# Particles for Tracking - PowerPoint PPT Presentation

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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

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## Particles for Tracking

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

• 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 Filter

• Consider

• A nonlinear function

• Two candidate distributions

• Different diversity of hypotheses

• Different part of function

### 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 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 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

• 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

• Particle Filtering can offer significant gains

• Can capitalise on model fidelity

• Can mirror problem structure

• Questions?