CS 7638 Midterm 1- Probability, Histogram
Filters, Kalman Filters, Particle Filters, Bicycle
Motion Questions with Verified Correct
Answers
localization
This is where you are in space. GPS is a traditional way to do this, but self-driving cars need
less than 10 centimeters of error in real-time.
uniform maximum confusion
The equal probability that the robot could be at any location in space. This usually happens
with the initial belief.
posterior belief
The updated belief after new measurements are taken.
P(X|Z)
The probability of "X" given measurement "Z"
exact motion
The probability of a robot's location shifts with its movement. This assumes there is 0 noise.
inaccurate robot motion
Th
Q: Assuming a cyclical world and exact motion, what is the probability that the robot is
in cell 2 be after TWO movements to the right?
cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2]
, 0.2
A robot correctly follows a movement request with a probability of 0.9. Otherwise, it
will stay in current location with a probability of 0.1. Assuming a cyclical world, what is
the probability of the 3-cell grid, after ONE movement to the left?
cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2]
1 [0.39] | 2 [0.22] | 3 [0.29]
limit distribution
The location probabilities in a robot's grid cell become uniform if you move the robot infinite
times with inaccurate robot motion.
localization summary
Belief is a probability of the robot's location. Sensing is a product with normalization.
Movement is a convolution (aka addition) using the total probability theorem.
Q: Which probability theorem or rule does a measurement/sense use?
Bayes' Theorem
Q: Which probability theorem or rule does movement use?
The Total Probability Rule
Bayes' Theorem
A method used to compute posterior probabilities. Measurement or sense functions use this
theorem. The denominator in the image can also be written as P(B).
Total Probability Rule or Law of Probability
Filters, Kalman Filters, Particle Filters, Bicycle
Motion Questions with Verified Correct
Answers
localization
This is where you are in space. GPS is a traditional way to do this, but self-driving cars need
less than 10 centimeters of error in real-time.
uniform maximum confusion
The equal probability that the robot could be at any location in space. This usually happens
with the initial belief.
posterior belief
The updated belief after new measurements are taken.
P(X|Z)
The probability of "X" given measurement "Z"
exact motion
The probability of a robot's location shifts with its movement. This assumes there is 0 noise.
inaccurate robot motion
Th
Q: Assuming a cyclical world and exact motion, what is the probability that the robot is
in cell 2 be after TWO movements to the right?
cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2]
, 0.2
A robot correctly follows a movement request with a probability of 0.9. Otherwise, it
will stay in current location with a probability of 0.1. Assuming a cyclical world, what is
the probability of the 3-cell grid, after ONE movement to the left?
cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2]
1 [0.39] | 2 [0.22] | 3 [0.29]
limit distribution
The location probabilities in a robot's grid cell become uniform if you move the robot infinite
times with inaccurate robot motion.
localization summary
Belief is a probability of the robot's location. Sensing is a product with normalization.
Movement is a convolution (aka addition) using the total probability theorem.
Q: Which probability theorem or rule does a measurement/sense use?
Bayes' Theorem
Q: Which probability theorem or rule does movement use?
The Total Probability Rule
Bayes' Theorem
A method used to compute posterior probabilities. Measurement or sense functions use this
theorem. The denominator in the image can also be written as P(B).
Total Probability Rule or Law of Probability
