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Improved discussion of Fox and Thrun.

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Roger Labbe 2014-09-09 17:30:38 -07:00
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Chapter02_Discrete_Bayes/discrete_bayes.ipynb
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@ -269,9 +269,13 @@
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"The Kalman filter belongs to a family of filters called *bayesian filters*. Without going into\n",
"The Kalman filter belongs to a family of filters called *bayesian filters*. Most textbook treatments of the Kalman filter present the Bayesian formula, perhaps shows how it factors into the Kalman filter equations, but mostly keeps the discussion at a very abstract level. \n",
"\n",
"blah blah"
"That approach requires a fairly sophisticated understanding of several fields of mathematics, and it still leaves much of the work of understanding and forming an intuitive grasp of the situation in the hands of the reader.\n",
"\n",
"I will use a different way to develop the topic, to which I owe the work of Dieter Fox and Sebastian Thrun a great debt. It depends on building an intuition on how Bayesian statistics work by tracking an object through a hallwya - they use a robot, I use a dog (I like dogs). The first published example of this that I can find weems to be Fox 1999 [1], with a fuller example in Fox [2] 2003. Sebastian Thrun also uses this formulation in his excellent Coursera course Artificial Intelligence for Robotics [3] In fact, if you like watching videos, I highly recommend pausing reading this book in favor of first few lessons of that course, and then come back to this book for a deeper dive into the topic.\n",
"\n",
"Let's now use a simple thought experiment, much like we did with the g-h filter, to see how we might reason about the use of probabilities for filtering and tracking."
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@ -290,9 +294,6 @@
"\n",
"I want to track my dog Simon, so I attach the device to his collar and then fire up Python, ready to try to write code to track him through the building. At first blush this may appear impossible. If I start listening to the sensor of Simon's collar I might read 'door', 'hall', 'hall', and so on. How can I use that information to determine where Simon is?\n",
"\n",
"> This formulation, tracking an object in a hallway, has been used to explain the discrete Bayesian filter many times. The first published source that I am aware of is Fox 2003 [1]. Sebastian Thrun also uses this formulation in his excellent Coursera course *Artificial Intelligence for Robotics* [2] In fact, if you like watching videos, I highly recommend pausing reading this book in favor of first few lessons of that course, and then come back to this book for a deeper dive into the topic. \n",
"\n",
"\n",
"To keep the problem small, we will assume that there are only 10 positions in a single hallway to consider, which we will number 0 to 9, where 1 is to the right of 0, 2 is to the right of 1, and so on. For reasons that will be clear later, we will also assume that the hallway is circular or rectangular. If you move right from position 9, you will be at position 0. \n",
"\n",
"When I begin listening to the sensor I have no reason to believe that Simon is at any particular position in the hallway. He is equally likely to be in any position. The probability that he is in each position is therefore 1/10. \n",
@ -1217,11 +1218,14 @@
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" * [1] Dieter Fox, et. al. \"Bayesian Filters for Location Estimation\". IEEE Pervasive Computing, September 2003.\n",
" * [1] D. Fox, W. Burgard, and S. Thrun. \"Monte carlo localization: Efficient position estimation for mobile robots.\" In *Journal of Artifical Intelligence Research*, 1999.\n",
" http://www.cs.cmu.edu/afs/cs/project/jair/pub/volume11/fox99a-html/jair-localize.html\\\n",
"\n",
" * [2] Dieter Fox, et. al. \"Bayesian Filters for Location Estimation\". In *IEEE Pervasive Computing*, September 2003.\n",
" http://swarmlab.unimaas.nl/wp-content/uploads/2012/07/fox2003bayesian.pdf\n",
" \n",
" \n",
" * [2] Sebastian Thrun. \"Artificial Intelligence for Robotics\".\n",
" * [3] Sebastian Thrun. \"Artificial Intelligence for Robotics\".\n",
" https://www.udacity.com/course/cs373\n",
" \n",
" "