Probabilistic Tracking And Localization

Complete the following exercises. Show your work. You may either submit through blackboard, or submit a neatly-written paper copy before the deadline.

• Consider the simpleright-moving robot we discussed in class . Assuming that the initial probability distribution over locations is uniform, what is the final probability distribution over locations given the following series of sensor readings:
  
  a
  b
  d
  
  
• We discussed an example of using a Kalman filter to track an object moving in 2d at a fixed velocity: kalman_demo.py. That code is vague on the subject of units. It is not clear how much time passes between observations, or how the position values are measured. Rewrite the code to conform to the following specifications:
  • All distances are in meters.
  • Velocities are in meters/second.
  • State and sensor updates happen at a rate of 10HZ.
  The only code you will need to modify is the Phi array in the movingKF function. The main method will not need to be modified (apart from comments explaining what units are being used.)
• Create a function named moving3dKF that creates a Kalman filter suitable for tracking on object moving at a fixed velocity in three dimensions.