CS 7638 Midterm 1 (Fall 2023) - Probability, Histogram Filters, Kalman Filter
Particle Filters, Bicycle Motion
1. localization This is where you are in space. GPS is a tradi-
tional way to do this, but self-driving cars need
less than 10 centimeters of error in real-time.
2. uniform maximum confusion The equal probability that the robot could be at
any location in space. This usually happens with
the initial belief.
3. posterior belief The updated belief after new measurements are
taken.
4. P(X|Z) The probability of "X" given measurement "Z"
5. exact motion The probability of a robot's location shifts with
its movement. This assumes there is 0 noise.
6. inaccurate robot motion Th
7. Q: Assuming a cyclical world and exact 0.2
motion, what is the probability that the
robot is in cell 2 be after TWO move-
ments to the right?
cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2]
8. A robot correctly follows a movement 1 [0.39] | 2 [0.22] | 3 [0.29]
request with a probability of 0.9. Other-
wise, it will stay in current location with
a probability of 0.1. Assuming a cycli-
1/7
, CS 7638 Midterm 1 (Fall 2023) - Probability, Histogram Filters, Kalman Filter
Particle Filters, Bicycle Motion
cal 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]
9. limit distribution The location probabilities in a robot's grid cell
become uniform if you move the robot infinite
times with inaccurate robot motion.
10. localization summary Belief is a probability of the robot's location.
Sensing is a product with normalization. Move-
ment is a convolution (aka addition) using the
total probability theorem.
11. Q: Which probability theorem or rule Bayes' Theorem
does a measurement/sense use?
12. Q: Which probability theorem or rule The Total Probability Rule
does movement use?
13. Bayes' Theorem A method used to compute posterior probabili-
ties. Measurement or sense functions use this
theorem. The denominator in the image can
also be written as P(B).
14. Total Probability Rule or Law of Probabil- P(A) = P(A l B₁)(P(B₁) + P(A l B₂)P(B₂) +....P(A
ity l Bn)P(Bn). The unconditional probability of
event, given conditional probabilities. Move-
ment functions use this.
15. Histogram Filters
2/7
Particle Filters, Bicycle Motion
1. localization This is where you are in space. GPS is a tradi-
tional way to do this, but self-driving cars need
less than 10 centimeters of error in real-time.
2. uniform maximum confusion The equal probability that the robot could be at
any location in space. This usually happens with
the initial belief.
3. posterior belief The updated belief after new measurements are
taken.
4. P(X|Z) The probability of "X" given measurement "Z"
5. exact motion The probability of a robot's location shifts with
its movement. This assumes there is 0 noise.
6. inaccurate robot motion Th
7. Q: Assuming a cyclical world and exact 0.2
motion, what is the probability that the
robot is in cell 2 be after TWO move-
ments to the right?
cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2]
8. A robot correctly follows a movement 1 [0.39] | 2 [0.22] | 3 [0.29]
request with a probability of 0.9. Other-
wise, it will stay in current location with
a probability of 0.1. Assuming a cycli-
1/7
, CS 7638 Midterm 1 (Fall 2023) - Probability, Histogram Filters, Kalman Filter
Particle Filters, Bicycle Motion
cal 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]
9. limit distribution The location probabilities in a robot's grid cell
become uniform if you move the robot infinite
times with inaccurate robot motion.
10. localization summary Belief is a probability of the robot's location.
Sensing is a product with normalization. Move-
ment is a convolution (aka addition) using the
total probability theorem.
11. Q: Which probability theorem or rule Bayes' Theorem
does a measurement/sense use?
12. Q: Which probability theorem or rule The Total Probability Rule
does movement use?
13. Bayes' Theorem A method used to compute posterior probabili-
ties. Measurement or sense functions use this
theorem. The denominator in the image can
also be written as P(B).
14. Total Probability Rule or Law of Probabil- P(A) = P(A l B₁)(P(B₁) + P(A l B₂)P(B₂) +....P(A
ity l Bn)P(Bn). The unconditional probability of
event, given conditional probabilities. Move-
ment functions use this.
15. Histogram Filters
2/7
