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cs-677sp2010:filters-lab [2014/12/12 20:37]
ryancha created
cs-677sp2010:filters-lab [2014/12/12 20:37] (current)
ryancha
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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 ===
cs-677sp2010/filters-lab.txt · Last modified: 2014/12/12 20:37 by ryancha
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