Particles for Tracking Simon Maskell2 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 EKF’s 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?