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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

Particles for Tracking

Simon Maskell

2 December 2002


Contents
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
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


Particle filter1
Particle Filter

  • Consider

    • A nonlinear function

    • Two candidate distributions

      • Different diversity of hypotheses

      • Different part of function


Particle filter2
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


Particle filter3
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


Particle filter4
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


Some demos
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


Conclusions
Conclusions

  • Particle Filtering can offer significant gains

    • Can capitalise on model fidelity

    • Can mirror problem structure

  • Questions?


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