# Unit1: What does it mean to shift probabilities

 3 1 I am trying to wrap my head around "Robot motion" concept in localization To begin with, we are given an initial "distribution over the cells" with values of [1/9, 1/3, 1/3, 1/9, 1/9] I understand this to be the probabilities that the Robot is in the corresponding cells, having made an observation of "red" in its most recent step. Now Robot "moves" to right. So what I am unable to grasp is why the probabilities shift to right by one cell? Lets say that Robot was actually in cell-1(zero-indexed, i.e., the first red-cell) when he made the observation that he is on "red" cell. so based on that we get the above prob-distribution. Now lets say he moves right by one cell. What does the shifted-by-one probability array [1/9, 1/9, 1/3, 1/3, 1/9] represent? Thanks asked 23 Feb '12, 08:55 sreeneel 217●2●4●10 accept rate: 50% qntmfred 3.7k●12●41●67 Thanks Leonardo, Conrado & icogs Its clear now .. I think the crucial point is to remember that if you believe that you are in a state-x with a prob X, then when you move one step, you are ONLY X-confident that you are in state x+1 Also videos 18-23 help reinforce this concept (23 Feb '12, 09:44) sreeneel

 7 If Robot was in cell-1 and then shifted to the right it will now be in cell-2. Therefore the probability that it is now in cell-2 == probability that it was previously in cell-1. Similarly, probability that it is now in cell-3 == probability that it was previously in cell-2. The net effect is that the probabilities for all cells shifts/rotates to the right. answered 23 Feb '12, 09:29 icogs 466●1●6●13
 3 The vector is the belief state of the robot. Initially, it believes that it can be anywhere, so the vector is [1/5, 1/5, 1/5, 1/5, 1/5] When it senses the "red", its beliefs change to match that observation, so the vector becomes [1/9, 1/3, 1/3, 1/9, 1/9]. Then it moves to the right. It is sure he moved to the right, so if it believed with confidence 1/3 that it was in the 3rd cell, it will be 1/3 confident that it is now in the 4th cell. Doing the same procedure for each position of the vector, his belief vector becomes [1/9, 1/9, 1/3, 1/3, 1/9]. The idea is that the vector represents the belief state of the robot and the values are the certainty of the robot about whether it is in that cell. answered 23 Feb '12, 09:27 Conrado Silv... 4.3k●7●27●68
 2 Lets take and simpler example. p = [0.5, 0.0, 0.5, 0.0] assume that you always move correctly when issue the move command before moving, you have 50% confidence that you are in the first block and 50% confidence that you are in the third block. What happens if you move one block to the right (before any further measurement) ? Well, if you always move correctly you will have 50% confidence that you are in the second block and 50% you are in the fourh block. p = [0.0, 0.5, 0.0, 0.5] Or you can take an extreme example where you know your location : p = [0.0. 0.0, 1.0, 0.0] if you move to the left, what is the new probability distribution ? answered 23 Feb '12, 09:27 Leonardo Stern 1.5k●4●12●35
 0 i guess it has something to do with the fact that the robot doesn't know where it is , all it knows that there are 5 doors in a certain order [1/9, 1/3, 1/3, 1/9, 1/9] initially and that it is in a red cell not a particular cell , but just a red one. i took "shifting the probabilities" for granted :D , now that you mention this , i wanna know what it represents too :D answered 23 Feb '12, 09:08 Mohamed Wahe... 385●2●6●15 1 Yes, it _does_not_know for sure that it is in cell-1, and it is trying to figure out where in the 1-D world it is in. In my original comment, I was only assuming that it is in cell-1 for argument sake. (23 Feb '12, 09:18) sreeneel
 0 Search for question, "2nd video, why is the belief shifted at all?" Among the answers, look at the one that starts with "OK, I think I'm getting it now." It discusses shift and eliminates the confusion of advancing to being in front of a second door. Discussion there should help with deeper understanding. answered 23 Feb '12, 14:37 melr 3.6k●19●30●41
Question text:

Markdown Basics

• *italic* or _italic_
• **bold** or __bold__
• image?![alt text](/path/img.jpg "Title")
• numbered list: 1. Foo 2. Bar
• to add a line break simply add two spaces to where you would like the new line to be.
• basic HTML tags are also supported

×5,185
×69
×1
×1