1. Ad Hoc Positioning System (APS) Using AOA Dragos¸ Niculescu and Badri Nath INFOCOM ’03 1 Seoyeon Kang September 23, 2008

2. Outline Introduction Angle of arrival(AOA) theory Ad hoc positioning system(APS) algorithm Error control Simulation Future work & conclusion 2

3. Introduction 3 Ad hoc networks Challenges Background Problem definition

4. Ad hoc networks Decentralized wireless network Each node is willing to forward data for other nodes Each node acts as a router Large number of unattended nodes with varying capability – Ranging, compass, AOA, etc. 4

5. Challenges Cost of deployment Capability and complexity of nodes Routing without the use of large conventional routing table Etc. 5

6. Challenges Availability of position would enable routing without the use of large routing tables How to get position information – Using capabilities How to export capabilities in network 6

7. Background Orientation – Heading – Defined by the angles it forms with the axes of a reference frame 7 NORTH

8. Background Angle of arrival(AOA) – To sense the direction from which a signal is received – By knowing ranges x 1, x 2, and distance L – The node can infer the orientation Θ 8 Ultrasound receiver x 1 x2x2

9. Background Related works with other capabilities – Time of arrival(TOA) – Time difference of arrival(TDOA) – Signal strength Based on AOA – Less computational resources and infrastructures 9

10. Problem definition How all nodes determine their orientation and position in an ad-hoc network where only a fraction of the nodes have positioning capabilities, under the assumption that each node has the AOA capability 10

11. AOA theory Terms Problem definition Finding headings Finding positions – Triangulation using AOA 11

12. Terms Bearing – Angle measurement with respect to another object Radial – Reverse bearing – Angle under which an object is seen from another point 12

13. Problem definition Given imprecise bearing to neighbor – By AOA capability A small fraction of the nodes have self positioning capability – Landmarks Find headings and positions for all nodes 13

14. Finding headings 14 A’s heading :

15. Finding positions 15 Triangulation using AOA Given – Positions for the vertices of a triangle – Angles at which an interior point “sees” the vertices Reduction to trilateration

16. Review of trilateration Given – Positions for the vertices of a triangle – Distances to vertices 16 Finding positions

17. For each pair of landmarks – Create an trilateration – A triangulation problem of size n  a trilateration problem of size 17 Finding positions

18. Using triplets of landmarks – trilateration problems of size 3 Less memory 18 D(x,y) Finding positions L1 L2 L5 L4 L3

19. APS(ad hoc positioning system) Algorithm Concepts of original APS – Information is forwarded in a hop by hop fashion – Each node estimates position based on landmarks Extend to angle measurements – DV-Bearing – DV-Radial 19

20. Orientation forwarding DV-Bearing 20

21. Orientation forwarding DV-Radial 21

22. Orientation forwarding Tradeoffs between DV-Bearing and DV-Radial 22

23. Network density 23 What kind of node density is needed in order to achieve a certain condition with high probability

24. Error control Bearing measurements are affected by errors Forwarding may amplify and compound smaller errors into larger errors 24

25. Limiting the propagation of packets Set TTL to limit error propagation 25

26. Threshold to eliminate triangles Ignore small angles Tradeoff – coverage vs. positioning error 26

27. Elimination of outliers Compute centroid and remove outliers then recompute 27

28. Simulation Isotropic topology 28 1000nodes Avg. degree=10.5 Gaussian noise 20% landmarks Threshold 0.35(≈ 20˚) DV-Bearing TTL=5 DV-Radial TTL=4

29. Positioning error 1.0 means that the position is one hop away from true position 29

30. Bearing error 30 How forwarding method compounds and propagates error

31. Heading error Error in the absolute orientation averaged over all nodes 31

32. Coverage Percentage of regular nodes which are able to resolve for a position 32

33. Tracking example 33

34. Future work Extension to mobility – A moving landmark provides more information Error estimation – Transmitting of the error estimation with DV data – Weights for each landmark Multimodal sensing – With compasses and accelerometers 34

35. Summary A method that infers position and orientation in ad hoc network with only few landmarks – Orientation forwarding DV-Bearing and DV-Radial – Triangulation using AOA Advantages – Do not require additional infrastructures – Less computational resources – Scalable 35

36. Thank you 36