Bayes Filter Python Problem

MTRE 6100, Homework #2 Please use Python to develop a program to solve the problem in Homework 1. Expect results: ����� and 𝒃𝒃𝒃𝒃𝒃𝒃 for each step, their graphs are 1. A pdf showing all of your program outputs to show 𝒃𝒃𝒃𝒃𝒃𝒃 optional (+1 extra credit out of 20 points for the plots) 2. Please ensure to add a step for the measurement (sensor reading). You may use random variables to simulate the measurement at different grid locations or have the user input the measurement (e.g. wall or door). 3. Please submit all source code. To receive credit, ensure your code executes properly. 4. Please pay extra attention to coding best practices. a. Comment your code b. Remove old unused code c. Ensure enough spacing d. Be consistent in your naming convention. Don’t use two types of cases e.g. (camelCase and snake_case) ————————————————————————————————————————————–Appendix: Please review the Bayes filter example in the lecture slides. Problem: In a real-world application, the robot may begin in any of the grid positions (P0, P1, P2, P3), and through the various transitions, the robot can identify its location with a certain probability. There are two stages to Bayes filter to update the belief* and belief. To have the same calculated values as the solution. Assume the robot begins in P0 with the following probabilities. When under a given control 𝑢𝑢𝑡𝑡 = 1, the robot should move to the next grid position (for example, from P0 to P1). However, during the displacement and due to hardware variations in noises, slippage, etc, the robot may move with the following probabilities.      70% of the time it moves correctly to the next grid (e.g. P1 from P0), 20% of the time it will slip and stay in the same grid (e.g. P0 from P0), 10% of the time it will move two grids over (P2 from P0). 0% chance the robot can move to the yellow grid located after P3. Similarly, 0% change the robot will move backward. Bayes filter includes an environment observation (measurement) stage. However, just like in real life, not all sensors are accurate due various reasons. For the measurement probabilities please use the following probabilities to update the model. 𝑝𝑝(𝑧𝑧𝑡𝑡 |𝑥𝑥𝑡𝑡 ) is: • • When the robot is in front of a wall (faces the wall), 𝑥𝑥𝑡𝑡 ∈ [𝑃𝑃0, 𝑃𝑃2]:  75% of the time it will detect the wall, 𝑝𝑝(𝑧𝑧𝑡𝑡 = 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 |𝑥𝑥𝑡𝑡 ) = 0.75  25% of the time it will detect incorrectly and see a door, 𝑝𝑝(𝑧𝑧𝑡𝑡 = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑|𝑥𝑥𝑡𝑡 ) = 0.25 When the robot is in front of a door (faces the door), 𝑥𝑥𝑡𝑡 ∈ [𝑃𝑃1, 𝑃𝑃3]:  30% of the time it will detect incorrectly and see a wall, 𝑝𝑝(𝑧𝑧𝑡𝑡 = 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 |𝑥𝑥𝑡𝑡 ) = 0.3  70% of the time it will detect correctly and detect a door, 𝑝𝑝(𝑧𝑧𝑡𝑡 = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑|𝑥𝑥𝑡𝑡 ) = 0.7 All other situations keep the same as the description of the lecture slides. Determine its location through various stages (at least 2). Please show your solution in detail.