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Particles for Tracking

Particles for Tracking. Simon Maskell 2 December 2002. 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. Particle Filter.

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Particles for Tracking

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  1. Particles for Tracking Simon Maskell 2 December 2002

  2. 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

  3. 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 EKF’s approximation loses lots of information

  4. Particle Filter • Consider • A nonlinear function • Two candidate distributions • Different diversity of hypotheses • Different part of function

  5. 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

  6. 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

  7. 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

  8. 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

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

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