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Particles for Tracking

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Particles for Tracking

Simon Maskell

2 December 2002

- Particle filtering (on an intuitive level)
- Nonlinear non-Gaussian problems

- Some Demos
- Tracking in clutter
- Tracking with constraints
- Tracking dim targets
- Mutual triangulation

- Conclusions

- 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

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

- 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

- 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

- Importance sampling

- 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

- Specific examples of potential to improve performance

- 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

- Particle Filtering can offer significant gains
- Can capitalise on model fidelity
- Can mirror problem structure

- Questions?