Particle Filters

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/mcl/

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.

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.

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)

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)

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 Selection: Re-sampling

Example 1 of a Particle Filter Something is known

Particle Filters – Example 1

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

Particle Filters – Example 1 Use measurement model to compute weights (weight:observation probability)

Particle Filters – Example 1 Resample

Example 2 of a Particle Filter Nothing is known

Particle Filters – Example 2 Initialize particles uniformly

Particle Filters – Example 2

Particle Filters – Example 2

Particle Filters – Example 2

Particle Filters – Example 2

Particle Filters – Example 2

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)

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

Paul E. Rybski Haris Baltzakis Sources

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