Robotics - Localization & Bayesian Filtering - AIRLab - Politecnico di ...
Robotics - Localization & Bayesian Filtering - AIRLab - Politecnico di ...
Robotics - Localization & Bayesian Filtering - AIRLab - Politecnico di ...
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Introduction Taxonomy Probability Recall Bayes Rule <strong>Bayesian</strong> <strong>Filtering</strong> Markov <strong>Localization</strong>18/58Discrete Random Variables - PropertiesProperties - 2Consider two event A and Be.g., A is “<strong>di</strong>e outcome is 2 or 3 ”, B is “<strong>di</strong>e outcome is even”Pr(A ∨ B) = Pr(A) + Pr(B) − Pr(A ∧ B)e.g., A ∨ B is “<strong>di</strong>e outcome is 2 or 3 or 4 or 6”, Pr(A ∨ B) = 2 3 = 1 3 + 1 2 − 1 6If A ∧ B = Ø → Pr(A ∨ B) = Pr(A) + Pr(B)Pr(A) = 1 − Pr(A)Pr(A ∨ A) = Pr(A) + Pr(A) − Pr(A ∧ A) = 1RemarksRelative-frequency (i.e., outcome ofexperiments) are alternative (notrigorous) ways of introduce theconcept of probability.
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