UT CS 344R - Lecture 16: Particle Filters (12 pages)

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Lecture 16: Particle Filters



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Lecture 16: Particle Filters

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Pages:
12
School:
University of Texas at Austin
Course:
Cs 344r - Robotics

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Lecture 16 Particle Filters CS 344R 393R Robotics Benjamin Kuipers Markov Localization Bel x t P zt x t P x t ut 1 x t 1 Bel x t 1 dx t 1 The integral is evaluated over all xt 1 It computes the probability of reaching xt from any location xt 1 using the action ut 1 The equation is evaluated for every xt It computes the posterior probability distribution of xt Computational efficiency is a problem o k2 if there are k poses xt k reflects resolution of position and orientation 1 Action and Sensor Models Action model P xt ut 1 xt 1 Sensor model P zt xt Distributions over possible values of xt or zt given specific values of other variables We discussed these last time Monte Carlo Simulation Given a probability distribution over inputs computing the distribution over outcomes can be hard Simulating a concrete instance is easy Sample concrete instances particles from the input distribution Collect the outcomes The distribution of sample outcomes approximates the desired distribution This has been called particle filtering 2 Actions Disperse the Distribution N particles approximate a probability distribution The distribution disperses under actions Monte Carlo Localization A concrete instance is a particular pose A pose is position plus orientation A probability distribution is represented by a collection of N poses Each pose has an importance factor The importance factors sum to 1 Initialize with N uniformly distributed poses Equal importance factors of N 1 3 Localization Movie known map Representing a Distribution The distribution Bel xt is represented by a set St of N weighted samples St where x i t w i i 1 LN t N w i t 1 i 1 A particle filter is a Bayes filter that uses this sample representation 4 Importance Sampling Sample from a proposal distribution Correct to approximate a target distribution Simple Example Uniform distribution Weighting by sensor model Prediction by action model Weighting by sensor model 5 The Basic Particle Filter Algorithm Input ut 1 zt St 1 St



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