Question 1¶
A linear sensor is calibrated using a linear model and least squares.
Which sensor property is directly improved by calibration?
Question 2¶
A linear sensor is modeled as:
r=as+b.
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What is the sensitivity of this sensor?
Question 3¶
TODO:
- Add assumption that only humidity is the variable that affects the temperature readings, and it is an established fact.
- Also add references to definitions of reliability, bias and ...
- Add another question with ground truth for humidity, and calibration results.
A digital thermometer reports temperature in discrete steps of 0.1Β°C. Because of humidity variations, the thermometerβs readings vary from day to day. The true temperature and the reported value on each day are:
Day 1 (low humidity): true temperature 22.0Β°C, reported 21.9Β°C
Day 2 (medium humidity): true temperature 22.5Β°C, reported 22.1Β°C
Day 3 (high humidity): true temperature 22.6Β°C, reported 22.3Β°C
Day 4 (medium humidity): true temperature 22.0Β°C, reported 22.0Β°C
Day 5 (low humidity): true temperature 22.5Β°C, reported 21.8Β°C
Which of the following statements are DEFINITELY correct?
Question 4¶
A point-sized mobile robot moves in an environment:
E \subset \mathbb{R}^2.
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The robot position is given by coordinates (π₯,π¦) β πΈ and it has no other degrees of freedom.
Let the state space be denoted by π. Which of the following statements correctly describe the state space π?
Question 5¶
A point-sized mobile robot moves in an environment:
E \subset \mathbb{R}^2.
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The robot position is (π₯,π¦) β πΈ and the robot heading is π β πΒΉ.
Let the state space be denoted by π. Which of the following statements correctly describe the state space π?
Question 6¶
Consider 10 point-sized mobile robots moving in a planar square environment
E = [-1,1]^2 \subset \mathbb{R}^2.
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Each robot has no heading and no additional degrees of freedom. Let the state space of the system be denoted by π, and the state of the robot π is its position:
p_i = (x_i,y_i) \in E, \quad i = 1,\dots,10.
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Let the detection region be a fixed set π β πΈ.
Which of the following statements are TRUE?
Question 7¶
Consider a point-sized mobile robot with a heading that moves within a planar square environment:
E = [-1,1]^2 \subset \mathbb{R}^2.
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The robot state is (π₯,π¦,π), in which (π₯,π¦) β πΈ and π β πΒΉ. Let the observation space be π β β.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y,
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which maps each physical state to a sensor observation.
Which of the following are TRUE statements about a sensor mapping β that measures the distance from the robotβs position to the closest wall?
Question 8¶
Consider a point-sized mobile robot with a heading that moves within a planar disc environment:
E = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 1\} \subset \mathbb{R}^2.
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The robot state is (π₯,π¦,π), where (π₯,π¦) β πΈ and π β πΒΉ. Let the observation space be π β β.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y.
\\\
Which of the following are TRUE statements about a sensor mapping β that measures the distance from the robotβs position to the closest wall of the environment?
Question 9¶
Consider a point-sized mobile robot with a heading that moves within a planar square environment:
E = [-1,1]^2 \subset \mathbb{R}^2.
\\\
The robot state is (π₯,π¦,π), where (π₯,π¦) β πΈ and π β πΒΉ. Let the observation space be π β β.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y.
\\\
Which of the following are TRUE statements about a sensor mapping β that measures the distance to the wall along the robotβs heading?
Question 10¶
Consider a point-sized mobile robot with a heading that moves within a planar circular environment:
E = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 1\}.
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The robot state is (π₯,π¦,π), where (π₯,π¦) β πΈ and π β πΒΉ. Let the observation space be π β β.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y.
\\\
Which of the following are TRUE statements about a sensor mapping β that measures the distance to the wall along the robotβs heading?