Particles for Tracking

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Particles for Tracking

• Simon Maskell
• 2 December 2002

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Contents

• Particle filtering (on an intuitive level)
• Nonlinear non-Gaussian problems
• Some Demos
• Tracking in clutter
• Tracking with constraints
• Tracking dim targets
• Mutual triangulation
• Conclusions

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Particle Filter

• Kalman filter is optimal if and only if
• dynamic model is linear Gaussian
• measurement model is linear Gaussian
• Extended Kalman filter (EKF) approximates models
• Ok, if models almost linear Gaussian in locality
  of target
• Hence large EKF based tracking literature
• Particle filter approximates pdf explicitly as a
  sample set
• Better, if EKFs approximation loses lots of
  information

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Particle Filter

• Consider
• A nonlinear function
• Two candidate distributions
• Different diversity of hypotheses
• Different part of function

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Particle Filter

• Look at variation in gradient of tangent across
  hypotheses
• Determined by diversity of hypotheses and
  curvature
• Bearings only tracking
• Nonlinearity pronounced since range typically
  uncertain

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Particle Filter

• An Extended Kalman Filter infers states from
  measurements
• Restricts the models to be of a given form
• A particle filter generates a number of
  hypotheses
• Predicts particles forwards
• Hypotheses appear to use dynamics and
  measurements
• Importance sampling
• Choice of importance density is VERY VERY
  important

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Particle Filter

• Offers the potential to capitalise on models
• Approximating models can lose information
• Lost information can be critical to performance
• Solution structure can mirror problem structure
• Specific examples of potential to improve
  performance
• May not need to explore a deep history of
  associations
• Using difficult information
• Doppler Blind Zones / Terrain Masking
• Out-of-sequence measurements
• Stealthy Targets

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Some Demos

• Tracking in clutter
• Heavy tailed likelihood
• Tracking with constraints
• Obscuration can be informative
• Tracking dim targets
• Correlate images through time
• Mutual triangulation
• Bearing of sensors and sensors bearings of target

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Conclusions

• Particle Filtering can offer significant gains
• Can capitalise on model fidelity
• Can mirror problem structure
• Questions?