Incremental Bayes
Incremental Bayes (details) 1st positive measurement
P(+|O) P(O)
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P(+|O) P(O) + P(+|¬O) P(¬O)
0.9 x 0.1 + 0.05 x 0.9
= 0.67 2nd positive measurement
P(+|O) P(O|+)
P(+|O) P(O|+) + P(+|¬O) P(¬O|+)
P(O|+,+) =
0.9 x 0.67
0.9 x 0.67 + 0.05 x 0.33
Incremental Bayes (derivation)
P(H|M1, M2) = = =
P(M1,M2|H) P(H) P(M1,M2)
P(M1,M2|H) P(H)
P(M1,M2|H) P(H) + P(M1,M2|¬H) P(¬H) P(M2|H) P(M1|H) P(H)
P(M2|H)P(M1|H) P(H) + P(M2|¬H) P(M1|¬H) P(¬H) P(M2|H) [P(M1|H) P(H) / P(M1)]
P(M2|H)[P(M1|H) P(H) / P(M1)] + P(M2|¬H) [P(M1|¬H) P(¬H) / P(M1)]
P(M2|H) P(H|M1) P(M2|H)P(H|M1) + P(M2|¬H) P(¬H|M1)
Examples of skills from Week 11 You should be able to demonstrate skills such as the following:
• Determine the number of degrees of freedom of a robot, and whether it is holonomic
• Characterise sources of uncertainty in a robot application scenario
• Explain the basic concepts of localisation and mapping
• Formulate an application problem using incremental Bayes
• Model the configuration space for a simple robot
• Compare different approaches to motion planning given a particular configuration space
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