l20abwbayesian

l20abwbayesian - 3/6/00 1 9/13/00 copyright Brian Wil iams,...

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Unformatted text preview: 3/6/00 1 9/13/00 copyright Brian Wil iams, 2000 1 courtesy of JPL Bayesian Estimation for Dynamic Systems Brian C. Williams 16.410/16.413 Session 20 B rian C . W il iam s, copyright 2000 9/13/00 copyright Brian Wil iams, 2000 2 Reading Assignments AIMA (Russell and Norvig) Ch 15.1-.3, 20.3 State Estimation and Hidden Markov Models From Monday: Ch 13 Review of Probabilities Ch 14.1-4 Probabilistic Reasoning No homework due this week. 9/13/00 copyright Brian Wil iams, 2000 3 Outline Overview Belief State Update Sequential, Model-based Diagnosis Robot Localization 3/6/00 9/13/00 copyright Brian Wil iams, 2000 4 Multiple Faults Occur courtesy of NASA and pressure jacket burst, panel flies off. How do we rank order a large set of consistent diagnoses? APOLLO 13 three shorts, tank-line Courtesy of Kanna Rajan, NASA Ames. Used with permission. How does a robot determine its position from noise data, as it moves around? x 1 x 2 : p(x 2 |x 1 ,a)= .9 x 3 : p(x 3 |x 1 ,a)=.05 x 4 : p(x 4 |x 1 ,a)=.05 Observations can be features such as corridor features, junction features, etc. How does a robot understand what is being said to it? Courtesy of NASA. 2 T 9/13/00 copyright Brian Wil iams, 2000 7 Estimating Dynamic Systems Given a sequence of observations and commands: What is the likelihood of a particular state? Belief State Update : (filtering and smoothing) What is the most likely sequence of states that got me here? Decoding: ( Viterbi Algorithm) What is the most likely sequence of observations generated? Evaluation/Prediction: What HMM most likely generated these observations? Learning: ( Baum-Welch Algorithm , Expectation-Maximization Algorithm) S X 0 X1 XN-1 XN S T 9/13/00 copyright Brian Wil iams, 2000 8 Outline Overview Belief State Update Sequential, Model-based Diagnosis HMMs and Belief State Update Robot Localization 9/13/00 copyright Brian Wil iams, 2000 9 Diagnoses: (42 of 64 candidates) Fully Explained Failures [A=G, B=G, C=S0] [A=G, B=S1, C=S0] [A=S0, B=G, C=G] . . . Fault Isolated, But Unexplained [A=G, B=G, C=U] [A=G, B=U, C=G] [A=U, B=G, C=G] Partial Explained [A=G, B=U, C=S0] [A=U, B=S1, C=G] [A=S0, B=U, C=G] . . . X Y A B C 0 0 in out 3/6/00 3 3/6/00 9/13/00 copyright Brian Wil iams, 2000 10 Due to the unknown mode, there tends to be an exponential number of diagnoses. U Candidates with UNKNOWN failure modes Candidates with KNOWN failure modes Good Good G F1 Fn G U But these diagnoses represent a small fraction of the probability density space. Most of the density space may be represented by enumerating the few most likely diagnoses 9/13/00 copyright Brian Wil iams, 2000 11 Sequential Input: Set of component mode variables M, with finite domains....
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This note was uploaded on 11/07/2011 for the course AERO 16.410 taught by Professor Brianwilliams during the Fall '05 term at MIT.

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l20abwbayesian - 3/6/00 1 9/13/00 copyright Brian Wil iams,...

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