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

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

Introduction 3 Ad hoc networks Challenges Background Problem definition

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

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

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

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

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

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

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

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

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

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

Finding headings 14 A’s heading :

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

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

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

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

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

Orientation forwarding DV-Bearing 20

Orientation forwarding DV-Radial 21

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

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

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

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

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

Elimination of outliers Compute centroid and remove outliers then recompute 27

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

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

Bearing error 30 How forwarding method compounds and propagates error

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

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

Tracking example 33

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

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

Thank you 36