Robotics - Localization & Bayesian Filtering - AIRLab - Politecnico di ...

Introduction Taxonomy Probability Recall Bayes Rule Bayesian Filtering Markov Localization26/58Total probability, marginalsTotal probability:∫ ∞ · · · ∫ ∞x 1 =−∞ x fx n=−∞ 1...x n (x 1, . . . , x n)dx 1 . . . dx n = 1Marginal distribution:∫ ∞fx,y (x, y)dx = fy (y)−∞∫ ∞fx,y (x, y)dy = fx(x)−∞Marginal distribution with conditioning:∫ ∞−∞ f y|x(y|x)f x(x)dx = f y (y)∫ ∞−∞ f x|y (x|y)f y (y)dy = f x(x)