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cs-677sp2010:filters-lab [2014/12/12 20:37] ryancha created |
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x, y coordinates. The robot moves by specifying a direction (in | x, y coordinates. The robot moves by specifying a direction (in | ||

radians from vertical) and a distance. The robot senses its | radians from vertical) and a distance. The robot senses its | ||

- | position as the distance from 2 beacons (<math>d_{A}</math> the distance from | + | position as the distance from 2 beacons ($d_{A}$ the distance from |

- | beacon A and <math>d_{B}</math> the distance from beacon B) | + | beacon A and $d_{B}$ the distance from beacon B) |

=== Prior === | === Prior === | ||

- | <math>x_{0} \sim N(0,1) \!</math> | + | $x_{0} \sim N(0,1) \!$ |

- | <math>y_{0} \sim N(0,1) \!</math> | + | $y_{0} \sim N(0,1) \!$ |

=== System or Transition Model === | === System or Transition Model === | ||

- | The movement of the robot is random in <math>d</math>, the distance | + | The movement of the robot is random in $d$, the distance |

- | travelled, and <math>\theta</math>, the angle chosen. The intended distance | + | travelled, and $\theta$, the angle chosen. The intended distance |

- | (5) and direction <math>\left(\frac{\pi}{5}\right)</math> are fixed. | + | (5) and direction $\left(\frac{\pi}{5}\right)$ are fixed. |

- | <math> d \sim N(5,1)\!</math> | + | $ d \sim N(5,1)\!$ |

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Warning this line is broken. The current version of the wiki will not parse it. I have commented it out. The line following it seems to work. | Warning this line is broken. The current version of the wiki will not parse it. I have commented it out. The line following it seems to work. | ||

- | <math> \theta \sim \mathit{Uniform} ((\pi/5-\pi/36), (\pi/5+\pi/36))\!</math> | + | $ \theta \sim \mathit{Uniform} ((\pi/5-\pi/36), (\pi/5+\pi/36))\!$ |

--> | --> | ||

- | <math> \theta \sim \mathit{Uniform} \left(\frac{\pi}{5}-\frac{\pi}{36},\frac{\pi}{5}+\frac{\pi}{36}\right)</math> | + | $ \theta \sim \mathit{Uniform} \left(\frac{\pi}{5}-\frac{\pi}{36},\frac{\pi}{5}+\frac{\pi}{36}\right)$ |

- | <math>x_{t+1}|x_{t} = x_{t} + d \cdot \cos \left(\theta\right)</math> | + | $x_{t+1}|x_{t} = x_{t} + d \cdot \cos \left(\theta\right)$ |

- | <math>y_{t+1}|y_{t} = y_{t} + d \cdot \sin \left(\theta\right)</math> | + | $y_{t+1}|y_{t} = y_{t} + d \cdot \sin \left(\theta\right)$ |

=== Observation or Sensor Model === | === Observation or Sensor Model === | ||

The robot senses its position as the distance from beacon A | The robot senses its position as the distance from beacon A | ||

- | (<math>d_{A}</math>) and the distance from beacon B(<math>d_{B}</math>). Both are | + | ($d_{A}$) and the distance from beacon B($d_{B}$). Both are |

imperfect measures as shown below: | imperfect measures as shown below: | ||

- | <math>d_{A} = \sqrt{(-100-x)^{2}+(100-y)^{2}} </math> | + | $d_{A} = \sqrt{(-100-x)^{2}+(100-y)^{2}} $ |

- | <math>d_{B} = \sqrt{(150-x)^{2}+(90-y)^{2}} </math> | + | $d_{B} = \sqrt{(150-x)^{2}+(90-y)^{2}} $ |

- | <math>r_{A} \sim N (d_{A}, 1)\!</math> | + | $r_{A} \sim N (d_{A}, 1)\!$ |

- | <math>r_{B} \sim N (d_{B}, 1)\!</math> | + | $r_{B} \sim N (d_{B}, 1)\!$ |

=== Sample data === | === Sample data === |