1. 3D Position Determination Hasti AhleHagh Professor. W.R. Michalson

2. Outline  Problem Formulation  Location Estimation  Location Discovery in Presence of Errors  Deployment Problem  Future Work  Conclusion

3. Objective  Calculate a node location by combining distances from its neighbors  Optimize the quality of solution while guarantees the coverage  Establish accurate location of all nodes by combining information from four far away anchor nodes. Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

4.  Input - - for pair if  Output - determine - Graph Model Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

5.  Coordinate System Selection:  Calculation of a Node Position: Coordinate System Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

6.  Calculation of a Node Position: Location Calculation Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

7.  Calculation of a Node Position: Location Calculation Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

8. Example 15 14 1 11 16 9 8 12 5 3 10 2 17 4 19 13 18 7 6 20 21 22 24 25 26 23 0 12 2 Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

9. Example 15 14 1 11 16 9 8 12 5 3 10 2 17 4 19 13 18 7 6 20 21 22 24 25 26 23 0 12 2 Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

10. Example 15 14 1 11 16 9 8 12 5 3 10 2 17 4 19 13 18 7 6 20 21 22 24 25 26 23 0 12 2 Problem Formulation. Error Free Location Discovery. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

11. Example 15 14 1 11 16 9 8 12 5 3 10 2 17 4 19 13 18 7 6 20 21 22 24 25 26 23 0 12 2 Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

12. Positioning algorithm Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

13. Positioning algorithm Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

14. Positioning algorithm a1 b11b12b13 c112 c111 c113 b122 b121 b123 b122 b121 b123 a2 b21b22b23 c212 c211 c1213 c222 c221 c223 b232 b231 b233 Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

15.  QUESTION: What is the error function where is the error in distance measurements and is the error in the nodes location ?  distributed localization -> simulation study  error function has almost the same behavior for each n-hop neighbor Error Propagation Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

16. Simulation Results Node Num=40, Xloc=87m, Yloc=36m, Zloc=8m, Rs=50m 1-hop Neighbors 2-hop Neighbors Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

17.  QUESTION: What is the cause of error in the network?  Propagation of error  Some error in the rotation angle cause a considerable error in node location Sources of Error Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

18. Simulation Results Node Num=80, Xloc=110m, Yloc=45m, Zloc=10m, Rs=100m Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

19. Simulation Results Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

20. Simulation Results Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

21. Simulation Results Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

22.  QUESTION: Which percentage of the sensor nodes is able to find their physical location after running the location discovery procedure? Coverage Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

23. Simulation Results Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

24.  Deploying atomic tri-lateration procedure for calculating the position of a node in the presence of noisy information  Adding node with GPS information and study error propagation and coverage with percolation  Evaluate the effect of error in input distance on the output location calculation  Add optimization algorithms to the location discovery Future Work Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion

25.  Here we addressed location discovery by deploying geometric and graph theory  We developed Monte Carlo simulation to identify the network scalability  Evaluated the effect of error in input distance on the output location calculation Conclusion Problem Formulation. Location Estimation. Location Discovery in Presence of Errors. Deployment Problem. Future Work. Conclusion