Particle Filters

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Particle Filters
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Application Examples

• Robot localization
• Robot mapping
• Visual Tracking
• e.g. human motion (body parts)
• Prediction of (financial) time series
• e.g. mapping gold price to stock price
• Target recognition from single or multiple images
• Guidance of missiles
• Contour grouping
• Nice video demos
• http//www.cs.washington.edu/ai/Mobile_Robotics/m
  cl/

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2nd Book Advert

• Statistical Pattern Recognition
• Andrew Webb, DERA
• ISBN 0340741643,
• Paperback 1999 29.99
• Butterworth Heinemann
• Contents
• Introduction to SPR, Estimation, Density
  estimation, Linear discriminant analysis,
  Nonlinear discriminant analysis - neural
  networks, Nonlinear discriminant analysis -
  statistical methods, Classification trees,
  Feature selction and extraction, Clustering,
  Additional topics, Measures of dissimilarity,
  Parameter estimation, Linear algebra, Data,
  Probability theory.

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Homework

• Implement all three particle filter algorithms
• SIS Particle Filter Algorithm (p. 27)
• Basic SIR Particle Filter algorithm (p. 39,40)
• Generic SIR Particle Filter algorithm (p. 42)
• and evaluate their performance on a problem of
  your choice.
• Groups of two are allowed.
• Submit a report and a ready to run Matlab code
  (with a script and the data).
• Present a report to the class.

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Particle Filters

• Often control models are non-linear and noise is
  non-gausian.
• We use particles to represent the distribution
• Survival of the fittest

Motion model

Proposal distribution
Observation model (weight)
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Particle Filters SIS-R algorithm

• Initialize particles randomly (Uniformly or
  according to prior knowledge)
• At each time step
• For each particle
• Use motion model to predict new pose (sample from
  transition priors)
• Use observation model to assign a weight to each
  particle (posterior/proposal)

Sequential importance sampling

Motion model

Proposal distribution
Observation model (weight)
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Particle Filters RE-SAMPLING

• Initialize particles randomly (Uniformly or
  according to prior knowledge)
• At each time step
• For each particle
• Use motion model to predict new pose (sample from
  transition priors)
• Use observation model to assign a weight to each
  particle (posterior/proposal)
• Create A new set of equally weighted particles by
  sampling the distribution of the weighted
  particles produced in the previous step.

Sequential importance sampling

SelectionRe-sampling
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Example 1 of a Particle Filter
Something is known
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Particle Filters Example 1

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Particle Filters Example 1
Use motion model to predict new pose (move each
particle by sampling from the transition prior)

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Particle Filters Example 1
Use measurement model to compute
weights (weightobservation probability)

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Particle Filters Example 1

Resample
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Example 2 of a Particle Filter
Nothing is known
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Particle Filters Example 2

Initialize particles uniformly
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Particle Filters Example 2

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Particle Filters Example 2

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Particle Filters Example 2

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Particle Filters Example 2

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Particle Filters Example 2

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Discussion of Continuous State Approaches
Kalman Filters
pluses

• Perform very accurately if the inputs are precise
  (performance is optimal with respect to any
  criterion in the linear case).
• Computational efficiency.

minuses

• Requirement that the initial state is known.
• Inability to recover from catastrophic failures
• Inability to track Multiple Hypotheses the state
  (Gaussians have only one mode)

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Discussion of Discrete State Approaches
Particle Filters

• Ability (to some degree) to operate even when its
  initial pose is unknown (start from uniform
  distribution).
• Ability to deal with noisy measurements.
• Ability to represent ambiguities (multi modal
  distributions).

• Computational time scales heavily with the number
  of possible states (dimensionality of the grid,
  number of samples, size of the map).
• Accuracy is limited by the size of the grid
  cells/number of particles-sampling method.
• Required number of particles is unknown

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Sources

• Paul E. Rybski
• Haris Baltzakis

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PR Virtual Architecture with Kalman Filters

• Sensor records samples
• Image processing step extracts specific features
• Target size, vertical position, horizontal
  position, target bearing, elevation, etc.
• Kalman filters extract sensor noise
• Results are sent to a central location to be
  displayed