Project 2. Consensus Filters for Sensor Networks Solution

Hard copy submission in the class: Return the hardcopy of your project report and DO NOT include source code in your hardcopy submission.



Electronic copy submission: Include source code in your electronic submission.



Name/Zip your files as: “PR2-First_Lastname” then email your project

report to Bravehung@yahoo.com: Before 11.30pm May 1st, 2018.




Case 1. Estimate single cell (single scalar value): 50 points




We randomly generate a connected network of 10 nodes in the area of 4x4. The cell is located at the center of this area. The ground truth of the measurement at this location is 50.








































Show the results of the convergence of consensus filter 1 (Weighted Average Consensus) associated with two different weights, i.e., weight design 1 and weight design 2. Explain the obtained results.(UG: 20points; G:15points)



Show the results of the convergence of consensus filter 2 (Average Consensus) with both Max-degree and Metropolis weights for a network of 10 nodes (area of 4x4), and a network of 50 nodes (area of 20x20). Explain the obtained results. (UG: 20points; G:15points)
Show the convergence of the node which has the smallest number of neighbors and the node which has the largest number of neighbors. Observe the obtained results and give explanation. (UG: 15points; G:10points)


























































































Show the convergence of the node which has the smallest number of neighbors and the node which has the largest number of neighbors in the dynamic network case where the node’s neighbors are changing over time. Observe the obtained results and give explanation. (Grad Students Only): 10points






Some notes to be considered:




Since we implement this consensus for a static sensor network (t is constant) the weight may not get updated in case both node i and its neighbors do not sense the cell. Therefore we should assume that at least one of node i’s neighbors can sense cell k. (You can try to enlarge the sensing range.)



When node i can not sense the cell, you may try to set up the weight is empty instead of zero to avoid wrong update.






Case 2. Estimate multiple cells (scalar field): 50 points
























































































0




-0.5




-1




-1.5




-2




-2.5




-3




30




20
25
20
10
15
10
0
5
0












Scalar field F in 3D







25










20










15










10










5










0
5
10
15
20
25
0






Scalar field F in 2D













The field F has a size x×y = 25×25, and it is partitioned into 25×25 = 625 cells. You can set variables x and y run as: 0 to 25 with scale of 1 as presented in the above scalar field figures.




Generate a connected network of 30 nodes to cover the entire area. You can select the node’s sensing range (may be rsi = 5). (UG: 10points; G:10points)
Running the Consensus 1 (Weighted Average Consensus) to obtain the estimate at each cell of the field F. Then, build the map of this scalar field. (UG: 25points; G:20points)



Plot the error between the build map and the original one in both 2D and 3D (ignore if difficult), respectively, and give explanation for the obtained results. (UG: 15points; G:10points)



Running the Consensus 2 (Average Consensus) to find out the confidence (weight) of the estimate at each cell, then plot the confidence (weight) in both 2D and 3D. (Graduate
Students Only): 10 points




Optional to any student: If you would like to apply flocking control in project 1 to do scalar field mapping, you can get 10% bonus point for this project.



Note: If you feel difficult to model the scalar field F, you can download the .txt data file or Matlab data file of the field F. The data file will contain a valued matrix of 25x25, and all you need to do is to assign each scalar value with its own (x, y) coordinate.