3630-08-lec12-uncertainty

3630-08-lec12-uncertainty - Introduction Representation...

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Unformatted text preview: Introduction Representation Uncertainty Propagation Summary Uncertainty Henrik I Christensen Robotics & Intelligent Machines @ GT Georgia Institute of Technology, Atlanta, GA 30332-0760 [email protected] Henrik I Christensen ([email protected]) Uncertainty 1 / 29 Introduction Representation Uncertainty Propagation Summary Outline 1 Introduction 2 Representation of Uncertainty 3 Uncertainty Propagation 4 Summary Henrik I Christensen ([email protected]) Uncertainty 2 / 29 Introduction Representation Uncertainty Propagation Summary Introduction All sensors and processes have associated uncertainty How do we capture/model the uncertainty? How do we propagate information with uncertainty through the system? What are typical models and how can they be used? We need the basics before we start talking about “features” in more detail Henrik I Christensen ([email protected]) Uncertainty 3 / 29 Introduction Representation Uncertainty Propagation Summary The Robot Structure Henrik I Christensen ([email protected]) Uncertainty 4 / 29 Introduction Representation Uncertainty Propagation Summary Outline 1 Introduction 2 Representation of Uncertainty 3 Uncertainty Propagation 4 Summary Henrik I Christensen ([email protected]) Uncertainty 5 / 29 Introduction Representation Uncertainty Propagation Summary Uncertain values 1 Probability of events 2 Random variables x : real number = f(experiment) discrete x ∈ M where M is a finite set of outcomes P ( x i = x ) = p i ∈ [0 , 1] p i are probabilities continuous x ∈ R P ( x ∈ [ x 1 , x 2 ]) = Z x 2 t = x 1 p x ( t ) dt = P x ( x 2 )- P x ( x 1 ) p x ( x ) is a probability density function (pdf) P x ( x ) is a cumulative density function, distribution (cpdf) Henrik I Christensen ([email protected]) Uncertainty 6 / 29 Introduction Representation Uncertainty Propagation Summary Normal / Gaussian Distribution The Normal or Gaussian distribution, pdf: G ( x ) = p x ( x ) = 1 √ 2 π e- 1 2 x 2 The cumulative distribution is the socalled error function erf ( x ) = Z x t =-∞ G ( t ) dt The general Gaussian has non-zero mean and non-unity std. dev. I.e....
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This note was uploaded on 01/27/2011 for the course CS 3803 taught by Professor Staff during the Spring '10 term at Georgia Tech.

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3630-08-lec12-uncertainty - Introduction Representation...

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