1. Marios Karagiannis 13/10/2010

2. Distance estimation Many localization techniques (ranged based) require distance estimation Many estimation techniques have been proposed RF and Ultrasound ToA RSSI strength Etc. These techniques have something in common Errors in estimation

3. Error models Linear error model

4. Error models Constant error model

5. Error models Random error model

6. Error models Logarithmic error model

7. Which ones is closer to reality? Weve run an experiment We used RSSI strength 52 positions 6 anchors Built a map of RSSI strengths for each anchor Extracted a couple of slices from the map Compared with error models

8. Experiment

9. Experiment results (sample)

10. Experiment results (slice)

12. Error exists But how do we reduce it with not extra information available? We use geometry! Step 1: We draw circles Center is the nearby anchor Radius is the (erroneous) calculated distance

13. Examples No error in distance calculations

14. Examples Error in distance calculations

15. And then what? Step 2: We calculate the intersection points of all the circles Step 3: We find the barycenter of a subgroup of these intersection points. How? Using any of the following filtering techniques

16. Technique 1 We examine each pair of circles. If they intersect: For each intersection point(IP1 and IP2) we assign 0 Favor Points For Each Circle (C) different than the two circles in the pair If d(IP1,Center Of C)>d(IP2,Center Of C) Points(IP1)++; Else Points(IP2)++; If Points(IP1)>0 and Points(IP2)==0) IP1 is included in the cluster If Points(IP2)>0 and Points(IP1)==0) IP2 is included in the cluster If (Points(IP1)>0 and Points(IP2)>0) Nothing is included in the cluster

17. Technique 1 Example

18. Technique 2 We examine all intersection points If an intersection point is in all each circle C (d(IP,center(C))<R(C) where R(C) is the radius of circle C) then the point is included in the cluster

19. Technique 2 Example

20. Technique 3 Same as technique 1 but with stricter conditions The Favor Points of any Intersection Point must be equal to the total number of circles – 2 (because we subtract the two circles that are producing the intersection points)

21. Technique 3 Example

22. Results We simulated using 4 networks And 200 iterations for each method on each network SizeNodesRadiusMean Conn. 1m x 1m1000.044.582 1m x 1m1000.057.199 1m x 1m1000.0610.394 1m x 1m1000.0713.96

23. Results Network 1

24. Results Network 2

25. Results Network 3

26. Results Network 4

27. Thank you Questions?