pints network. multiple target tracking nonlinear filtering used for detection, tracking, and...
TRANSCRIPT
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PINTS Network
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Multiple Target Tracking
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Nonlinear Filtering
• Used for detection, tracking, and prediction of a target in a noisy environment
• Based entirely in probability– A filter won’t tell you exactly where a target is,
but it will tell you that there’s a 95% chance that it is within a certain region
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Targets
• Targets are what filters work with• There are many different sorts of targets:
– Physical• Dinghy lost at sea• Performer on stage
– Financial• Investing• Fraud
– Other• Radio Frequencies• Port Scans
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The Three Parts
• Filtering can be thought of as being divided into three parts:
– Signal Model (Target)– Observation Model (Noisy Environment)– Conditional Distribution (The Answer!)
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Signal Model
• Model of how your target behaves
• Typical described using a Stochastic Differential Equation (SDE)
• Exists on some d-dimensional domain– For physical signals domain usually includes
dimensions for position, velocity, etc
• Basically tells you the probability that the target will move in any given way.
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Boat Signal
• Domain is five dimensional:– X, Y position– Orientation– Speed– State (motoring, drifting, etc)
• Signal Model gives you the probabilistic distribution of what state the boat will be in at time t + 1, given it is currently at position Xt
• So, for example, the model might tell you that there’s a 40% chance that the boat will move north.
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Observation Model
• Observation model tells about what information is available to the filter.
• Typically very poor:– Incomplete:
• Missing information• Might know location but not velocity or vice versa
– Corrupted:• Target might occasionally disappear completely from
observation
– Noisy:• Lots of false information on top of real target
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Infra-red camera observation
• Observation model typically used with boat signal• Models infra-red satellite camera looking down at ocean• Not corrupted, but partial and very noisy!
– Only has position, no orientation, speed, or state
• Picture looks like TV static• To construct:
– Start with black picture– Add 1 to boat shaped area at location of boat– Add Normal Random Variable to each pixel– Colour each pixel according to the total number it ends up with
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Conditional Distribution
• The output of the filter
• Used to answer various questions:– Where is the target now?– What are the chances that it’s within a certain
region?– Where will it be in 5 seconds?
• Just like a distribution for a random variable
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Filtering Summary
• Filter has a model for both the signal it’s tracking and the type of observations it’s receiving.
• Input: Observations
• Output: Conditional Distribution
• Very powerful tool for a wide variety of applications
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Surveillance (Lockheed Martin)
Communications(Optovation)
Automated Theatre Effects(APR Inc.)
Manufacturing(Visionsmart)
Filtering Applications
Network Security(Random Knowledge Inc.)
Medical Imaging
Pollution Monitoring
Fraud Detection(Random Knowledge Inc.)
Finance(Random Knowledge Inc.)
Fish Farming
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Tracking a boat• Location : Where is the boat ? • Speed : How fast is the boat traveling ?• Orientation : Which way is the boat heading ?• Motion Type : Is the boat drifting, rowing, or motorized ?
Present Future Past
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Tracking a performer on stage• Location : Where is the Performer ?
• Speed : How fast is the Performer traveling ?
• Orientation : Which way is the Performer heading ?
• Motion Type : Is the Performer in Walk or Pivot Mode?
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Signal
(Port Scanner)
Observation
(Normal Traffic)
Port Scanner
Present
Port Scanner
Not Present
Detecting a port scanner