Markov chain approach to optimal sensor coverage

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Markov chain approach to optimal sensor coverage
Sergiy Gorovyy, Anton Molyboha, Michael
Zabarankin Stevens Institute of Technology
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Outline

• Motivation
• Problem formulation
• Techniques
• Examples
• 1) Noiseless environment
• 2) Static noise
• 3) Dynamic noise
• Conclusions

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Motivation

• Coverage problem
• Active radars in military applications
• Security applications
• Surveillance systems
• Failure detection

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Coverage problem
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Signal Model
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Signal Model
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Probability of detection
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Markov Chain Approach
Objective function probability of detection
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Markov Chain Approach
Problem formulation
Constraints
M transition probability matrix
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Markov Chain Optimization
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Detection Model
Detection
Probability of detection
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Example Detection Model
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Example Optimal Markov Chain
1.00
0.61
1.00
0.39
0.18
1.00
0.24
0.24
0.34
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Example Detection
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Adaptation to Noise
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Adaptation To Noise
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Detection model
Detection
Probability of detection
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Example Influence Of Noise
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Example Moving Noise
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Example Markov Chain With Noise
1.00
0.61
0.35
0.38
1.00
0.01
1.00
0.65
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Example Detection With Noise
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Example Detection with Moving Noise
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Example Detection with Moving Noise
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Example Detection with Moving Noise
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Conclusions

• Formulation of optimal sensor coverage problem
• 1) Ambient noise
• 2) Ambient noise Static noise source
• 3) Ambient noise Dynamic noise source
• Linear programming for discretized space
• Adaptive approach based on Markov chains allowed
  to construct a system that can adjust itself to
  different changes in environment