error

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Azimuth Correlation

• Radar data correlated in azimuth

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Azimuth Correlation Functions

• EM Algorithm to Find Estimates of

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Azimuth Correlation Covariance Images
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Azimuth Correlation Results

• Percentage of Correct Classification and
  Orientation Estimation Error

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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

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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 dont match actual data

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Questions
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References
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References